Properties

Label 9200.2.a.ca.1.1
Level $9200$
Weight $2$
Character 9200.1
Self dual yes
Analytic conductor $73.462$
Analytic rank $0$
Dimension $2$
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: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Defining polynomial: \(x^{2} - x - 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 230)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.30278\) of defining polynomial
Character \(\chi\) \(=\) 9200.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.302776 q^{3} +3.30278 q^{7} -2.90833 q^{9} +O(q^{10})\) \(q-0.302776 q^{3} +3.30278 q^{7} -2.90833 q^{9} +1.69722 q^{11} -3.30278 q^{13} -6.90833 q^{17} -5.90833 q^{19} -1.00000 q^{21} -1.00000 q^{23} +1.78890 q^{27} -2.60555 q^{29} +7.90833 q^{31} -0.513878 q^{33} -8.00000 q^{37} +1.00000 q^{39} +0.908327 q^{41} -9.21110 q^{43} -2.60555 q^{47} +3.90833 q^{49} +2.09167 q^{51} +11.2111 q^{53} +1.78890 q^{57} +3.39445 q^{59} +11.5139 q^{61} -9.60555 q^{63} -4.00000 q^{67} +0.302776 q^{69} +16.3028 q^{71} +5.81665 q^{73} +5.60555 q^{77} +14.4222 q^{79} +8.18335 q^{81} +11.2111 q^{83} +0.788897 q^{87} -10.9083 q^{91} -2.39445 q^{93} -6.30278 q^{97} -4.93608 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{3} + 3q^{7} + 5q^{9} + O(q^{10}) \) \( 2q + 3q^{3} + 3q^{7} + 5q^{9} + 7q^{11} - 3q^{13} - 3q^{17} - q^{19} - 2q^{21} - 2q^{23} + 18q^{27} + 2q^{29} + 5q^{31} + 17q^{33} - 16q^{37} + 2q^{39} - 9q^{41} - 4q^{43} + 2q^{47} - 3q^{49} + 15q^{51} + 8q^{53} + 18q^{57} + 14q^{59} + 5q^{61} - 12q^{63} - 8q^{67} - 3q^{69} + 29q^{71} - 10q^{73} + 4q^{77} + 38q^{81} + 8q^{83} + 16q^{87} - 11q^{91} - 12q^{93} - 9q^{97} + 37q^{99} + O(q^{100}) \)

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
\(3\) −0.302776 −0.174808 −0.0874038 0.996173i \(-0.527857\pi\)
−0.0874038 + 0.996173i \(0.527857\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 3.30278 1.24833 0.624166 0.781292i \(-0.285439\pi\)
0.624166 + 0.781292i \(0.285439\pi\)
\(8\) 0 0
\(9\) −2.90833 −0.969442
\(10\) 0 0
\(11\) 1.69722 0.511732 0.255866 0.966712i \(-0.417639\pi\)
0.255866 + 0.966712i \(0.417639\pi\)
\(12\) 0 0
\(13\) −3.30278 −0.916025 −0.458013 0.888946i \(-0.651439\pi\)
−0.458013 + 0.888946i \(0.651439\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −6.90833 −1.67552 −0.837758 0.546042i \(-0.816134\pi\)
−0.837758 + 0.546042i \(0.816134\pi\)
\(18\) 0 0
\(19\) −5.90833 −1.35546 −0.677732 0.735309i \(-0.737037\pi\)
−0.677732 + 0.735309i \(0.737037\pi\)
\(20\) 0 0
\(21\) −1.00000 −0.218218
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 1.78890 0.344273
\(28\) 0 0
\(29\) −2.60555 −0.483839 −0.241919 0.970296i \(-0.577777\pi\)
−0.241919 + 0.970296i \(0.577777\pi\)
\(30\) 0 0
\(31\) 7.90833 1.42038 0.710189 0.704011i \(-0.248610\pi\)
0.710189 + 0.704011i \(0.248610\pi\)
\(32\) 0 0
\(33\) −0.513878 −0.0894547
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −8.00000 −1.31519 −0.657596 0.753371i \(-0.728427\pi\)
−0.657596 + 0.753371i \(0.728427\pi\)
\(38\) 0 0
\(39\) 1.00000 0.160128
\(40\) 0 0
\(41\) 0.908327 0.141857 0.0709284 0.997481i \(-0.477404\pi\)
0.0709284 + 0.997481i \(0.477404\pi\)
\(42\) 0 0
\(43\) −9.21110 −1.40468 −0.702340 0.711842i \(-0.747861\pi\)
−0.702340 + 0.711842i \(0.747861\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.60555 −0.380059 −0.190029 0.981778i \(-0.560858\pi\)
−0.190029 + 0.981778i \(0.560858\pi\)
\(48\) 0 0
\(49\) 3.90833 0.558332
\(50\) 0 0
\(51\) 2.09167 0.292893
\(52\) 0 0
\(53\) 11.2111 1.53996 0.769982 0.638066i \(-0.220265\pi\)
0.769982 + 0.638066i \(0.220265\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.78890 0.236945
\(58\) 0 0
\(59\) 3.39445 0.441920 0.220960 0.975283i \(-0.429081\pi\)
0.220960 + 0.975283i \(0.429081\pi\)
\(60\) 0 0
\(61\) 11.5139 1.47420 0.737101 0.675783i \(-0.236194\pi\)
0.737101 + 0.675783i \(0.236194\pi\)
\(62\) 0 0
\(63\) −9.60555 −1.21019
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 0 0
\(69\) 0.302776 0.0364499
\(70\) 0 0
\(71\) 16.3028 1.93478 0.967392 0.253285i \(-0.0815110\pi\)
0.967392 + 0.253285i \(0.0815110\pi\)
\(72\) 0 0
\(73\) 5.81665 0.680788 0.340394 0.940283i \(-0.389440\pi\)
0.340394 + 0.940283i \(0.389440\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.60555 0.638812
\(78\) 0 0
\(79\) 14.4222 1.62262 0.811312 0.584613i \(-0.198754\pi\)
0.811312 + 0.584613i \(0.198754\pi\)
\(80\) 0 0
\(81\) 8.18335 0.909261
\(82\) 0 0
\(83\) 11.2111 1.23058 0.615289 0.788301i \(-0.289039\pi\)
0.615289 + 0.788301i \(0.289039\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0.788897 0.0845787
\(88\) 0 0
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) −10.9083 −1.14350
\(92\) 0 0
\(93\) −2.39445 −0.248293
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −6.30278 −0.639950 −0.319975 0.947426i \(-0.603675\pi\)
−0.319975 + 0.947426i \(0.603675\pi\)
\(98\) 0 0
\(99\) −4.93608 −0.496095
\(100\) 0 0
\(101\) 2.60555 0.259262 0.129631 0.991562i \(-0.458621\pi\)
0.129631 + 0.991562i \(0.458621\pi\)
\(102\) 0 0
\(103\) 8.11943 0.800031 0.400016 0.916508i \(-0.369005\pi\)
0.400016 + 0.916508i \(0.369005\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.60555 −0.251888 −0.125944 0.992037i \(-0.540196\pi\)
−0.125944 + 0.992037i \(0.540196\pi\)
\(108\) 0 0
\(109\) 1.48612 0.142345 0.0711723 0.997464i \(-0.477326\pi\)
0.0711723 + 0.997464i \(0.477326\pi\)
\(110\) 0 0
\(111\) 2.42221 0.229906
\(112\) 0 0
\(113\) 16.4222 1.54487 0.772436 0.635093i \(-0.219038\pi\)
0.772436 + 0.635093i \(0.219038\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 9.60555 0.888034
\(118\) 0 0
\(119\) −22.8167 −2.09160
\(120\) 0 0
\(121\) −8.11943 −0.738130
\(122\) 0 0
\(123\) −0.275019 −0.0247977
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 9.81665 0.871087 0.435544 0.900168i \(-0.356556\pi\)
0.435544 + 0.900168i \(0.356556\pi\)
\(128\) 0 0
\(129\) 2.78890 0.245549
\(130\) 0 0
\(131\) 11.2111 0.979519 0.489759 0.871858i \(-0.337085\pi\)
0.489759 + 0.871858i \(0.337085\pi\)
\(132\) 0 0
\(133\) −19.5139 −1.69207
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −3.90833 −0.333911 −0.166955 0.985964i \(-0.553394\pi\)
−0.166955 + 0.985964i \(0.553394\pi\)
\(138\) 0 0
\(139\) 12.6056 1.06919 0.534594 0.845109i \(-0.320464\pi\)
0.534594 + 0.845109i \(0.320464\pi\)
\(140\) 0 0
\(141\) 0.788897 0.0664372
\(142\) 0 0
\(143\) −5.60555 −0.468760
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −1.18335 −0.0976007
\(148\) 0 0
\(149\) 13.3028 1.08981 0.544903 0.838499i \(-0.316567\pi\)
0.544903 + 0.838499i \(0.316567\pi\)
\(150\) 0 0
\(151\) −8.90833 −0.724949 −0.362475 0.931994i \(-0.618068\pi\)
−0.362475 + 0.931994i \(0.618068\pi\)
\(152\) 0 0
\(153\) 20.0917 1.62432
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 18.6056 1.48488 0.742442 0.669910i \(-0.233667\pi\)
0.742442 + 0.669910i \(0.233667\pi\)
\(158\) 0 0
\(159\) −3.39445 −0.269197
\(160\) 0 0
\(161\) −3.30278 −0.260295
\(162\) 0 0
\(163\) 9.30278 0.728650 0.364325 0.931272i \(-0.381300\pi\)
0.364325 + 0.931272i \(0.381300\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.78890 0.525341 0.262670 0.964886i \(-0.415397\pi\)
0.262670 + 0.964886i \(0.415397\pi\)
\(168\) 0 0
\(169\) −2.09167 −0.160898
\(170\) 0 0
\(171\) 17.1833 1.31404
\(172\) 0 0
\(173\) −19.6972 −1.49755 −0.748776 0.662823i \(-0.769358\pi\)
−0.748776 + 0.662823i \(0.769358\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −1.02776 −0.0772509
\(178\) 0 0
\(179\) −9.39445 −0.702174 −0.351087 0.936343i \(-0.614188\pi\)
−0.351087 + 0.936343i \(0.614188\pi\)
\(180\) 0 0
\(181\) 17.1194 1.27248 0.636239 0.771492i \(-0.280489\pi\)
0.636239 + 0.771492i \(0.280489\pi\)
\(182\) 0 0
\(183\) −3.48612 −0.257702
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −11.7250 −0.857416
\(188\) 0 0
\(189\) 5.90833 0.429768
\(190\) 0 0
\(191\) 8.60555 0.622676 0.311338 0.950299i \(-0.399223\pi\)
0.311338 + 0.950299i \(0.399223\pi\)
\(192\) 0 0
\(193\) 17.8167 1.28247 0.641235 0.767344i \(-0.278422\pi\)
0.641235 + 0.767344i \(0.278422\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4.30278 −0.306560 −0.153280 0.988183i \(-0.548984\pi\)
−0.153280 + 0.988183i \(0.548984\pi\)
\(198\) 0 0
\(199\) 20.4222 1.44769 0.723846 0.689962i \(-0.242373\pi\)
0.723846 + 0.689962i \(0.242373\pi\)
\(200\) 0 0
\(201\) 1.21110 0.0854246
\(202\) 0 0
\(203\) −8.60555 −0.603991
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 2.90833 0.202143
\(208\) 0 0
\(209\) −10.0278 −0.693634
\(210\) 0 0
\(211\) −7.21110 −0.496433 −0.248216 0.968705i \(-0.579844\pi\)
−0.248216 + 0.968705i \(0.579844\pi\)
\(212\) 0 0
\(213\) −4.93608 −0.338215
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 26.1194 1.77310
\(218\) 0 0
\(219\) −1.76114 −0.119007
\(220\) 0 0
\(221\) 22.8167 1.53481
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.6056 −0.969404 −0.484702 0.874679i \(-0.661072\pi\)
−0.484702 + 0.874679i \(0.661072\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) −1.69722 −0.111669
\(232\) 0 0
\(233\) −25.8167 −1.69131 −0.845653 0.533734i \(-0.820788\pi\)
−0.845653 + 0.533734i \(0.820788\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −4.36669 −0.283647
\(238\) 0 0
\(239\) −5.21110 −0.337078 −0.168539 0.985695i \(-0.553905\pi\)
−0.168539 + 0.985695i \(0.553905\pi\)
\(240\) 0 0
\(241\) −14.4222 −0.929016 −0.464508 0.885569i \(-0.653769\pi\)
−0.464508 + 0.885569i \(0.653769\pi\)
\(242\) 0 0
\(243\) −7.84441 −0.503219
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 19.5139 1.24164
\(248\) 0 0
\(249\) −3.39445 −0.215114
\(250\) 0 0
\(251\) −12.5139 −0.789869 −0.394934 0.918709i \(-0.629233\pi\)
−0.394934 + 0.918709i \(0.629233\pi\)
\(252\) 0 0
\(253\) −1.69722 −0.106704
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.81665 0.113320 0.0566599 0.998394i \(-0.481955\pi\)
0.0566599 + 0.998394i \(0.481955\pi\)
\(258\) 0 0
\(259\) −26.4222 −1.64180
\(260\) 0 0
\(261\) 7.57779 0.469054
\(262\) 0 0
\(263\) 3.51388 0.216675 0.108338 0.994114i \(-0.465447\pi\)
0.108338 + 0.994114i \(0.465447\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 4.18335 0.255063 0.127532 0.991835i \(-0.459295\pi\)
0.127532 + 0.991835i \(0.459295\pi\)
\(270\) 0 0
\(271\) 2.69722 0.163845 0.0819224 0.996639i \(-0.473894\pi\)
0.0819224 + 0.996639i \(0.473894\pi\)
\(272\) 0 0
\(273\) 3.30278 0.199893
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 27.2111 1.63496 0.817478 0.575959i \(-0.195371\pi\)
0.817478 + 0.575959i \(0.195371\pi\)
\(278\) 0 0
\(279\) −23.0000 −1.37697
\(280\) 0 0
\(281\) −26.6056 −1.58715 −0.793577 0.608470i \(-0.791784\pi\)
−0.793577 + 0.608470i \(0.791784\pi\)
\(282\) 0 0
\(283\) 2.00000 0.118888 0.0594438 0.998232i \(-0.481067\pi\)
0.0594438 + 0.998232i \(0.481067\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.00000 0.177084
\(288\) 0 0
\(289\) 30.7250 1.80735
\(290\) 0 0
\(291\) 1.90833 0.111868
\(292\) 0 0
\(293\) −23.2111 −1.35601 −0.678004 0.735059i \(-0.737155\pi\)
−0.678004 + 0.735059i \(0.737155\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 3.03616 0.176176
\(298\) 0 0
\(299\) 3.30278 0.191004
\(300\) 0 0
\(301\) −30.4222 −1.75351
\(302\) 0 0
\(303\) −0.788897 −0.0453210
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −11.6972 −0.667596 −0.333798 0.942645i \(-0.608330\pi\)
−0.333798 + 0.942645i \(0.608330\pi\)
\(308\) 0 0
\(309\) −2.45837 −0.139852
\(310\) 0 0
\(311\) −22.4222 −1.27145 −0.635723 0.771917i \(-0.719298\pi\)
−0.635723 + 0.771917i \(0.719298\pi\)
\(312\) 0 0
\(313\) −19.7250 −1.11492 −0.557461 0.830203i \(-0.688224\pi\)
−0.557461 + 0.830203i \(0.688224\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −17.7250 −0.995534 −0.497767 0.867311i \(-0.665847\pi\)
−0.497767 + 0.867311i \(0.665847\pi\)
\(318\) 0 0
\(319\) −4.42221 −0.247596
\(320\) 0 0
\(321\) 0.788897 0.0440320
\(322\) 0 0
\(323\) 40.8167 2.27110
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −0.449961 −0.0248829
\(328\) 0 0
\(329\) −8.60555 −0.474439
\(330\) 0 0
\(331\) −16.6056 −0.912724 −0.456362 0.889794i \(-0.650848\pi\)
−0.456362 + 0.889794i \(0.650848\pi\)
\(332\) 0 0
\(333\) 23.2666 1.27500
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 22.5139 1.22641 0.613205 0.789924i \(-0.289880\pi\)
0.613205 + 0.789924i \(0.289880\pi\)
\(338\) 0 0
\(339\) −4.97224 −0.270055
\(340\) 0 0
\(341\) 13.4222 0.726853
\(342\) 0 0
\(343\) −10.2111 −0.551348
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 28.5416 1.53220 0.766098 0.642724i \(-0.222196\pi\)
0.766098 + 0.642724i \(0.222196\pi\)
\(348\) 0 0
\(349\) −27.2111 −1.45658 −0.728288 0.685271i \(-0.759684\pi\)
−0.728288 + 0.685271i \(0.759684\pi\)
\(350\) 0 0
\(351\) −5.90833 −0.315363
\(352\) 0 0
\(353\) 10.4222 0.554718 0.277359 0.960766i \(-0.410541\pi\)
0.277359 + 0.960766i \(0.410541\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 6.90833 0.365627
\(358\) 0 0
\(359\) −11.2111 −0.591699 −0.295850 0.955235i \(-0.595603\pi\)
−0.295850 + 0.955235i \(0.595603\pi\)
\(360\) 0 0
\(361\) 15.9083 0.837280
\(362\) 0 0
\(363\) 2.45837 0.129031
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 14.7889 0.771974 0.385987 0.922504i \(-0.373861\pi\)
0.385987 + 0.922504i \(0.373861\pi\)
\(368\) 0 0
\(369\) −2.64171 −0.137522
\(370\) 0 0
\(371\) 37.0278 1.92239
\(372\) 0 0
\(373\) −4.60555 −0.238466 −0.119233 0.992866i \(-0.538044\pi\)
−0.119233 + 0.992866i \(0.538044\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.60555 0.443208
\(378\) 0 0
\(379\) −14.9083 −0.765789 −0.382895 0.923792i \(-0.625073\pi\)
−0.382895 + 0.923792i \(0.625073\pi\)
\(380\) 0 0
\(381\) −2.97224 −0.152273
\(382\) 0 0
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 26.7889 1.36176
\(388\) 0 0
\(389\) −25.9361 −1.31501 −0.657506 0.753449i \(-0.728388\pi\)
−0.657506 + 0.753449i \(0.728388\pi\)
\(390\) 0 0
\(391\) 6.90833 0.349369
\(392\) 0 0
\(393\) −3.39445 −0.171227
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −10.7250 −0.538271 −0.269136 0.963102i \(-0.586738\pi\)
−0.269136 + 0.963102i \(0.586738\pi\)
\(398\) 0 0
\(399\) 5.90833 0.295786
\(400\) 0 0
\(401\) −8.60555 −0.429741 −0.214870 0.976643i \(-0.568933\pi\)
−0.214870 + 0.976643i \(0.568933\pi\)
\(402\) 0 0
\(403\) −26.1194 −1.30110
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −13.5778 −0.673026
\(408\) 0 0
\(409\) −25.9083 −1.28108 −0.640542 0.767923i \(-0.721290\pi\)
−0.640542 + 0.767923i \(0.721290\pi\)
\(410\) 0 0
\(411\) 1.18335 0.0583702
\(412\) 0 0
\(413\) 11.2111 0.551662
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −3.81665 −0.186902
\(418\) 0 0
\(419\) −3.63331 −0.177499 −0.0887493 0.996054i \(-0.528287\pi\)
−0.0887493 + 0.996054i \(0.528287\pi\)
\(420\) 0 0
\(421\) 30.6972 1.49609 0.748046 0.663647i \(-0.230992\pi\)
0.748046 + 0.663647i \(0.230992\pi\)
\(422\) 0 0
\(423\) 7.57779 0.368445
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 38.0278 1.84029
\(428\) 0 0
\(429\) 1.69722 0.0819428
\(430\) 0 0
\(431\) 30.2389 1.45655 0.728277 0.685283i \(-0.240321\pi\)
0.728277 + 0.685283i \(0.240321\pi\)
\(432\) 0 0
\(433\) 24.0917 1.15777 0.578886 0.815409i \(-0.303488\pi\)
0.578886 + 0.815409i \(0.303488\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 5.90833 0.282634
\(438\) 0 0
\(439\) 14.6972 0.701460 0.350730 0.936477i \(-0.385933\pi\)
0.350730 + 0.936477i \(0.385933\pi\)
\(440\) 0 0
\(441\) −11.3667 −0.541271
\(442\) 0 0
\(443\) 17.4861 0.830791 0.415395 0.909641i \(-0.363643\pi\)
0.415395 + 0.909641i \(0.363643\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −4.02776 −0.190506
\(448\) 0 0
\(449\) −2.09167 −0.0987122 −0.0493561 0.998781i \(-0.515717\pi\)
−0.0493561 + 0.998781i \(0.515717\pi\)
\(450\) 0 0
\(451\) 1.54163 0.0725927
\(452\) 0 0
\(453\) 2.69722 0.126727
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 32.4222 1.51665 0.758323 0.651879i \(-0.226019\pi\)
0.758323 + 0.651879i \(0.226019\pi\)
\(458\) 0 0
\(459\) −12.3583 −0.576836
\(460\) 0 0
\(461\) 10.1833 0.474286 0.237143 0.971475i \(-0.423789\pi\)
0.237143 + 0.971475i \(0.423789\pi\)
\(462\) 0 0
\(463\) 17.6333 0.819489 0.409745 0.912200i \(-0.365618\pi\)
0.409745 + 0.912200i \(0.365618\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −1.81665 −0.0840647 −0.0420324 0.999116i \(-0.513383\pi\)
−0.0420324 + 0.999116i \(0.513383\pi\)
\(468\) 0 0
\(469\) −13.2111 −0.610032
\(470\) 0 0
\(471\) −5.63331 −0.259569
\(472\) 0 0
\(473\) −15.6333 −0.718820
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −32.6056 −1.49291
\(478\) 0 0
\(479\) 30.0000 1.37073 0.685367 0.728197i \(-0.259642\pi\)
0.685367 + 0.728197i \(0.259642\pi\)
\(480\) 0 0
\(481\) 26.4222 1.20475
\(482\) 0 0
\(483\) 1.00000 0.0455016
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 9.81665 0.444835 0.222418 0.974952i \(-0.428605\pi\)
0.222418 + 0.974952i \(0.428605\pi\)
\(488\) 0 0
\(489\) −2.81665 −0.127373
\(490\) 0 0
\(491\) 4.18335 0.188792 0.0943959 0.995535i \(-0.469908\pi\)
0.0943959 + 0.995535i \(0.469908\pi\)
\(492\) 0 0
\(493\) 18.0000 0.810679
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 53.8444 2.41525
\(498\) 0 0
\(499\) 31.6333 1.41610 0.708051 0.706162i \(-0.249575\pi\)
0.708051 + 0.706162i \(0.249575\pi\)
\(500\) 0 0
\(501\) −2.05551 −0.0918335
\(502\) 0 0
\(503\) 29.7250 1.32537 0.662686 0.748898i \(-0.269417\pi\)
0.662686 + 0.748898i \(0.269417\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.633308 0.0281262
\(508\) 0 0
\(509\) −35.4500 −1.57129 −0.785646 0.618676i \(-0.787669\pi\)
−0.785646 + 0.618676i \(0.787669\pi\)
\(510\) 0 0
\(511\) 19.2111 0.849849
\(512\) 0 0
\(513\) −10.5694 −0.466650
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −4.42221 −0.194488
\(518\) 0 0
\(519\) 5.96384 0.261784
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) −20.4222 −0.893001 −0.446500 0.894783i \(-0.647330\pi\)
−0.446500 + 0.894783i \(0.647330\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −54.6333 −2.37986
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −9.87217 −0.428416
\(532\) 0 0
\(533\) −3.00000 −0.129944
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 2.84441 0.122745
\(538\) 0 0
\(539\) 6.63331 0.285717
\(540\) 0 0
\(541\) 28.8444 1.24012 0.620059 0.784555i \(-0.287109\pi\)
0.620059 + 0.784555i \(0.287109\pi\)
\(542\) 0 0
\(543\) −5.18335 −0.222439
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −10.5139 −0.449541 −0.224770 0.974412i \(-0.572163\pi\)
−0.224770 + 0.974412i \(0.572163\pi\)
\(548\) 0 0
\(549\) −33.4861 −1.42915
\(550\) 0 0
\(551\) 15.3944 0.655826
\(552\) 0 0
\(553\) 47.6333 2.02557
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −22.4222 −0.950059 −0.475030 0.879970i \(-0.657563\pi\)
−0.475030 + 0.879970i \(0.657563\pi\)
\(558\) 0 0
\(559\) 30.4222 1.28672
\(560\) 0 0
\(561\) 3.55004 0.149883
\(562\) 0 0
\(563\) −3.63331 −0.153126 −0.0765628 0.997065i \(-0.524395\pi\)
−0.0765628 + 0.997065i \(0.524395\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 27.0278 1.13506
\(568\) 0 0
\(569\) 28.4222 1.19152 0.595760 0.803162i \(-0.296851\pi\)
0.595760 + 0.803162i \(0.296851\pi\)
\(570\) 0 0
\(571\) 16.1194 0.674577 0.337289 0.941401i \(-0.390490\pi\)
0.337289 + 0.941401i \(0.390490\pi\)
\(572\) 0 0
\(573\) −2.60555 −0.108848
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −2.00000 −0.0832611 −0.0416305 0.999133i \(-0.513255\pi\)
−0.0416305 + 0.999133i \(0.513255\pi\)
\(578\) 0 0
\(579\) −5.39445 −0.224186
\(580\) 0 0
\(581\) 37.0278 1.53617
\(582\) 0 0
\(583\) 19.0278 0.788049
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 16.5416 0.682746 0.341373 0.939928i \(-0.389108\pi\)
0.341373 + 0.939928i \(0.389108\pi\)
\(588\) 0 0
\(589\) −46.7250 −1.92527
\(590\) 0 0
\(591\) 1.30278 0.0535890
\(592\) 0 0
\(593\) 1.81665 0.0746010 0.0373005 0.999304i \(-0.488124\pi\)
0.0373005 + 0.999304i \(0.488124\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6.18335 −0.253068
\(598\) 0 0
\(599\) 35.3305 1.44357 0.721783 0.692119i \(-0.243323\pi\)
0.721783 + 0.692119i \(0.243323\pi\)
\(600\) 0 0
\(601\) 42.9361 1.75140 0.875700 0.482856i \(-0.160401\pi\)
0.875700 + 0.482856i \(0.160401\pi\)
\(602\) 0 0
\(603\) 11.6333 0.473745
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 46.0555 1.86934 0.934668 0.355522i \(-0.115697\pi\)
0.934668 + 0.355522i \(0.115697\pi\)
\(608\) 0 0
\(609\) 2.60555 0.105582
\(610\) 0 0
\(611\) 8.60555 0.348143
\(612\) 0 0
\(613\) −3.57779 −0.144506 −0.0722529 0.997386i \(-0.523019\pi\)
−0.0722529 + 0.997386i \(0.523019\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −18.9083 −0.761221 −0.380610 0.924736i \(-0.624286\pi\)
−0.380610 + 0.924736i \(0.624286\pi\)
\(618\) 0 0
\(619\) 12.3305 0.495606 0.247803 0.968810i \(-0.420291\pi\)
0.247803 + 0.968810i \(0.420291\pi\)
\(620\) 0 0
\(621\) −1.78890 −0.0717860
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3.03616 0.121253
\(628\) 0 0
\(629\) 55.2666 2.20362
\(630\) 0 0
\(631\) −23.3944 −0.931318 −0.465659 0.884964i \(-0.654183\pi\)
−0.465659 + 0.884964i \(0.654183\pi\)
\(632\) 0 0
\(633\) 2.18335 0.0867802
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −12.9083 −0.511447
\(638\) 0 0
\(639\) −47.4138 −1.87566
\(640\) 0 0
\(641\) −36.0000 −1.42191 −0.710957 0.703235i \(-0.751738\pi\)
−0.710957 + 0.703235i \(0.751738\pi\)
\(642\) 0 0
\(643\) −34.2389 −1.35025 −0.675124 0.737704i \(-0.735910\pi\)
−0.675124 + 0.737704i \(0.735910\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 26.8444 1.05536 0.527681 0.849442i \(-0.323062\pi\)
0.527681 + 0.849442i \(0.323062\pi\)
\(648\) 0 0
\(649\) 5.76114 0.226145
\(650\) 0 0
\(651\) −7.90833 −0.309952
\(652\) 0 0
\(653\) −41.7250 −1.63282 −0.816412 0.577469i \(-0.804040\pi\)
−0.816412 + 0.577469i \(0.804040\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −16.9167 −0.659985
\(658\) 0 0
\(659\) −15.6333 −0.608987 −0.304494 0.952514i \(-0.598487\pi\)
−0.304494 + 0.952514i \(0.598487\pi\)
\(660\) 0 0
\(661\) −34.9083 −1.35778 −0.678888 0.734242i \(-0.737538\pi\)
−0.678888 + 0.734242i \(0.737538\pi\)
\(662\) 0 0
\(663\) −6.90833 −0.268297
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 2.60555 0.100887
\(668\) 0 0
\(669\) 1.21110 0.0468239
\(670\) 0 0
\(671\) 19.5416 0.754396
\(672\) 0 0
\(673\) 37.6333 1.45066 0.725329 0.688403i \(-0.241688\pi\)
0.725329 + 0.688403i \(0.241688\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −16.4222 −0.631157 −0.315578 0.948900i \(-0.602198\pi\)
−0.315578 + 0.948900i \(0.602198\pi\)
\(678\) 0 0
\(679\) −20.8167 −0.798870
\(680\) 0 0
\(681\) 4.42221 0.169459
\(682\) 0 0
\(683\) −0.275019 −0.0105233 −0.00526166 0.999986i \(-0.501675\pi\)
−0.00526166 + 0.999986i \(0.501675\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −0.605551 −0.0231032
\(688\) 0 0
\(689\) −37.0278 −1.41065
\(690\) 0 0
\(691\) −51.8167 −1.97120 −0.985599 0.169098i \(-0.945914\pi\)
−0.985599 + 0.169098i \(0.945914\pi\)
\(692\) 0 0
\(693\) −16.3028 −0.619291
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −6.27502 −0.237683
\(698\) 0 0
\(699\) 7.81665 0.295653
\(700\) 0 0
\(701\) 32.0917 1.21209 0.606043 0.795432i \(-0.292756\pi\)
0.606043 + 0.795432i \(0.292756\pi\)
\(702\) 0 0
\(703\) 47.2666 1.78269
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 8.60555 0.323645
\(708\) 0 0
\(709\) −15.8806 −0.596407 −0.298204 0.954502i \(-0.596387\pi\)
−0.298204 + 0.954502i \(0.596387\pi\)
\(710\) 0 0
\(711\) −41.9445 −1.57304
\(712\) 0 0
\(713\) −7.90833 −0.296169
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 1.57779 0.0589238
\(718\) 0 0
\(719\) −10.6972 −0.398939 −0.199470 0.979904i \(-0.563922\pi\)
−0.199470 + 0.979904i \(0.563922\pi\)
\(720\) 0 0
\(721\) 26.8167 0.998704
\(722\) 0 0
\(723\) 4.36669 0.162399
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 2.90833 0.107864 0.0539319 0.998545i \(-0.482825\pi\)
0.0539319 + 0.998545i \(0.482825\pi\)
\(728\) 0 0
\(729\) −22.1749 −0.821294
\(730\) 0 0
\(731\) 63.6333 2.35356
\(732\) 0 0
\(733\) −29.6333 −1.09453 −0.547266 0.836959i \(-0.684331\pi\)
−0.547266 + 0.836959i \(0.684331\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −6.78890 −0.250072
\(738\) 0 0
\(739\) −35.6333 −1.31079 −0.655396 0.755285i \(-0.727498\pi\)
−0.655396 + 0.755285i \(0.727498\pi\)
\(740\) 0 0
\(741\) −5.90833 −0.217048
\(742\) 0 0
\(743\) −32.3305 −1.18609 −0.593046 0.805169i \(-0.702075\pi\)
−0.593046 + 0.805169i \(0.702075\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −32.6056 −1.19297
\(748\) 0 0
\(749\) −8.60555 −0.314440
\(750\) 0 0
\(751\) −21.8167 −0.796101 −0.398051 0.917364i \(-0.630313\pi\)
−0.398051 + 0.917364i \(0.630313\pi\)
\(752\) 0 0
\(753\) 3.78890 0.138075
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −13.2111 −0.480166 −0.240083 0.970752i \(-0.577175\pi\)
−0.240083 + 0.970752i \(0.577175\pi\)
\(758\) 0 0
\(759\) 0.513878 0.0186526
\(760\) 0 0
\(761\) −49.5416 −1.79588 −0.897941 0.440115i \(-0.854938\pi\)
−0.897941 + 0.440115i \(0.854938\pi\)
\(762\) 0 0
\(763\) 4.90833 0.177693
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −11.2111 −0.404809
\(768\) 0 0
\(769\) 45.2666 1.63236 0.816178 0.577801i \(-0.196089\pi\)
0.816178 + 0.577801i \(0.196089\pi\)
\(770\) 0 0
\(771\) −0.550039 −0.0198092
\(772\) 0 0
\(773\) −12.0000 −0.431610 −0.215805 0.976436i \(-0.569238\pi\)
−0.215805 + 0.976436i \(0.569238\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 8.00000 0.286998
\(778\) 0 0
\(779\) −5.36669 −0.192282
\(780\) 0 0
\(781\) 27.6695 0.990091
\(782\) 0 0
\(783\) −4.66106 −0.166573
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 37.4500 1.33495 0.667473 0.744634i \(-0.267376\pi\)
0.667473 + 0.744634i \(0.267376\pi\)
\(788\) 0 0
\(789\) −1.06392 −0.0378764
\(790\) 0 0
\(791\) 54.2389 1.92851
\(792\) 0 0
\(793\) −38.0278 −1.35041
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −1.81665 −0.0643492 −0.0321746 0.999482i \(-0.510243\pi\)
−0.0321746 + 0.999482i \(0.510243\pi\)
\(798\) 0 0
\(799\) 18.0000 0.636794
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 9.87217 0.348381
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −1.26662 −0.0445870
\(808\) 0 0
\(809\) 50.7250 1.78340 0.891698 0.452631i \(-0.149515\pi\)
0.891698 + 0.452631i \(0.149515\pi\)
\(810\) 0 0
\(811\) 41.0278 1.44068 0.720340 0.693621i \(-0.243986\pi\)
0.720340 + 0.693621i \(0.243986\pi\)
\(812\) 0 0
\(813\) −0.816654 −0.0286413
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 54.4222 1.90399
\(818\) 0 0
\(819\) 31.7250 1.10856
\(820\) 0 0
\(821\) −30.0000 −1.04701 −0.523504 0.852023i \(-0.675375\pi\)
−0.523504 + 0.852023i \(0.675375\pi\)
\(822\) 0 0
\(823\) −15.2111 −0.530226 −0.265113 0.964217i \(-0.585409\pi\)
−0.265113 + 0.964217i \(0.585409\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −29.4500 −1.02408 −0.512038 0.858963i \(-0.671109\pi\)
−0.512038 + 0.858963i \(0.671109\pi\)
\(828\) 0 0
\(829\) 31.2111 1.08401 0.542003 0.840376i \(-0.317666\pi\)
0.542003 + 0.840376i \(0.317666\pi\)
\(830\) 0 0
\(831\) −8.23886 −0.285803
\(832\) 0 0
\(833\) −27.0000 −0.935495
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 14.1472 0.488998
\(838\) 0 0
\(839\) 43.8167 1.51272 0.756359 0.654156i \(-0.226976\pi\)
0.756359 + 0.654156i \(0.226976\pi\)
\(840\) 0 0
\(841\) −22.2111 −0.765900
\(842\) 0 0
\(843\) 8.05551 0.277447
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −26.8167 −0.921431
\(848\) 0 0
\(849\) −0.605551 −0.0207825
\(850\) 0 0
\(851\) 8.00000 0.274236
\(852\) 0 0
\(853\) 21.7250 0.743849 0.371925 0.928263i \(-0.378698\pi\)
0.371925 + 0.928263i \(0.378698\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −9.63331 −0.329068 −0.164534 0.986371i \(-0.552612\pi\)
−0.164534 + 0.986371i \(0.552612\pi\)
\(858\) 0 0
\(859\) 35.8167 1.22205 0.611024 0.791612i \(-0.290758\pi\)
0.611024 + 0.791612i \(0.290758\pi\)
\(860\) 0 0
\(861\) −0.908327 −0.0309557
\(862\) 0 0
\(863\) −41.4500 −1.41097 −0.705487 0.708723i \(-0.749271\pi\)
−0.705487 + 0.708723i \(0.749271\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −9.30278 −0.315939
\(868\) 0 0
\(869\) 24.4777 0.830350
\(870\) 0 0
\(871\) 13.2111 0.447641
\(872\) 0 0
\(873\) 18.3305 0.620395
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 48.1749 1.62675 0.813376 0.581738i \(-0.197627\pi\)
0.813376 + 0.581738i \(0.197627\pi\)
\(878\) 0 0
\(879\) 7.02776 0.237040
\(880\) 0 0
\(881\) 55.2666 1.86198 0.930990 0.365045i \(-0.118946\pi\)
0.930990 + 0.365045i \(0.118946\pi\)
\(882\) 0 0
\(883\) 8.27502 0.278477 0.139238 0.990259i \(-0.455535\pi\)
0.139238 + 0.990259i \(0.455535\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 27.6333 0.927836 0.463918 0.885878i \(-0.346443\pi\)
0.463918 + 0.885878i \(0.346443\pi\)
\(888\) 0 0
\(889\) 32.4222 1.08741
\(890\) 0 0
\(891\) 13.8890 0.465298
\(892\) 0 0
\(893\) 15.3944 0.515156
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −1.00000 −0.0333890
\(898\) 0 0
\(899\) −20.6056 −0.687234
\(900\) 0 0
\(901\) −77.4500 −2.58023
\(902\) 0 0
\(903\) 9.21110 0.306526
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 48.6611 1.61576 0.807882 0.589344i \(-0.200614\pi\)
0.807882 + 0.589344i \(0.200614\pi\)
\(908\) 0 0
\(909\) −7.57779 −0.251340
\(910\) 0 0
\(911\) 4.18335 0.138600 0.0693002 0.997596i \(-0.477923\pi\)
0.0693002 + 0.997596i \(0.477923\pi\)
\(912\) 0 0
\(913\) 19.0278 0.629727
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 37.0278 1.22276
\(918\) 0 0
\(919\) −44.0000 −1.45143 −0.725713 0.687998i \(-0.758490\pi\)
−0.725713 + 0.687998i \(0.758490\pi\)
\(920\) 0 0
\(921\) 3.54163 0.116701
\(922\) 0 0
\(923\) −53.8444 −1.77231
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −23.6140 −0.775584
\(928\) 0 0
\(929\) −14.3667 −0.471356 −0.235678 0.971831i \(-0.575731\pi\)
−0.235678 + 0.971831i \(0.575731\pi\)
\(930\) 0 0
\(931\) −23.0917 −0.756799
\(932\) 0 0
\(933\) 6.78890 0.222259
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −37.9638 −1.24022 −0.620112 0.784513i \(-0.712913\pi\)
−0.620112 + 0.784513i \(0.712913\pi\)
\(938\) 0 0
\(939\) 5.97224 0.194897
\(940\) 0 0
\(941\) 25.9361 0.845492 0.422746 0.906248i \(-0.361066\pi\)
0.422746 + 0.906248i \(0.361066\pi\)
\(942\) 0 0
\(943\) −0.908327 −0.0295792
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −4.93608 −0.160401 −0.0802006 0.996779i \(-0.525556\pi\)
−0.0802006 + 0.996779i \(0.525556\pi\)
\(948\) 0 0
\(949\) −19.2111 −0.623619
\(950\) 0 0
\(951\) 5.36669 0.174027
\(952\) 0 0
\(953\) 41.3305 1.33883 0.669414 0.742890i \(-0.266545\pi\)
0.669414 + 0.742890i \(0.266545\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 1.33894 0.0432817
\(958\) 0 0
\(959\) −12.9083 −0.416832
\(960\) 0 0
\(961\) 31.5416 1.01747
\(962\) 0 0
\(963\) 7.57779 0.244191
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −12.6056 −0.405367 −0.202684 0.979244i \(-0.564966\pi\)
−0.202684 + 0.979244i \(0.564966\pi\)
\(968\) 0 0
\(969\) −12.3583 −0.397005
\(970\) 0 0
\(971\) 17.0917 0.548498 0.274249 0.961659i \(-0.411571\pi\)
0.274249 + 0.961659i \(0.411571\pi\)
\(972\) 0 0
\(973\) 41.6333 1.33470
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −6.51388 −0.208397 −0.104199 0.994556i \(-0.533228\pi\)
−0.104199 + 0.994556i \(0.533228\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −4.32213 −0.137995
\(982\) 0 0
\(983\) 34.5416 1.10171 0.550854 0.834602i \(-0.314302\pi\)
0.550854 + 0.834602i \(0.314302\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 2.60555 0.0829356
\(988\) 0 0
\(989\) 9.21110 0.292896
\(990\) 0 0
\(991\) 15.3305 0.486990 0.243495 0.969902i \(-0.421706\pi\)
0.243495 + 0.969902i \(0.421706\pi\)
\(992\) 0 0
\(993\) 5.02776 0.159551
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 16.7889 0.531710 0.265855 0.964013i \(-0.414346\pi\)
0.265855 + 0.964013i \(0.414346\pi\)
\(998\) 0 0
\(999\) −14.3112 −0.452786
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.ca.1.1 2
4.3 odd 2 1150.2.a.m.1.2 2
5.4 even 2 1840.2.a.j.1.2 2
20.3 even 4 1150.2.b.f.599.2 4
20.7 even 4 1150.2.b.f.599.3 4
20.19 odd 2 230.2.a.b.1.1 2
40.19 odd 2 7360.2.a.bc.1.2 2
40.29 even 2 7360.2.a.bu.1.1 2
60.59 even 2 2070.2.a.w.1.2 2
460.459 even 2 5290.2.a.j.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
230.2.a.b.1.1 2 20.19 odd 2
1150.2.a.m.1.2 2 4.3 odd 2
1150.2.b.f.599.2 4 20.3 even 4
1150.2.b.f.599.3 4 20.7 even 4
1840.2.a.j.1.2 2 5.4 even 2
2070.2.a.w.1.2 2 60.59 even 2
5290.2.a.j.1.1 2 460.459 even 2
7360.2.a.bc.1.2 2 40.19 odd 2
7360.2.a.bu.1.1 2 40.29 even 2
9200.2.a.ca.1.1 2 1.1 even 1 trivial