Properties

Label 3200.2.a.bh.1.2
Level $3200$
Weight $2$
Character 3200.1
Self dual yes
Analytic conductor $25.552$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3200 = 2^{7} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3200.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(25.5521286468\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
Defining polynomial: \( x^{2} - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.41421\) of defining polynomial
Character \(\chi\) \(=\) 3200.1

$q$-expansion

\(f(q)\) \(=\) \(q+0.414214 q^{3} +4.82843 q^{7} -2.82843 q^{9} +O(q^{10})\) \(q+0.414214 q^{3} +4.82843 q^{7} -2.82843 q^{9} -3.24264 q^{11} +5.65685 q^{13} +5.82843 q^{17} +4.41421 q^{19} +2.00000 q^{21} -0.828427 q^{23} -2.41421 q^{27} -8.00000 q^{29} +4.82843 q^{31} -1.34315 q^{33} +3.65685 q^{37} +2.34315 q^{39} -0.656854 q^{41} -10.0000 q^{43} -1.65685 q^{47} +16.3137 q^{49} +2.41421 q^{51} -3.65685 q^{53} +1.82843 q^{57} +7.65685 q^{59} -6.00000 q^{61} -13.6569 q^{63} +11.2426 q^{67} -0.343146 q^{69} +1.65685 q^{71} -0.171573 q^{73} -15.6569 q^{77} +7.17157 q^{79} +7.48528 q^{81} +7.24264 q^{83} -3.31371 q^{87} +11.8284 q^{89} +27.3137 q^{91} +2.00000 q^{93} -5.31371 q^{97} +9.17157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} + 4 q^{7} + 2 q^{11} + 6 q^{17} + 6 q^{19} + 4 q^{21} + 4 q^{23} - 2 q^{27} - 16 q^{29} + 4 q^{31} - 14 q^{33} - 4 q^{37} + 16 q^{39} + 10 q^{41} - 20 q^{43} + 8 q^{47} + 10 q^{49} + 2 q^{51} + 4 q^{53} - 2 q^{57} + 4 q^{59} - 12 q^{61} - 16 q^{63} + 14 q^{67} - 12 q^{69} - 8 q^{71} - 6 q^{73} - 20 q^{77} + 20 q^{79} - 2 q^{81} + 6 q^{83} + 16 q^{87} + 18 q^{89} + 32 q^{91} + 4 q^{93} + 12 q^{97} + 24 q^{99}+O(q^{100}) \) 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
\(3\) 0.414214 0.239146 0.119573 0.992825i \(-0.461847\pi\)
0.119573 + 0.992825i \(0.461847\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.82843 1.82497 0.912487 0.409106i \(-0.134159\pi\)
0.912487 + 0.409106i \(0.134159\pi\)
\(8\) 0 0
\(9\) −2.82843 −0.942809
\(10\) 0 0
\(11\) −3.24264 −0.977693 −0.488846 0.872370i \(-0.662582\pi\)
−0.488846 + 0.872370i \(0.662582\pi\)
\(12\) 0 0
\(13\) 5.65685 1.56893 0.784465 0.620174i \(-0.212938\pi\)
0.784465 + 0.620174i \(0.212938\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.82843 1.41360 0.706801 0.707413i \(-0.250138\pi\)
0.706801 + 0.707413i \(0.250138\pi\)
\(18\) 0 0
\(19\) 4.41421 1.01269 0.506345 0.862331i \(-0.330996\pi\)
0.506345 + 0.862331i \(0.330996\pi\)
\(20\) 0 0
\(21\) 2.00000 0.436436
\(22\) 0 0
\(23\) −0.828427 −0.172739 −0.0863695 0.996263i \(-0.527527\pi\)
−0.0863695 + 0.996263i \(0.527527\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.41421 −0.464616
\(28\) 0 0
\(29\) −8.00000 −1.48556 −0.742781 0.669534i \(-0.766494\pi\)
−0.742781 + 0.669534i \(0.766494\pi\)
\(30\) 0 0
\(31\) 4.82843 0.867211 0.433606 0.901103i \(-0.357241\pi\)
0.433606 + 0.901103i \(0.357241\pi\)
\(32\) 0 0
\(33\) −1.34315 −0.233812
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.65685 0.601183 0.300592 0.953753i \(-0.402816\pi\)
0.300592 + 0.953753i \(0.402816\pi\)
\(38\) 0 0
\(39\) 2.34315 0.375204
\(40\) 0 0
\(41\) −0.656854 −0.102583 −0.0512917 0.998684i \(-0.516334\pi\)
−0.0512917 + 0.998684i \(0.516334\pi\)
\(42\) 0 0
\(43\) −10.0000 −1.52499 −0.762493 0.646997i \(-0.776025\pi\)
−0.762493 + 0.646997i \(0.776025\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.65685 −0.241677 −0.120839 0.992672i \(-0.538558\pi\)
−0.120839 + 0.992672i \(0.538558\pi\)
\(48\) 0 0
\(49\) 16.3137 2.33053
\(50\) 0 0
\(51\) 2.41421 0.338058
\(52\) 0 0
\(53\) −3.65685 −0.502308 −0.251154 0.967947i \(-0.580810\pi\)
−0.251154 + 0.967947i \(0.580810\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.82843 0.242181
\(58\) 0 0
\(59\) 7.65685 0.996838 0.498419 0.866936i \(-0.333914\pi\)
0.498419 + 0.866936i \(0.333914\pi\)
\(60\) 0 0
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 0 0
\(63\) −13.6569 −1.72060
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 11.2426 1.37351 0.686754 0.726890i \(-0.259035\pi\)
0.686754 + 0.726890i \(0.259035\pi\)
\(68\) 0 0
\(69\) −0.343146 −0.0413099
\(70\) 0 0
\(71\) 1.65685 0.196632 0.0983162 0.995155i \(-0.468654\pi\)
0.0983162 + 0.995155i \(0.468654\pi\)
\(72\) 0 0
\(73\) −0.171573 −0.0200811 −0.0100405 0.999950i \(-0.503196\pi\)
−0.0100405 + 0.999950i \(0.503196\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −15.6569 −1.78426
\(78\) 0 0
\(79\) 7.17157 0.806865 0.403432 0.915009i \(-0.367817\pi\)
0.403432 + 0.915009i \(0.367817\pi\)
\(80\) 0 0
\(81\) 7.48528 0.831698
\(82\) 0 0
\(83\) 7.24264 0.794983 0.397492 0.917606i \(-0.369881\pi\)
0.397492 + 0.917606i \(0.369881\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.31371 −0.355267
\(88\) 0 0
\(89\) 11.8284 1.25381 0.626905 0.779095i \(-0.284321\pi\)
0.626905 + 0.779095i \(0.284321\pi\)
\(90\) 0 0
\(91\) 27.3137 2.86325
\(92\) 0 0
\(93\) 2.00000 0.207390
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −5.31371 −0.539525 −0.269763 0.962927i \(-0.586945\pi\)
−0.269763 + 0.962927i \(0.586945\pi\)
\(98\) 0 0
\(99\) 9.17157 0.921778
\(100\) 0 0
\(101\) −14.9706 −1.48963 −0.744813 0.667273i \(-0.767461\pi\)
−0.744813 + 0.667273i \(0.767461\pi\)
\(102\) 0 0
\(103\) 9.65685 0.951518 0.475759 0.879576i \(-0.342173\pi\)
0.475759 + 0.879576i \(0.342173\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 16.0711 1.55365 0.776824 0.629717i \(-0.216829\pi\)
0.776824 + 0.629717i \(0.216829\pi\)
\(108\) 0 0
\(109\) −0.343146 −0.0328674 −0.0164337 0.999865i \(-0.505231\pi\)
−0.0164337 + 0.999865i \(0.505231\pi\)
\(110\) 0 0
\(111\) 1.51472 0.143771
\(112\) 0 0
\(113\) −14.6569 −1.37880 −0.689400 0.724380i \(-0.742126\pi\)
−0.689400 + 0.724380i \(0.742126\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −16.0000 −1.47920
\(118\) 0 0
\(119\) 28.1421 2.57979
\(120\) 0 0
\(121\) −0.485281 −0.0441165
\(122\) 0 0
\(123\) −0.272078 −0.0245324
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 8.14214 0.722498 0.361249 0.932469i \(-0.382350\pi\)
0.361249 + 0.932469i \(0.382350\pi\)
\(128\) 0 0
\(129\) −4.14214 −0.364695
\(130\) 0 0
\(131\) −17.3137 −1.51271 −0.756353 0.654164i \(-0.773021\pi\)
−0.756353 + 0.654164i \(0.773021\pi\)
\(132\) 0 0
\(133\) 21.3137 1.84813
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 5.00000 0.427179 0.213589 0.976924i \(-0.431485\pi\)
0.213589 + 0.976924i \(0.431485\pi\)
\(138\) 0 0
\(139\) −8.89949 −0.754845 −0.377423 0.926041i \(-0.623190\pi\)
−0.377423 + 0.926041i \(0.623190\pi\)
\(140\) 0 0
\(141\) −0.686292 −0.0577962
\(142\) 0 0
\(143\) −18.3431 −1.53393
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 6.75736 0.557338
\(148\) 0 0
\(149\) −19.3137 −1.58224 −0.791120 0.611661i \(-0.790502\pi\)
−0.791120 + 0.611661i \(0.790502\pi\)
\(150\) 0 0
\(151\) −10.4853 −0.853280 −0.426640 0.904422i \(-0.640303\pi\)
−0.426640 + 0.904422i \(0.640303\pi\)
\(152\) 0 0
\(153\) −16.4853 −1.33276
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 8.34315 0.665856 0.332928 0.942952i \(-0.391963\pi\)
0.332928 + 0.942952i \(0.391963\pi\)
\(158\) 0 0
\(159\) −1.51472 −0.120125
\(160\) 0 0
\(161\) −4.00000 −0.315244
\(162\) 0 0
\(163\) −5.72792 −0.448645 −0.224323 0.974515i \(-0.572017\pi\)
−0.224323 + 0.974515i \(0.572017\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 13.6569 1.05680 0.528400 0.848996i \(-0.322792\pi\)
0.528400 + 0.848996i \(0.322792\pi\)
\(168\) 0 0
\(169\) 19.0000 1.46154
\(170\) 0 0
\(171\) −12.4853 −0.954773
\(172\) 0 0
\(173\) −1.65685 −0.125968 −0.0629841 0.998015i \(-0.520062\pi\)
−0.0629841 + 0.998015i \(0.520062\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 3.17157 0.238390
\(178\) 0 0
\(179\) 24.4142 1.82480 0.912402 0.409295i \(-0.134225\pi\)
0.912402 + 0.409295i \(0.134225\pi\)
\(180\) 0 0
\(181\) −4.34315 −0.322823 −0.161412 0.986887i \(-0.551605\pi\)
−0.161412 + 0.986887i \(0.551605\pi\)
\(182\) 0 0
\(183\) −2.48528 −0.183717
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −18.8995 −1.38207
\(188\) 0 0
\(189\) −11.6569 −0.847911
\(190\) 0 0
\(191\) 18.4853 1.33755 0.668774 0.743466i \(-0.266819\pi\)
0.668774 + 0.743466i \(0.266819\pi\)
\(192\) 0 0
\(193\) 13.8284 0.995392 0.497696 0.867352i \(-0.334180\pi\)
0.497696 + 0.867352i \(0.334180\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.65685 −0.260540 −0.130270 0.991479i \(-0.541584\pi\)
−0.130270 + 0.991479i \(0.541584\pi\)
\(198\) 0 0
\(199\) 14.3431 1.01676 0.508379 0.861133i \(-0.330245\pi\)
0.508379 + 0.861133i \(0.330245\pi\)
\(200\) 0 0
\(201\) 4.65685 0.328469
\(202\) 0 0
\(203\) −38.6274 −2.71111
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.34315 0.162860
\(208\) 0 0
\(209\) −14.3137 −0.990100
\(210\) 0 0
\(211\) 8.89949 0.612666 0.306333 0.951924i \(-0.400898\pi\)
0.306333 + 0.951924i \(0.400898\pi\)
\(212\) 0 0
\(213\) 0.686292 0.0470239
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 23.3137 1.58264
\(218\) 0 0
\(219\) −0.0710678 −0.00480232
\(220\) 0 0
\(221\) 32.9706 2.21784
\(222\) 0 0
\(223\) −2.34315 −0.156909 −0.0784543 0.996918i \(-0.524998\pi\)
−0.0784543 + 0.996918i \(0.524998\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −1.31371 −0.0871939 −0.0435969 0.999049i \(-0.513882\pi\)
−0.0435969 + 0.999049i \(0.513882\pi\)
\(228\) 0 0
\(229\) −23.3137 −1.54061 −0.770307 0.637674i \(-0.779897\pi\)
−0.770307 + 0.637674i \(0.779897\pi\)
\(230\) 0 0
\(231\) −6.48528 −0.426700
\(232\) 0 0
\(233\) −9.31371 −0.610161 −0.305081 0.952327i \(-0.598683\pi\)
−0.305081 + 0.952327i \(0.598683\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 2.97056 0.192959
\(238\) 0 0
\(239\) −26.6274 −1.72238 −0.861192 0.508279i \(-0.830282\pi\)
−0.861192 + 0.508279i \(0.830282\pi\)
\(240\) 0 0
\(241\) 4.17157 0.268715 0.134357 0.990933i \(-0.457103\pi\)
0.134357 + 0.990933i \(0.457103\pi\)
\(242\) 0 0
\(243\) 10.3431 0.663513
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 24.9706 1.58884
\(248\) 0 0
\(249\) 3.00000 0.190117
\(250\) 0 0
\(251\) 17.2426 1.08835 0.544173 0.838973i \(-0.316844\pi\)
0.544173 + 0.838973i \(0.316844\pi\)
\(252\) 0 0
\(253\) 2.68629 0.168886
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 17.3137 1.08000 0.540000 0.841665i \(-0.318424\pi\)
0.540000 + 0.841665i \(0.318424\pi\)
\(258\) 0 0
\(259\) 17.6569 1.09714
\(260\) 0 0
\(261\) 22.6274 1.40060
\(262\) 0 0
\(263\) 6.48528 0.399900 0.199950 0.979806i \(-0.435922\pi\)
0.199950 + 0.979806i \(0.435922\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 4.89949 0.299844
\(268\) 0 0
\(269\) 17.6569 1.07656 0.538279 0.842767i \(-0.319075\pi\)
0.538279 + 0.842767i \(0.319075\pi\)
\(270\) 0 0
\(271\) 24.8284 1.50822 0.754110 0.656748i \(-0.228069\pi\)
0.754110 + 0.656748i \(0.228069\pi\)
\(272\) 0 0
\(273\) 11.3137 0.684737
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −1.65685 −0.0995507 −0.0497754 0.998760i \(-0.515851\pi\)
−0.0497754 + 0.998760i \(0.515851\pi\)
\(278\) 0 0
\(279\) −13.6569 −0.817614
\(280\) 0 0
\(281\) 24.6274 1.46915 0.734574 0.678528i \(-0.237382\pi\)
0.734574 + 0.678528i \(0.237382\pi\)
\(282\) 0 0
\(283\) −15.7279 −0.934928 −0.467464 0.884012i \(-0.654832\pi\)
−0.467464 + 0.884012i \(0.654832\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −3.17157 −0.187212
\(288\) 0 0
\(289\) 16.9706 0.998268
\(290\) 0 0
\(291\) −2.20101 −0.129025
\(292\) 0 0
\(293\) −5.31371 −0.310430 −0.155215 0.987881i \(-0.549607\pi\)
−0.155215 + 0.987881i \(0.549607\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 7.82843 0.454251
\(298\) 0 0
\(299\) −4.68629 −0.271015
\(300\) 0 0
\(301\) −48.2843 −2.78306
\(302\) 0 0
\(303\) −6.20101 −0.356239
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −5.24264 −0.299213 −0.149607 0.988746i \(-0.547801\pi\)
−0.149607 + 0.988746i \(0.547801\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) −5.51472 −0.312711 −0.156356 0.987701i \(-0.549975\pi\)
−0.156356 + 0.987701i \(0.549975\pi\)
\(312\) 0 0
\(313\) 10.0000 0.565233 0.282617 0.959233i \(-0.408798\pi\)
0.282617 + 0.959233i \(0.408798\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 13.6569 0.767045 0.383523 0.923531i \(-0.374711\pi\)
0.383523 + 0.923531i \(0.374711\pi\)
\(318\) 0 0
\(319\) 25.9411 1.45242
\(320\) 0 0
\(321\) 6.65685 0.371549
\(322\) 0 0
\(323\) 25.7279 1.43154
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −0.142136 −0.00786012
\(328\) 0 0
\(329\) −8.00000 −0.441054
\(330\) 0 0
\(331\) 3.10051 0.170419 0.0852096 0.996363i \(-0.472844\pi\)
0.0852096 + 0.996363i \(0.472844\pi\)
\(332\) 0 0
\(333\) −10.3431 −0.566801
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −18.6569 −1.01630 −0.508152 0.861268i \(-0.669671\pi\)
−0.508152 + 0.861268i \(0.669671\pi\)
\(338\) 0 0
\(339\) −6.07107 −0.329735
\(340\) 0 0
\(341\) −15.6569 −0.847866
\(342\) 0 0
\(343\) 44.9706 2.42818
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.899495 −0.0482874 −0.0241437 0.999708i \(-0.507686\pi\)
−0.0241437 + 0.999708i \(0.507686\pi\)
\(348\) 0 0
\(349\) −6.68629 −0.357909 −0.178954 0.983857i \(-0.557271\pi\)
−0.178954 + 0.983857i \(0.557271\pi\)
\(350\) 0 0
\(351\) −13.6569 −0.728949
\(352\) 0 0
\(353\) −32.6274 −1.73658 −0.868291 0.496055i \(-0.834781\pi\)
−0.868291 + 0.496055i \(0.834781\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 11.6569 0.616946
\(358\) 0 0
\(359\) 3.17157 0.167389 0.0836946 0.996491i \(-0.473328\pi\)
0.0836946 + 0.996491i \(0.473328\pi\)
\(360\) 0 0
\(361\) 0.485281 0.0255411
\(362\) 0 0
\(363\) −0.201010 −0.0105503
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −32.9706 −1.72105 −0.860525 0.509409i \(-0.829864\pi\)
−0.860525 + 0.509409i \(0.829864\pi\)
\(368\) 0 0
\(369\) 1.85786 0.0967166
\(370\) 0 0
\(371\) −17.6569 −0.916698
\(372\) 0 0
\(373\) −10.6863 −0.553315 −0.276658 0.960969i \(-0.589227\pi\)
−0.276658 + 0.960969i \(0.589227\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −45.2548 −2.33074
\(378\) 0 0
\(379\) 2.89949 0.148937 0.0744685 0.997223i \(-0.476274\pi\)
0.0744685 + 0.997223i \(0.476274\pi\)
\(380\) 0 0
\(381\) 3.37258 0.172783
\(382\) 0 0
\(383\) −23.4558 −1.19854 −0.599269 0.800548i \(-0.704542\pi\)
−0.599269 + 0.800548i \(0.704542\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 28.2843 1.43777
\(388\) 0 0
\(389\) 17.3137 0.877840 0.438920 0.898526i \(-0.355361\pi\)
0.438920 + 0.898526i \(0.355361\pi\)
\(390\) 0 0
\(391\) −4.82843 −0.244184
\(392\) 0 0
\(393\) −7.17157 −0.361758
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −31.3137 −1.57159 −0.785795 0.618487i \(-0.787746\pi\)
−0.785795 + 0.618487i \(0.787746\pi\)
\(398\) 0 0
\(399\) 8.82843 0.441974
\(400\) 0 0
\(401\) −30.4558 −1.52089 −0.760446 0.649401i \(-0.775020\pi\)
−0.760446 + 0.649401i \(0.775020\pi\)
\(402\) 0 0
\(403\) 27.3137 1.36059
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −11.8579 −0.587773
\(408\) 0 0
\(409\) −27.9706 −1.38306 −0.691528 0.722350i \(-0.743062\pi\)
−0.691528 + 0.722350i \(0.743062\pi\)
\(410\) 0 0
\(411\) 2.07107 0.102158
\(412\) 0 0
\(413\) 36.9706 1.81920
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −3.68629 −0.180518
\(418\) 0 0
\(419\) −24.5563 −1.19966 −0.599828 0.800129i \(-0.704764\pi\)
−0.599828 + 0.800129i \(0.704764\pi\)
\(420\) 0 0
\(421\) 4.00000 0.194948 0.0974740 0.995238i \(-0.468924\pi\)
0.0974740 + 0.995238i \(0.468924\pi\)
\(422\) 0 0
\(423\) 4.68629 0.227855
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −28.9706 −1.40198
\(428\) 0 0
\(429\) −7.59798 −0.366834
\(430\) 0 0
\(431\) −16.1421 −0.777539 −0.388770 0.921335i \(-0.627100\pi\)
−0.388770 + 0.921335i \(0.627100\pi\)
\(432\) 0 0
\(433\) 16.1716 0.777156 0.388578 0.921416i \(-0.372966\pi\)
0.388578 + 0.921416i \(0.372966\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.65685 −0.174931
\(438\) 0 0
\(439\) 23.3137 1.11270 0.556351 0.830947i \(-0.312201\pi\)
0.556351 + 0.830947i \(0.312201\pi\)
\(440\) 0 0
\(441\) −46.1421 −2.19724
\(442\) 0 0
\(443\) 8.55635 0.406524 0.203262 0.979124i \(-0.434846\pi\)
0.203262 + 0.979124i \(0.434846\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −8.00000 −0.378387
\(448\) 0 0
\(449\) 16.4558 0.776599 0.388300 0.921533i \(-0.373063\pi\)
0.388300 + 0.921533i \(0.373063\pi\)
\(450\) 0 0
\(451\) 2.12994 0.100295
\(452\) 0 0
\(453\) −4.34315 −0.204059
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −28.6569 −1.34051 −0.670256 0.742130i \(-0.733816\pi\)
−0.670256 + 0.742130i \(0.733816\pi\)
\(458\) 0 0
\(459\) −14.0711 −0.656781
\(460\) 0 0
\(461\) 5.65685 0.263466 0.131733 0.991285i \(-0.457946\pi\)
0.131733 + 0.991285i \(0.457946\pi\)
\(462\) 0 0
\(463\) −20.9706 −0.974585 −0.487292 0.873239i \(-0.662015\pi\)
−0.487292 + 0.873239i \(0.662015\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 13.3137 0.616085 0.308042 0.951373i \(-0.400326\pi\)
0.308042 + 0.951373i \(0.400326\pi\)
\(468\) 0 0
\(469\) 54.2843 2.50661
\(470\) 0 0
\(471\) 3.45584 0.159237
\(472\) 0 0
\(473\) 32.4264 1.49097
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 10.3431 0.473580
\(478\) 0 0
\(479\) −40.8284 −1.86550 −0.932749 0.360526i \(-0.882597\pi\)
−0.932749 + 0.360526i \(0.882597\pi\)
\(480\) 0 0
\(481\) 20.6863 0.943214
\(482\) 0 0
\(483\) −1.65685 −0.0753895
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −37.1127 −1.68174 −0.840868 0.541240i \(-0.817955\pi\)
−0.840868 + 0.541240i \(0.817955\pi\)
\(488\) 0 0
\(489\) −2.37258 −0.107292
\(490\) 0 0
\(491\) 28.6274 1.29194 0.645969 0.763364i \(-0.276454\pi\)
0.645969 + 0.763364i \(0.276454\pi\)
\(492\) 0 0
\(493\) −46.6274 −2.09999
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 8.00000 0.358849
\(498\) 0 0
\(499\) −14.0000 −0.626726 −0.313363 0.949633i \(-0.601456\pi\)
−0.313363 + 0.949633i \(0.601456\pi\)
\(500\) 0 0
\(501\) 5.65685 0.252730
\(502\) 0 0
\(503\) −16.9706 −0.756680 −0.378340 0.925667i \(-0.623505\pi\)
−0.378340 + 0.925667i \(0.623505\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 7.87006 0.349522
\(508\) 0 0
\(509\) −14.0000 −0.620539 −0.310270 0.950649i \(-0.600419\pi\)
−0.310270 + 0.950649i \(0.600419\pi\)
\(510\) 0 0
\(511\) −0.828427 −0.0366475
\(512\) 0 0
\(513\) −10.6569 −0.470512
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 5.37258 0.236286
\(518\) 0 0
\(519\) −0.686292 −0.0301249
\(520\) 0 0
\(521\) −6.31371 −0.276609 −0.138304 0.990390i \(-0.544165\pi\)
−0.138304 + 0.990390i \(0.544165\pi\)
\(522\) 0 0
\(523\) 22.4142 0.980105 0.490053 0.871693i \(-0.336978\pi\)
0.490053 + 0.871693i \(0.336978\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 28.1421 1.22589
\(528\) 0 0
\(529\) −22.3137 −0.970161
\(530\) 0 0
\(531\) −21.6569 −0.939827
\(532\) 0 0
\(533\) −3.71573 −0.160946
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 10.1127 0.436395
\(538\) 0 0
\(539\) −52.8995 −2.27854
\(540\) 0 0
\(541\) 6.34315 0.272713 0.136357 0.990660i \(-0.456461\pi\)
0.136357 + 0.990660i \(0.456461\pi\)
\(542\) 0 0
\(543\) −1.79899 −0.0772020
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −16.5563 −0.707898 −0.353949 0.935265i \(-0.615161\pi\)
−0.353949 + 0.935265i \(0.615161\pi\)
\(548\) 0 0
\(549\) 16.9706 0.724286
\(550\) 0 0
\(551\) −35.3137 −1.50441
\(552\) 0 0
\(553\) 34.6274 1.47251
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −37.6569 −1.59557 −0.797786 0.602941i \(-0.793996\pi\)
−0.797786 + 0.602941i \(0.793996\pi\)
\(558\) 0 0
\(559\) −56.5685 −2.39259
\(560\) 0 0
\(561\) −7.82843 −0.330516
\(562\) 0 0
\(563\) −26.9706 −1.13667 −0.568337 0.822796i \(-0.692413\pi\)
−0.568337 + 0.822796i \(0.692413\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 36.1421 1.51783
\(568\) 0 0
\(569\) −3.68629 −0.154537 −0.0772687 0.997010i \(-0.524620\pi\)
−0.0772687 + 0.997010i \(0.524620\pi\)
\(570\) 0 0
\(571\) −35.9411 −1.50409 −0.752045 0.659112i \(-0.770932\pi\)
−0.752045 + 0.659112i \(0.770932\pi\)
\(572\) 0 0
\(573\) 7.65685 0.319870
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 15.2843 0.636293 0.318146 0.948042i \(-0.396940\pi\)
0.318146 + 0.948042i \(0.396940\pi\)
\(578\) 0 0
\(579\) 5.72792 0.238044
\(580\) 0 0
\(581\) 34.9706 1.45082
\(582\) 0 0
\(583\) 11.8579 0.491103
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −14.0711 −0.580775 −0.290388 0.956909i \(-0.593784\pi\)
−0.290388 + 0.956909i \(0.593784\pi\)
\(588\) 0 0
\(589\) 21.3137 0.878216
\(590\) 0 0
\(591\) −1.51472 −0.0623072
\(592\) 0 0
\(593\) 7.00000 0.287456 0.143728 0.989617i \(-0.454091\pi\)
0.143728 + 0.989617i \(0.454091\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 5.94113 0.243154
\(598\) 0 0
\(599\) −46.7696 −1.91095 −0.955476 0.295069i \(-0.904657\pi\)
−0.955476 + 0.295069i \(0.904657\pi\)
\(600\) 0 0
\(601\) 6.85786 0.279738 0.139869 0.990170i \(-0.455332\pi\)
0.139869 + 0.990170i \(0.455332\pi\)
\(602\) 0 0
\(603\) −31.7990 −1.29495
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −36.0000 −1.46119 −0.730597 0.682808i \(-0.760758\pi\)
−0.730597 + 0.682808i \(0.760758\pi\)
\(608\) 0 0
\(609\) −16.0000 −0.648353
\(610\) 0 0
\(611\) −9.37258 −0.379174
\(612\) 0 0
\(613\) −29.3137 −1.18397 −0.591985 0.805949i \(-0.701655\pi\)
−0.591985 + 0.805949i \(0.701655\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 0 0
\(619\) 9.31371 0.374350 0.187175 0.982327i \(-0.440067\pi\)
0.187175 + 0.982327i \(0.440067\pi\)
\(620\) 0 0
\(621\) 2.00000 0.0802572
\(622\) 0 0
\(623\) 57.1127 2.28817
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −5.92893 −0.236779
\(628\) 0 0
\(629\) 21.3137 0.849833
\(630\) 0 0
\(631\) 44.1421 1.75727 0.878635 0.477493i \(-0.158455\pi\)
0.878635 + 0.477493i \(0.158455\pi\)
\(632\) 0 0
\(633\) 3.68629 0.146517
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 92.2843 3.65644
\(638\) 0 0
\(639\) −4.68629 −0.185387
\(640\) 0 0
\(641\) −22.6863 −0.896055 −0.448027 0.894020i \(-0.647873\pi\)
−0.448027 + 0.894020i \(0.647873\pi\)
\(642\) 0 0
\(643\) 37.3137 1.47151 0.735755 0.677248i \(-0.236828\pi\)
0.735755 + 0.677248i \(0.236828\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −5.65685 −0.222394 −0.111197 0.993798i \(-0.535468\pi\)
−0.111197 + 0.993798i \(0.535468\pi\)
\(648\) 0 0
\(649\) −24.8284 −0.974601
\(650\) 0 0
\(651\) 9.65685 0.378482
\(652\) 0 0
\(653\) 6.00000 0.234798 0.117399 0.993085i \(-0.462544\pi\)
0.117399 + 0.993085i \(0.462544\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0.485281 0.0189326
\(658\) 0 0
\(659\) 25.1838 0.981020 0.490510 0.871435i \(-0.336810\pi\)
0.490510 + 0.871435i \(0.336810\pi\)
\(660\) 0 0
\(661\) −17.6569 −0.686772 −0.343386 0.939194i \(-0.611574\pi\)
−0.343386 + 0.939194i \(0.611574\pi\)
\(662\) 0 0
\(663\) 13.6569 0.530388
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.62742 0.256615
\(668\) 0 0
\(669\) −0.970563 −0.0375241
\(670\) 0 0
\(671\) 19.4558 0.751085
\(672\) 0 0
\(673\) 2.68629 0.103549 0.0517745 0.998659i \(-0.483512\pi\)
0.0517745 + 0.998659i \(0.483512\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 51.3137 1.97215 0.986073 0.166313i \(-0.0531862\pi\)
0.986073 + 0.166313i \(0.0531862\pi\)
\(678\) 0 0
\(679\) −25.6569 −0.984620
\(680\) 0 0
\(681\) −0.544156 −0.0208521
\(682\) 0 0
\(683\) 42.6985 1.63381 0.816906 0.576771i \(-0.195687\pi\)
0.816906 + 0.576771i \(0.195687\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −9.65685 −0.368432
\(688\) 0 0
\(689\) −20.6863 −0.788085
\(690\) 0 0
\(691\) −6.21320 −0.236361 −0.118181 0.992992i \(-0.537706\pi\)
−0.118181 + 0.992992i \(0.537706\pi\)
\(692\) 0 0
\(693\) 44.2843 1.68222
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −3.82843 −0.145012
\(698\) 0 0
\(699\) −3.85786 −0.145918
\(700\) 0 0
\(701\) 24.6863 0.932388 0.466194 0.884682i \(-0.345625\pi\)
0.466194 + 0.884682i \(0.345625\pi\)
\(702\) 0 0
\(703\) 16.1421 0.608812
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −72.2843 −2.71853
\(708\) 0 0
\(709\) −45.9411 −1.72536 −0.862678 0.505754i \(-0.831214\pi\)
−0.862678 + 0.505754i \(0.831214\pi\)
\(710\) 0 0
\(711\) −20.2843 −0.760720
\(712\) 0 0
\(713\) −4.00000 −0.149801
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −11.0294 −0.411902
\(718\) 0 0
\(719\) 27.4558 1.02393 0.511965 0.859006i \(-0.328918\pi\)
0.511965 + 0.859006i \(0.328918\pi\)
\(720\) 0 0
\(721\) 46.6274 1.73650
\(722\) 0 0
\(723\) 1.72792 0.0642621
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) −18.1716 −0.673021
\(730\) 0 0
\(731\) −58.2843 −2.15572
\(732\) 0 0
\(733\) −37.6569 −1.39089 −0.695444 0.718580i \(-0.744792\pi\)
−0.695444 + 0.718580i \(0.744792\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −36.4558 −1.34287
\(738\) 0 0
\(739\) 16.6274 0.611649 0.305825 0.952088i \(-0.401068\pi\)
0.305825 + 0.952088i \(0.401068\pi\)
\(740\) 0 0
\(741\) 10.3431 0.379965
\(742\) 0 0
\(743\) 13.7990 0.506236 0.253118 0.967435i \(-0.418544\pi\)
0.253118 + 0.967435i \(0.418544\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −20.4853 −0.749517
\(748\) 0 0
\(749\) 77.5980 2.83537
\(750\) 0 0
\(751\) 10.6274 0.387800 0.193900 0.981021i \(-0.437886\pi\)
0.193900 + 0.981021i \(0.437886\pi\)
\(752\) 0 0
\(753\) 7.14214 0.260274
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 14.3431 0.521310 0.260655 0.965432i \(-0.416061\pi\)
0.260655 + 0.965432i \(0.416061\pi\)
\(758\) 0 0
\(759\) 1.11270 0.0403884
\(760\) 0 0
\(761\) 17.2843 0.626554 0.313277 0.949662i \(-0.398573\pi\)
0.313277 + 0.949662i \(0.398573\pi\)
\(762\) 0 0
\(763\) −1.65685 −0.0599822
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 43.3137 1.56397
\(768\) 0 0
\(769\) −28.1127 −1.01377 −0.506885 0.862014i \(-0.669203\pi\)
−0.506885 + 0.862014i \(0.669203\pi\)
\(770\) 0 0
\(771\) 7.17157 0.258278
\(772\) 0 0
\(773\) −3.31371 −0.119186 −0.0595929 0.998223i \(-0.518980\pi\)
−0.0595929 + 0.998223i \(0.518980\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 7.31371 0.262378
\(778\) 0 0
\(779\) −2.89949 −0.103885
\(780\) 0 0
\(781\) −5.37258 −0.192246
\(782\) 0 0
\(783\) 19.3137 0.690216
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −28.6274 −1.02046 −0.510229 0.860039i \(-0.670439\pi\)
−0.510229 + 0.860039i \(0.670439\pi\)
\(788\) 0 0
\(789\) 2.68629 0.0956345
\(790\) 0 0
\(791\) −70.7696 −2.51628
\(792\) 0 0
\(793\) −33.9411 −1.20528
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 42.0000 1.48772 0.743858 0.668338i \(-0.232994\pi\)
0.743858 + 0.668338i \(0.232994\pi\)
\(798\) 0 0
\(799\) −9.65685 −0.341635
\(800\) 0 0
\(801\) −33.4558 −1.18210
\(802\) 0 0
\(803\) 0.556349 0.0196331
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 7.31371 0.257455
\(808\) 0 0
\(809\) −4.62742 −0.162691 −0.0813457 0.996686i \(-0.525922\pi\)
−0.0813457 + 0.996686i \(0.525922\pi\)
\(810\) 0 0
\(811\) 31.9411 1.12160 0.560802 0.827950i \(-0.310493\pi\)
0.560802 + 0.827950i \(0.310493\pi\)
\(812\) 0 0
\(813\) 10.2843 0.360685
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −44.1421 −1.54434
\(818\) 0 0
\(819\) −77.2548 −2.69950
\(820\) 0 0
\(821\) −4.62742 −0.161498 −0.0807490 0.996734i \(-0.525731\pi\)
−0.0807490 + 0.996734i \(0.525731\pi\)
\(822\) 0 0
\(823\) −20.9706 −0.730988 −0.365494 0.930814i \(-0.619100\pi\)
−0.365494 + 0.930814i \(0.619100\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 33.9289 1.17982 0.589912 0.807467i \(-0.299162\pi\)
0.589912 + 0.807467i \(0.299162\pi\)
\(828\) 0 0
\(829\) −20.0000 −0.694629 −0.347314 0.937749i \(-0.612906\pi\)
−0.347314 + 0.937749i \(0.612906\pi\)
\(830\) 0 0
\(831\) −0.686292 −0.0238072
\(832\) 0 0
\(833\) 95.0833 3.29444
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −11.6569 −0.402920
\(838\) 0 0
\(839\) 4.00000 0.138095 0.0690477 0.997613i \(-0.478004\pi\)
0.0690477 + 0.997613i \(0.478004\pi\)
\(840\) 0 0
\(841\) 35.0000 1.20690
\(842\) 0 0
\(843\) 10.2010 0.351341
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −2.34315 −0.0805114
\(848\) 0 0
\(849\) −6.51472 −0.223585
\(850\) 0 0
\(851\) −3.02944 −0.103848
\(852\) 0 0
\(853\) −28.6274 −0.980184 −0.490092 0.871671i \(-0.663037\pi\)
−0.490092 + 0.871671i \(0.663037\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −11.0000 −0.375753 −0.187876 0.982193i \(-0.560160\pi\)
−0.187876 + 0.982193i \(0.560160\pi\)
\(858\) 0 0
\(859\) 11.7868 0.402160 0.201080 0.979575i \(-0.435555\pi\)
0.201080 + 0.979575i \(0.435555\pi\)
\(860\) 0 0
\(861\) −1.31371 −0.0447711
\(862\) 0 0
\(863\) 4.00000 0.136162 0.0680808 0.997680i \(-0.478312\pi\)
0.0680808 + 0.997680i \(0.478312\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 7.02944 0.238732
\(868\) 0 0
\(869\) −23.2548 −0.788866
\(870\) 0 0
\(871\) 63.5980 2.15494
\(872\) 0 0
\(873\) 15.0294 0.508669
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −37.6569 −1.27158 −0.635791 0.771861i \(-0.719326\pi\)
−0.635791 + 0.771861i \(0.719326\pi\)
\(878\) 0 0
\(879\) −2.20101 −0.0742382
\(880\) 0 0
\(881\) −37.3137 −1.25713 −0.628565 0.777757i \(-0.716358\pi\)
−0.628565 + 0.777757i \(0.716358\pi\)
\(882\) 0 0
\(883\) 34.7574 1.16968 0.584839 0.811149i \(-0.301158\pi\)
0.584839 + 0.811149i \(0.301158\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −33.6569 −1.13009 −0.565043 0.825061i \(-0.691141\pi\)
−0.565043 + 0.825061i \(0.691141\pi\)
\(888\) 0 0
\(889\) 39.3137 1.31854
\(890\) 0 0
\(891\) −24.2721 −0.813145
\(892\) 0 0
\(893\) −7.31371 −0.244744
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.94113 −0.0648123
\(898\) 0 0
\(899\) −38.6274 −1.28830
\(900\) 0 0
\(901\) −21.3137 −0.710063
\(902\) 0 0
\(903\) −20.0000 −0.665558
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −22.6863 −0.753286 −0.376643 0.926359i \(-0.622922\pi\)
−0.376643 + 0.926359i \(0.622922\pi\)
\(908\) 0 0
\(909\) 42.3431 1.40443
\(910\) 0 0
\(911\) −20.2843 −0.672048 −0.336024 0.941853i \(-0.609082\pi\)
−0.336024 + 0.941853i \(0.609082\pi\)
\(912\) 0 0
\(913\) −23.4853 −0.777249
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −83.5980 −2.76065
\(918\) 0 0
\(919\) −44.8284 −1.47875 −0.739377 0.673292i \(-0.764880\pi\)
−0.739377 + 0.673292i \(0.764880\pi\)
\(920\) 0 0
\(921\) −2.17157 −0.0715558
\(922\) 0 0
\(923\) 9.37258 0.308502
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −27.3137 −0.897100
\(928\) 0 0
\(929\) −44.6274 −1.46418 −0.732089 0.681209i \(-0.761455\pi\)
−0.732089 + 0.681209i \(0.761455\pi\)
\(930\) 0 0
\(931\) 72.0122 2.36010
\(932\) 0 0
\(933\) −2.28427 −0.0747837
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −42.1127 −1.37576 −0.687881 0.725824i \(-0.741459\pi\)
−0.687881 + 0.725824i \(0.741459\pi\)
\(938\) 0 0
\(939\) 4.14214 0.135173
\(940\) 0 0
\(941\) −7.02944 −0.229153 −0.114577 0.993414i \(-0.536551\pi\)
−0.114577 + 0.993414i \(0.536551\pi\)
\(942\) 0 0
\(943\) 0.544156 0.0177202
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 45.5980 1.48174 0.740868 0.671651i \(-0.234415\pi\)
0.740868 + 0.671651i \(0.234415\pi\)
\(948\) 0 0
\(949\) −0.970563 −0.0315058
\(950\) 0 0
\(951\) 5.65685 0.183436
\(952\) 0 0
\(953\) −10.3137 −0.334094 −0.167047 0.985949i \(-0.553423\pi\)
−0.167047 + 0.985949i \(0.553423\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 10.7452 0.347342
\(958\) 0 0
\(959\) 24.1421 0.779590
\(960\) 0 0
\(961\) −7.68629 −0.247945
\(962\) 0 0
\(963\) −45.4558 −1.46479
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 2.62742 0.0844920 0.0422460 0.999107i \(-0.486549\pi\)
0.0422460 + 0.999107i \(0.486549\pi\)
\(968\) 0 0
\(969\) 10.6569 0.342347
\(970\) 0 0
\(971\) 23.1005 0.741330 0.370665 0.928767i \(-0.379130\pi\)
0.370665 + 0.928767i \(0.379130\pi\)
\(972\) 0 0
\(973\) −42.9706 −1.37757
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 38.1127 1.21933 0.609667 0.792658i \(-0.291303\pi\)
0.609667 + 0.792658i \(0.291303\pi\)
\(978\) 0 0
\(979\) −38.3553 −1.22584
\(980\) 0 0
\(981\) 0.970563 0.0309877
\(982\) 0 0
\(983\) 5.79899 0.184959 0.0924795 0.995715i \(-0.470521\pi\)
0.0924795 + 0.995715i \(0.470521\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −3.31371 −0.105477
\(988\) 0 0
\(989\) 8.28427 0.263425
\(990\) 0 0
\(991\) −34.0833 −1.08269 −0.541345 0.840800i \(-0.682085\pi\)
−0.541345 + 0.840800i \(0.682085\pi\)
\(992\) 0 0
\(993\) 1.28427 0.0407551
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −16.9706 −0.537463 −0.268732 0.963215i \(-0.586604\pi\)
−0.268732 + 0.963215i \(0.586604\pi\)
\(998\) 0 0
\(999\) −8.82843 −0.279319
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 3200.2.a.bh.1.2 yes 2
4.3 odd 2 3200.2.a.bi.1.1 yes 2
5.2 odd 4 3200.2.c.bb.2049.2 4
5.3 odd 4 3200.2.c.bb.2049.3 4
5.4 even 2 3200.2.a.bj.1.1 yes 2
8.3 odd 2 3200.2.a.bd.1.2 yes 2
8.5 even 2 3200.2.a.bm.1.1 yes 2
20.3 even 4 3200.2.c.z.2049.2 4
20.7 even 4 3200.2.c.z.2049.3 4
20.19 odd 2 3200.2.a.bg.1.2 yes 2
40.3 even 4 3200.2.c.ba.2049.3 4
40.13 odd 4 3200.2.c.y.2049.2 4
40.19 odd 2 3200.2.a.bn.1.1 yes 2
40.27 even 4 3200.2.c.ba.2049.2 4
40.29 even 2 3200.2.a.bc.1.2 2
40.37 odd 4 3200.2.c.y.2049.3 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3200.2.a.bc.1.2 2 40.29 even 2
3200.2.a.bd.1.2 yes 2 8.3 odd 2
3200.2.a.bg.1.2 yes 2 20.19 odd 2
3200.2.a.bh.1.2 yes 2 1.1 even 1 trivial
3200.2.a.bi.1.1 yes 2 4.3 odd 2
3200.2.a.bj.1.1 yes 2 5.4 even 2
3200.2.a.bm.1.1 yes 2 8.5 even 2
3200.2.a.bn.1.1 yes 2 40.19 odd 2
3200.2.c.y.2049.2 4 40.13 odd 4
3200.2.c.y.2049.3 4 40.37 odd 4
3200.2.c.z.2049.2 4 20.3 even 4
3200.2.c.z.2049.3 4 20.7 even 4
3200.2.c.ba.2049.2 4 40.27 even 4
3200.2.c.ba.2049.3 4 40.3 even 4
3200.2.c.bb.2049.2 4 5.2 odd 4
3200.2.c.bb.2049.3 4 5.3 odd 4