Properties

Label 1600.2.a.bb.1.2
Level $1600$
Weight $2$
Character 1600.1
Self dual yes
Analytic conductor $12.776$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(12.7760643234\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \(x^{2} - x - 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 800)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.618034\) of defining polynomial
Character \(\chi\) \(=\) 1600.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.23607 q^{3} -4.47214 q^{7} +2.00000 q^{9} +O(q^{10})\) \(q+2.23607 q^{3} -4.47214 q^{7} +2.00000 q^{9} -2.23607 q^{11} +4.00000 q^{13} +7.00000 q^{17} +6.70820 q^{19} -10.0000 q^{21} +4.47214 q^{23} -2.23607 q^{27} +4.47214 q^{31} -5.00000 q^{33} +2.00000 q^{37} +8.94427 q^{39} +5.00000 q^{41} +8.94427 q^{47} +13.0000 q^{49} +15.6525 q^{51} +6.00000 q^{53} +15.0000 q^{57} -8.94427 q^{59} -10.0000 q^{61} -8.94427 q^{63} -2.23607 q^{67} +10.0000 q^{69} -8.94427 q^{71} +9.00000 q^{73} +10.0000 q^{77} -4.47214 q^{79} -11.0000 q^{81} -11.1803 q^{83} -5.00000 q^{89} -17.8885 q^{91} +10.0000 q^{93} -2.00000 q^{97} -4.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{9} + O(q^{10}) \) \( 2 q + 4 q^{9} + 8 q^{13} + 14 q^{17} - 20 q^{21} - 10 q^{33} + 4 q^{37} + 10 q^{41} + 26 q^{49} + 12 q^{53} + 30 q^{57} - 20 q^{61} + 20 q^{69} + 18 q^{73} + 20 q^{77} - 22 q^{81} - 10 q^{89} + 20 q^{93} - 4 q^{97} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.23607 1.29099 0.645497 0.763763i \(-0.276650\pi\)
0.645497 + 0.763763i \(0.276650\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −4.47214 −1.69031 −0.845154 0.534522i \(-0.820491\pi\)
−0.845154 + 0.534522i \(0.820491\pi\)
\(8\) 0 0
\(9\) 2.00000 0.666667
\(10\) 0 0
\(11\) −2.23607 −0.674200 −0.337100 0.941469i \(-0.609446\pi\)
−0.337100 + 0.941469i \(0.609446\pi\)
\(12\) 0 0
\(13\) 4.00000 1.10940 0.554700 0.832050i \(-0.312833\pi\)
0.554700 + 0.832050i \(0.312833\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 0 0
\(19\) 6.70820 1.53897 0.769484 0.638666i \(-0.220514\pi\)
0.769484 + 0.638666i \(0.220514\pi\)
\(20\) 0 0
\(21\) −10.0000 −2.18218
\(22\) 0 0
\(23\) 4.47214 0.932505 0.466252 0.884652i \(-0.345604\pi\)
0.466252 + 0.884652i \(0.345604\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.23607 −0.430331
\(28\) 0 0
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 4.47214 0.803219 0.401610 0.915811i \(-0.368451\pi\)
0.401610 + 0.915811i \(0.368451\pi\)
\(32\) 0 0
\(33\) −5.00000 −0.870388
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 8.94427 1.43223
\(40\) 0 0
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 8.94427 1.30466 0.652328 0.757937i \(-0.273792\pi\)
0.652328 + 0.757937i \(0.273792\pi\)
\(48\) 0 0
\(49\) 13.0000 1.85714
\(50\) 0 0
\(51\) 15.6525 2.19179
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 15.0000 1.98680
\(58\) 0 0
\(59\) −8.94427 −1.16445 −0.582223 0.813029i \(-0.697817\pi\)
−0.582223 + 0.813029i \(0.697817\pi\)
\(60\) 0 0
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 0 0
\(63\) −8.94427 −1.12687
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −2.23607 −0.273179 −0.136590 0.990628i \(-0.543614\pi\)
−0.136590 + 0.990628i \(0.543614\pi\)
\(68\) 0 0
\(69\) 10.0000 1.20386
\(70\) 0 0
\(71\) −8.94427 −1.06149 −0.530745 0.847532i \(-0.678088\pi\)
−0.530745 + 0.847532i \(0.678088\pi\)
\(72\) 0 0
\(73\) 9.00000 1.05337 0.526685 0.850060i \(-0.323435\pi\)
0.526685 + 0.850060i \(0.323435\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 10.0000 1.13961
\(78\) 0 0
\(79\) −4.47214 −0.503155 −0.251577 0.967837i \(-0.580949\pi\)
−0.251577 + 0.967837i \(0.580949\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) −11.1803 −1.22720 −0.613601 0.789616i \(-0.710280\pi\)
−0.613601 + 0.789616i \(0.710280\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.00000 −0.529999 −0.264999 0.964249i \(-0.585372\pi\)
−0.264999 + 0.964249i \(0.585372\pi\)
\(90\) 0 0
\(91\) −17.8885 −1.87523
\(92\) 0 0
\(93\) 10.0000 1.03695
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 0 0
\(99\) −4.47214 −0.449467
\(100\) 0 0
\(101\) 2.00000 0.199007 0.0995037 0.995037i \(-0.468274\pi\)
0.0995037 + 0.995037i \(0.468274\pi\)
\(102\) 0 0
\(103\) 8.94427 0.881305 0.440653 0.897678i \(-0.354747\pi\)
0.440653 + 0.897678i \(0.354747\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 2.23607 0.216169 0.108084 0.994142i \(-0.465528\pi\)
0.108084 + 0.994142i \(0.465528\pi\)
\(108\) 0 0
\(109\) −6.00000 −0.574696 −0.287348 0.957826i \(-0.592774\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) 0 0
\(111\) 4.47214 0.424476
\(112\) 0 0
\(113\) 1.00000 0.0940721 0.0470360 0.998893i \(-0.485022\pi\)
0.0470360 + 0.998893i \(0.485022\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 8.00000 0.739600
\(118\) 0 0
\(119\) −31.3050 −2.86972
\(120\) 0 0
\(121\) −6.00000 −0.545455
\(122\) 0 0
\(123\) 11.1803 1.00810
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −4.47214 −0.396838 −0.198419 0.980117i \(-0.563581\pi\)
−0.198419 + 0.980117i \(0.563581\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −17.8885 −1.56293 −0.781465 0.623949i \(-0.785527\pi\)
−0.781465 + 0.623949i \(0.785527\pi\)
\(132\) 0 0
\(133\) −30.0000 −2.60133
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 0 0
\(139\) −2.23607 −0.189661 −0.0948304 0.995493i \(-0.530231\pi\)
−0.0948304 + 0.995493i \(0.530231\pi\)
\(140\) 0 0
\(141\) 20.0000 1.68430
\(142\) 0 0
\(143\) −8.94427 −0.747958
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 29.0689 2.39756
\(148\) 0 0
\(149\) 16.0000 1.31077 0.655386 0.755295i \(-0.272506\pi\)
0.655386 + 0.755295i \(0.272506\pi\)
\(150\) 0 0
\(151\) −13.4164 −1.09181 −0.545906 0.837846i \(-0.683814\pi\)
−0.545906 + 0.837846i \(0.683814\pi\)
\(152\) 0 0
\(153\) 14.0000 1.13183
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 18.0000 1.43656 0.718278 0.695756i \(-0.244931\pi\)
0.718278 + 0.695756i \(0.244931\pi\)
\(158\) 0 0
\(159\) 13.4164 1.06399
\(160\) 0 0
\(161\) −20.0000 −1.57622
\(162\) 0 0
\(163\) −2.23607 −0.175142 −0.0875712 0.996158i \(-0.527911\pi\)
−0.0875712 + 0.996158i \(0.527911\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.94427 −0.692129 −0.346064 0.938211i \(-0.612482\pi\)
−0.346064 + 0.938211i \(0.612482\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) 13.4164 1.02598
\(172\) 0 0
\(173\) 16.0000 1.21646 0.608229 0.793762i \(-0.291880\pi\)
0.608229 + 0.793762i \(0.291880\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −20.0000 −1.50329
\(178\) 0 0
\(179\) −2.23607 −0.167132 −0.0835658 0.996502i \(-0.526631\pi\)
−0.0835658 + 0.996502i \(0.526631\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) −22.3607 −1.65295
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −15.6525 −1.14462
\(188\) 0 0
\(189\) 10.0000 0.727393
\(190\) 0 0
\(191\) 13.4164 0.970777 0.485389 0.874299i \(-0.338678\pi\)
0.485389 + 0.874299i \(0.338678\pi\)
\(192\) 0 0
\(193\) −9.00000 −0.647834 −0.323917 0.946085i \(-0.605000\pi\)
−0.323917 + 0.946085i \(0.605000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) 8.94427 0.634043 0.317021 0.948418i \(-0.397317\pi\)
0.317021 + 0.948418i \(0.397317\pi\)
\(200\) 0 0
\(201\) −5.00000 −0.352673
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 8.94427 0.621670
\(208\) 0 0
\(209\) −15.0000 −1.03757
\(210\) 0 0
\(211\) 20.1246 1.38544 0.692718 0.721209i \(-0.256413\pi\)
0.692718 + 0.721209i \(0.256413\pi\)
\(212\) 0 0
\(213\) −20.0000 −1.37038
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −20.0000 −1.35769
\(218\) 0 0
\(219\) 20.1246 1.35990
\(220\) 0 0
\(221\) 28.0000 1.88348
\(222\) 0 0
\(223\) 26.8328 1.79686 0.898429 0.439119i \(-0.144709\pi\)
0.898429 + 0.439119i \(0.144709\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −17.8885 −1.18730 −0.593652 0.804722i \(-0.702314\pi\)
−0.593652 + 0.804722i \(0.702314\pi\)
\(228\) 0 0
\(229\) −20.0000 −1.32164 −0.660819 0.750546i \(-0.729791\pi\)
−0.660819 + 0.750546i \(0.729791\pi\)
\(230\) 0 0
\(231\) 22.3607 1.47122
\(232\) 0 0
\(233\) 26.0000 1.70332 0.851658 0.524097i \(-0.175597\pi\)
0.851658 + 0.524097i \(0.175597\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −10.0000 −0.649570
\(238\) 0 0
\(239\) 17.8885 1.15711 0.578557 0.815642i \(-0.303616\pi\)
0.578557 + 0.815642i \(0.303616\pi\)
\(240\) 0 0
\(241\) 5.00000 0.322078 0.161039 0.986948i \(-0.448515\pi\)
0.161039 + 0.986948i \(0.448515\pi\)
\(242\) 0 0
\(243\) −17.8885 −1.14755
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 26.8328 1.70733
\(248\) 0 0
\(249\) −25.0000 −1.58431
\(250\) 0 0
\(251\) 11.1803 0.705697 0.352848 0.935681i \(-0.385213\pi\)
0.352848 + 0.935681i \(0.385213\pi\)
\(252\) 0 0
\(253\) −10.0000 −0.628695
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.00000 0.124757 0.0623783 0.998053i \(-0.480131\pi\)
0.0623783 + 0.998053i \(0.480131\pi\)
\(258\) 0 0
\(259\) −8.94427 −0.555770
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 22.3607 1.37882 0.689409 0.724372i \(-0.257870\pi\)
0.689409 + 0.724372i \(0.257870\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −11.1803 −0.684226
\(268\) 0 0
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) −13.4164 −0.814989 −0.407494 0.913208i \(-0.633597\pi\)
−0.407494 + 0.913208i \(0.633597\pi\)
\(272\) 0 0
\(273\) −40.0000 −2.42091
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 0 0
\(279\) 8.94427 0.535480
\(280\) 0 0
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 0 0
\(283\) 6.70820 0.398761 0.199381 0.979922i \(-0.436107\pi\)
0.199381 + 0.979922i \(0.436107\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −22.3607 −1.31991
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 0 0
\(291\) −4.47214 −0.262161
\(292\) 0 0
\(293\) 14.0000 0.817889 0.408944 0.912559i \(-0.365897\pi\)
0.408944 + 0.912559i \(0.365897\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 5.00000 0.290129
\(298\) 0 0
\(299\) 17.8885 1.03452
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 4.47214 0.256917
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −15.6525 −0.893334 −0.446667 0.894700i \(-0.647389\pi\)
−0.446667 + 0.894700i \(0.647389\pi\)
\(308\) 0 0
\(309\) 20.0000 1.13776
\(310\) 0 0
\(311\) −22.3607 −1.26796 −0.633979 0.773350i \(-0.718579\pi\)
−0.633979 + 0.773350i \(0.718579\pi\)
\(312\) 0 0
\(313\) 6.00000 0.339140 0.169570 0.985518i \(-0.445762\pi\)
0.169570 + 0.985518i \(0.445762\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −12.0000 −0.673987 −0.336994 0.941507i \(-0.609410\pi\)
−0.336994 + 0.941507i \(0.609410\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 5.00000 0.279073
\(322\) 0 0
\(323\) 46.9574 2.61278
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −13.4164 −0.741929
\(328\) 0 0
\(329\) −40.0000 −2.20527
\(330\) 0 0
\(331\) −11.1803 −0.614527 −0.307264 0.951624i \(-0.599413\pi\)
−0.307264 + 0.951624i \(0.599413\pi\)
\(332\) 0 0
\(333\) 4.00000 0.219199
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −27.0000 −1.47078 −0.735392 0.677642i \(-0.763002\pi\)
−0.735392 + 0.677642i \(0.763002\pi\)
\(338\) 0 0
\(339\) 2.23607 0.121447
\(340\) 0 0
\(341\) −10.0000 −0.541530
\(342\) 0 0
\(343\) −26.8328 −1.44884
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 20.1246 1.08035 0.540173 0.841554i \(-0.318359\pi\)
0.540173 + 0.841554i \(0.318359\pi\)
\(348\) 0 0
\(349\) −30.0000 −1.60586 −0.802932 0.596071i \(-0.796728\pi\)
−0.802932 + 0.596071i \(0.796728\pi\)
\(350\) 0 0
\(351\) −8.94427 −0.477410
\(352\) 0 0
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −70.0000 −3.70479
\(358\) 0 0
\(359\) 31.3050 1.65221 0.826106 0.563515i \(-0.190551\pi\)
0.826106 + 0.563515i \(0.190551\pi\)
\(360\) 0 0
\(361\) 26.0000 1.36842
\(362\) 0 0
\(363\) −13.4164 −0.704179
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −26.8328 −1.40066 −0.700331 0.713818i \(-0.746964\pi\)
−0.700331 + 0.713818i \(0.746964\pi\)
\(368\) 0 0
\(369\) 10.0000 0.520579
\(370\) 0 0
\(371\) −26.8328 −1.39309
\(372\) 0 0
\(373\) −14.0000 −0.724893 −0.362446 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −15.6525 −0.804014 −0.402007 0.915637i \(-0.631687\pi\)
−0.402007 + 0.915637i \(0.631687\pi\)
\(380\) 0 0
\(381\) −10.0000 −0.512316
\(382\) 0 0
\(383\) 4.47214 0.228515 0.114258 0.993451i \(-0.463551\pi\)
0.114258 + 0.993451i \(0.463551\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 31.3050 1.58316
\(392\) 0 0
\(393\) −40.0000 −2.01773
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −28.0000 −1.40528 −0.702640 0.711546i \(-0.747995\pi\)
−0.702640 + 0.711546i \(0.747995\pi\)
\(398\) 0 0
\(399\) −67.0820 −3.35830
\(400\) 0 0
\(401\) 17.0000 0.848939 0.424470 0.905442i \(-0.360461\pi\)
0.424470 + 0.905442i \(0.360461\pi\)
\(402\) 0 0
\(403\) 17.8885 0.891092
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.47214 −0.221676
\(408\) 0 0
\(409\) 29.0000 1.43396 0.716979 0.697095i \(-0.245524\pi\)
0.716979 + 0.697095i \(0.245524\pi\)
\(410\) 0 0
\(411\) 6.70820 0.330891
\(412\) 0 0
\(413\) 40.0000 1.96827
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −5.00000 −0.244851
\(418\) 0 0
\(419\) 15.6525 0.764673 0.382337 0.924023i \(-0.375119\pi\)
0.382337 + 0.924023i \(0.375119\pi\)
\(420\) 0 0
\(421\) −20.0000 −0.974740 −0.487370 0.873195i \(-0.662044\pi\)
−0.487370 + 0.873195i \(0.662044\pi\)
\(422\) 0 0
\(423\) 17.8885 0.869771
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 44.7214 2.16422
\(428\) 0 0
\(429\) −20.0000 −0.965609
\(430\) 0 0
\(431\) −4.47214 −0.215415 −0.107708 0.994183i \(-0.534351\pi\)
−0.107708 + 0.994183i \(0.534351\pi\)
\(432\) 0 0
\(433\) −1.00000 −0.0480569 −0.0240285 0.999711i \(-0.507649\pi\)
−0.0240285 + 0.999711i \(0.507649\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 30.0000 1.43509
\(438\) 0 0
\(439\) −35.7771 −1.70755 −0.853774 0.520644i \(-0.825692\pi\)
−0.853774 + 0.520644i \(0.825692\pi\)
\(440\) 0 0
\(441\) 26.0000 1.23810
\(442\) 0 0
\(443\) −38.0132 −1.80606 −0.903030 0.429578i \(-0.858662\pi\)
−0.903030 + 0.429578i \(0.858662\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 35.7771 1.69220
\(448\) 0 0
\(449\) −19.0000 −0.896665 −0.448333 0.893867i \(-0.647982\pi\)
−0.448333 + 0.893867i \(0.647982\pi\)
\(450\) 0 0
\(451\) −11.1803 −0.526462
\(452\) 0 0
\(453\) −30.0000 −1.40952
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 7.00000 0.327446 0.163723 0.986506i \(-0.447650\pi\)
0.163723 + 0.986506i \(0.447650\pi\)
\(458\) 0 0
\(459\) −15.6525 −0.730595
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) −26.8328 −1.24703 −0.623513 0.781813i \(-0.714295\pi\)
−0.623513 + 0.781813i \(0.714295\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −17.8885 −0.827783 −0.413892 0.910326i \(-0.635831\pi\)
−0.413892 + 0.910326i \(0.635831\pi\)
\(468\) 0 0
\(469\) 10.0000 0.461757
\(470\) 0 0
\(471\) 40.2492 1.85459
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 12.0000 0.549442
\(478\) 0 0
\(479\) 13.4164 0.613011 0.306506 0.951869i \(-0.400840\pi\)
0.306506 + 0.951869i \(0.400840\pi\)
\(480\) 0 0
\(481\) 8.00000 0.364769
\(482\) 0 0
\(483\) −44.7214 −2.03489
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −4.47214 −0.202652 −0.101326 0.994853i \(-0.532308\pi\)
−0.101326 + 0.994853i \(0.532308\pi\)
\(488\) 0 0
\(489\) −5.00000 −0.226108
\(490\) 0 0
\(491\) 35.7771 1.61460 0.807299 0.590143i \(-0.200929\pi\)
0.807299 + 0.590143i \(0.200929\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 40.0000 1.79425
\(498\) 0 0
\(499\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(500\) 0 0
\(501\) −20.0000 −0.893534
\(502\) 0 0
\(503\) −26.8328 −1.19642 −0.598208 0.801341i \(-0.704120\pi\)
−0.598208 + 0.801341i \(0.704120\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 6.70820 0.297922
\(508\) 0 0
\(509\) −10.0000 −0.443242 −0.221621 0.975133i \(-0.571135\pi\)
−0.221621 + 0.975133i \(0.571135\pi\)
\(510\) 0 0
\(511\) −40.2492 −1.78052
\(512\) 0 0
\(513\) −15.0000 −0.662266
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −20.0000 −0.879599
\(518\) 0 0
\(519\) 35.7771 1.57044
\(520\) 0 0
\(521\) 13.0000 0.569540 0.284770 0.958596i \(-0.408083\pi\)
0.284770 + 0.958596i \(0.408083\pi\)
\(522\) 0 0
\(523\) −6.70820 −0.293329 −0.146665 0.989186i \(-0.546854\pi\)
−0.146665 + 0.989186i \(0.546854\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 31.3050 1.36367
\(528\) 0 0
\(529\) −3.00000 −0.130435
\(530\) 0 0
\(531\) −17.8885 −0.776297
\(532\) 0 0
\(533\) 20.0000 0.866296
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −5.00000 −0.215766
\(538\) 0 0
\(539\) −29.0689 −1.25209
\(540\) 0 0
\(541\) −8.00000 −0.343947 −0.171973 0.985102i \(-0.555014\pi\)
−0.171973 + 0.985102i \(0.555014\pi\)
\(542\) 0 0
\(543\) −4.47214 −0.191918
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 20.1246 0.860466 0.430233 0.902718i \(-0.358431\pi\)
0.430233 + 0.902718i \(0.358431\pi\)
\(548\) 0 0
\(549\) −20.0000 −0.853579
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 20.0000 0.850487
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −28.0000 −1.18640 −0.593199 0.805056i \(-0.702135\pi\)
−0.593199 + 0.805056i \(0.702135\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −35.0000 −1.47770
\(562\) 0 0
\(563\) 44.7214 1.88478 0.942390 0.334515i \(-0.108573\pi\)
0.942390 + 0.334515i \(0.108573\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 49.1935 2.06593
\(568\) 0 0
\(569\) 1.00000 0.0419222 0.0209611 0.999780i \(-0.493327\pi\)
0.0209611 + 0.999780i \(0.493327\pi\)
\(570\) 0 0
\(571\) 17.8885 0.748612 0.374306 0.927305i \(-0.377881\pi\)
0.374306 + 0.927305i \(0.377881\pi\)
\(572\) 0 0
\(573\) 30.0000 1.25327
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −43.0000 −1.79011 −0.895057 0.445952i \(-0.852865\pi\)
−0.895057 + 0.445952i \(0.852865\pi\)
\(578\) 0 0
\(579\) −20.1246 −0.836350
\(580\) 0 0
\(581\) 50.0000 2.07435
\(582\) 0 0
\(583\) −13.4164 −0.555651
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −20.1246 −0.830632 −0.415316 0.909677i \(-0.636329\pi\)
−0.415316 + 0.909677i \(0.636329\pi\)
\(588\) 0 0
\(589\) 30.0000 1.23613
\(590\) 0 0
\(591\) −40.2492 −1.65563
\(592\) 0 0
\(593\) 9.00000 0.369586 0.184793 0.982777i \(-0.440839\pi\)
0.184793 + 0.982777i \(0.440839\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 20.0000 0.818546
\(598\) 0 0
\(599\) −4.47214 −0.182727 −0.0913633 0.995818i \(-0.529122\pi\)
−0.0913633 + 0.995818i \(0.529122\pi\)
\(600\) 0 0
\(601\) −25.0000 −1.01977 −0.509886 0.860242i \(-0.670312\pi\)
−0.509886 + 0.860242i \(0.670312\pi\)
\(602\) 0 0
\(603\) −4.47214 −0.182119
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −17.8885 −0.726074 −0.363037 0.931775i \(-0.618260\pi\)
−0.363037 + 0.931775i \(0.618260\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 35.7771 1.44739
\(612\) 0 0
\(613\) −26.0000 −1.05013 −0.525065 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 0.0805170 0.0402585 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) 0 0
\(619\) −17.8885 −0.719001 −0.359501 0.933145i \(-0.617053\pi\)
−0.359501 + 0.933145i \(0.617053\pi\)
\(620\) 0 0
\(621\) −10.0000 −0.401286
\(622\) 0 0
\(623\) 22.3607 0.895862
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −33.5410 −1.33950
\(628\) 0 0
\(629\) 14.0000 0.558217
\(630\) 0 0
\(631\) −13.4164 −0.534099 −0.267049 0.963683i \(-0.586049\pi\)
−0.267049 + 0.963683i \(0.586049\pi\)
\(632\) 0 0
\(633\) 45.0000 1.78859
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 52.0000 2.06032
\(638\) 0 0
\(639\) −17.8885 −0.707660
\(640\) 0 0
\(641\) 10.0000 0.394976 0.197488 0.980305i \(-0.436722\pi\)
0.197488 + 0.980305i \(0.436722\pi\)
\(642\) 0 0
\(643\) −17.8885 −0.705455 −0.352728 0.935726i \(-0.614746\pi\)
−0.352728 + 0.935726i \(0.614746\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.94427 −0.351636 −0.175818 0.984423i \(-0.556257\pi\)
−0.175818 + 0.984423i \(0.556257\pi\)
\(648\) 0 0
\(649\) 20.0000 0.785069
\(650\) 0 0
\(651\) −44.7214 −1.75277
\(652\) 0 0
\(653\) −34.0000 −1.33052 −0.665261 0.746611i \(-0.731680\pi\)
−0.665261 + 0.746611i \(0.731680\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 18.0000 0.702247
\(658\) 0 0
\(659\) −6.70820 −0.261315 −0.130657 0.991428i \(-0.541709\pi\)
−0.130657 + 0.991428i \(0.541709\pi\)
\(660\) 0 0
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) 0 0
\(663\) 62.6099 2.43157
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 60.0000 2.31973
\(670\) 0 0
\(671\) 22.3607 0.863224
\(672\) 0 0
\(673\) −26.0000 −1.00223 −0.501113 0.865382i \(-0.667076\pi\)
−0.501113 + 0.865382i \(0.667076\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 32.0000 1.22986 0.614930 0.788582i \(-0.289184\pi\)
0.614930 + 0.788582i \(0.289184\pi\)
\(678\) 0 0
\(679\) 8.94427 0.343250
\(680\) 0 0
\(681\) −40.0000 −1.53280
\(682\) 0 0
\(683\) 11.1803 0.427804 0.213902 0.976855i \(-0.431383\pi\)
0.213902 + 0.976855i \(0.431383\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −44.7214 −1.70623
\(688\) 0 0
\(689\) 24.0000 0.914327
\(690\) 0 0
\(691\) −38.0132 −1.44609 −0.723044 0.690802i \(-0.757258\pi\)
−0.723044 + 0.690802i \(0.757258\pi\)
\(692\) 0 0
\(693\) 20.0000 0.759737
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 35.0000 1.32572
\(698\) 0 0
\(699\) 58.1378 2.19897
\(700\) 0 0
\(701\) 20.0000 0.755390 0.377695 0.925930i \(-0.376717\pi\)
0.377695 + 0.925930i \(0.376717\pi\)
\(702\) 0 0
\(703\) 13.4164 0.506009
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −8.94427 −0.336384
\(708\) 0 0
\(709\) −20.0000 −0.751116 −0.375558 0.926799i \(-0.622549\pi\)
−0.375558 + 0.926799i \(0.622549\pi\)
\(710\) 0 0
\(711\) −8.94427 −0.335436
\(712\) 0 0
\(713\) 20.0000 0.749006
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 40.0000 1.49383
\(718\) 0 0
\(719\) 4.47214 0.166783 0.0833913 0.996517i \(-0.473425\pi\)
0.0833913 + 0.996517i \(0.473425\pi\)
\(720\) 0 0
\(721\) −40.0000 −1.48968
\(722\) 0 0
\(723\) 11.1803 0.415801
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) −7.00000 −0.259259
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −44.0000 −1.62518 −0.812589 0.582838i \(-0.801942\pi\)
−0.812589 + 0.582838i \(0.801942\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 5.00000 0.184177
\(738\) 0 0
\(739\) 35.7771 1.31608 0.658041 0.752982i \(-0.271385\pi\)
0.658041 + 0.752982i \(0.271385\pi\)
\(740\) 0 0
\(741\) 60.0000 2.20416
\(742\) 0 0
\(743\) −31.3050 −1.14847 −0.574234 0.818691i \(-0.694700\pi\)
−0.574234 + 0.818691i \(0.694700\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −22.3607 −0.818134
\(748\) 0 0
\(749\) −10.0000 −0.365392
\(750\) 0 0
\(751\) 53.6656 1.95829 0.979143 0.203171i \(-0.0651246\pi\)
0.979143 + 0.203171i \(0.0651246\pi\)
\(752\) 0 0
\(753\) 25.0000 0.911051
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 8.00000 0.290765 0.145382 0.989376i \(-0.453559\pi\)
0.145382 + 0.989376i \(0.453559\pi\)
\(758\) 0 0
\(759\) −22.3607 −0.811641
\(760\) 0 0
\(761\) −43.0000 −1.55875 −0.779374 0.626559i \(-0.784463\pi\)
−0.779374 + 0.626559i \(0.784463\pi\)
\(762\) 0 0
\(763\) 26.8328 0.971413
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −35.7771 −1.29184
\(768\) 0 0
\(769\) −15.0000 −0.540914 −0.270457 0.962732i \(-0.587175\pi\)
−0.270457 + 0.962732i \(0.587175\pi\)
\(770\) 0 0
\(771\) 4.47214 0.161060
\(772\) 0 0
\(773\) 24.0000 0.863220 0.431610 0.902060i \(-0.357946\pi\)
0.431610 + 0.902060i \(0.357946\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −20.0000 −0.717496
\(778\) 0 0
\(779\) 33.5410 1.20173
\(780\) 0 0
\(781\) 20.0000 0.715656
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(788\) 0 0
\(789\) 50.0000 1.78005
\(790\) 0 0
\(791\) −4.47214 −0.159011
\(792\) 0 0
\(793\) −40.0000 −1.42044
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 18.0000 0.637593 0.318796 0.947823i \(-0.396721\pi\)
0.318796 + 0.947823i \(0.396721\pi\)
\(798\) 0 0
\(799\) 62.6099 2.21498
\(800\) 0 0
\(801\) −10.0000 −0.353333
\(802\) 0 0
\(803\) −20.1246 −0.710182
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −53.6656 −1.88912
\(808\) 0 0
\(809\) −30.0000 −1.05474 −0.527372 0.849635i \(-0.676823\pi\)
−0.527372 + 0.849635i \(0.676823\pi\)
\(810\) 0 0
\(811\) 17.8885 0.628152 0.314076 0.949398i \(-0.398305\pi\)
0.314076 + 0.949398i \(0.398305\pi\)
\(812\) 0 0
\(813\) −30.0000 −1.05215
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) −35.7771 −1.25015
\(820\) 0 0
\(821\) −50.0000 −1.74501 −0.872506 0.488603i \(-0.837507\pi\)
−0.872506 + 0.488603i \(0.837507\pi\)
\(822\) 0 0
\(823\) −26.8328 −0.935333 −0.467667 0.883905i \(-0.654905\pi\)
−0.467667 + 0.883905i \(0.654905\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 51.4296 1.78838 0.894191 0.447687i \(-0.147752\pi\)
0.894191 + 0.447687i \(0.147752\pi\)
\(828\) 0 0
\(829\) −4.00000 −0.138926 −0.0694629 0.997585i \(-0.522129\pi\)
−0.0694629 + 0.997585i \(0.522129\pi\)
\(830\) 0 0
\(831\) 17.8885 0.620547
\(832\) 0 0
\(833\) 91.0000 3.15296
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −10.0000 −0.345651
\(838\) 0 0
\(839\) −17.8885 −0.617581 −0.308791 0.951130i \(-0.599924\pi\)
−0.308791 + 0.951130i \(0.599924\pi\)
\(840\) 0 0
\(841\) −29.0000 −1.00000
\(842\) 0 0
\(843\) 67.0820 2.31043
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 26.8328 0.921986
\(848\) 0 0
\(849\) 15.0000 0.514799
\(850\) 0 0
\(851\) 8.94427 0.306606
\(852\) 0 0
\(853\) 34.0000 1.16414 0.582069 0.813139i \(-0.302243\pi\)
0.582069 + 0.813139i \(0.302243\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 3.00000 0.102478 0.0512390 0.998686i \(-0.483683\pi\)
0.0512390 + 0.998686i \(0.483683\pi\)
\(858\) 0 0
\(859\) 33.5410 1.14440 0.572202 0.820112i \(-0.306089\pi\)
0.572202 + 0.820112i \(0.306089\pi\)
\(860\) 0 0
\(861\) −50.0000 −1.70400
\(862\) 0 0
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 71.5542 2.43011
\(868\) 0 0
\(869\) 10.0000 0.339227
\(870\) 0 0
\(871\) −8.94427 −0.303065
\(872\) 0 0
\(873\) −4.00000 −0.135379
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 28.0000 0.945493 0.472746 0.881199i \(-0.343263\pi\)
0.472746 + 0.881199i \(0.343263\pi\)
\(878\) 0 0
\(879\) 31.3050 1.05589
\(880\) 0 0
\(881\) 30.0000 1.01073 0.505363 0.862907i \(-0.331359\pi\)
0.505363 + 0.862907i \(0.331359\pi\)
\(882\) 0 0
\(883\) 2.23607 0.0752497 0.0376248 0.999292i \(-0.488021\pi\)
0.0376248 + 0.999292i \(0.488021\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 8.94427 0.300319 0.150160 0.988662i \(-0.452021\pi\)
0.150160 + 0.988662i \(0.452021\pi\)
\(888\) 0 0
\(889\) 20.0000 0.670778
\(890\) 0 0
\(891\) 24.5967 0.824022
\(892\) 0 0
\(893\) 60.0000 2.00782
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 40.0000 1.33556
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 42.0000 1.39922
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −53.6656 −1.78194 −0.890969 0.454064i \(-0.849974\pi\)
−0.890969 + 0.454064i \(0.849974\pi\)
\(908\) 0 0
\(909\) 4.00000 0.132672
\(910\) 0 0
\(911\) 44.7214 1.48168 0.740842 0.671679i \(-0.234427\pi\)
0.740842 + 0.671679i \(0.234427\pi\)
\(912\) 0 0
\(913\) 25.0000 0.827379
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 80.0000 2.64183
\(918\) 0 0
\(919\) 13.4164 0.442566 0.221283 0.975210i \(-0.428975\pi\)
0.221283 + 0.975210i \(0.428975\pi\)
\(920\) 0 0
\(921\) −35.0000 −1.15329
\(922\) 0 0
\(923\) −35.7771 −1.17762
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 17.8885 0.587537
\(928\) 0 0
\(929\) 14.0000 0.459325 0.229663 0.973270i \(-0.426238\pi\)
0.229663 + 0.973270i \(0.426238\pi\)
\(930\) 0 0
\(931\) 87.2067 2.85808
\(932\) 0 0
\(933\) −50.0000 −1.63693
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 17.0000 0.555366 0.277683 0.960673i \(-0.410434\pi\)
0.277683 + 0.960673i \(0.410434\pi\)
\(938\) 0 0
\(939\) 13.4164 0.437828
\(940\) 0 0
\(941\) 28.0000 0.912774 0.456387 0.889781i \(-0.349143\pi\)
0.456387 + 0.889781i \(0.349143\pi\)
\(942\) 0 0
\(943\) 22.3607 0.728164
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 26.8328 0.871949 0.435975 0.899959i \(-0.356404\pi\)
0.435975 + 0.899959i \(0.356404\pi\)
\(948\) 0 0
\(949\) 36.0000 1.16861
\(950\) 0 0
\(951\) −26.8328 −0.870114
\(952\) 0 0
\(953\) −9.00000 −0.291539 −0.145769 0.989319i \(-0.546566\pi\)
−0.145769 + 0.989319i \(0.546566\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −13.4164 −0.433238
\(960\) 0 0
\(961\) −11.0000 −0.354839
\(962\) 0 0
\(963\) 4.47214 0.144113
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 53.6656 1.72577 0.862885 0.505400i \(-0.168655\pi\)
0.862885 + 0.505400i \(0.168655\pi\)
\(968\) 0 0
\(969\) 105.000 3.37309
\(970\) 0 0
\(971\) −55.9017 −1.79397 −0.896985 0.442060i \(-0.854248\pi\)
−0.896985 + 0.442060i \(0.854248\pi\)
\(972\) 0 0
\(973\) 10.0000 0.320585
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 3.00000 0.0959785 0.0479893 0.998848i \(-0.484719\pi\)
0.0479893 + 0.998848i \(0.484719\pi\)
\(978\) 0 0
\(979\) 11.1803 0.357325
\(980\) 0 0
\(981\) −12.0000 −0.383131
\(982\) 0 0
\(983\) 4.47214 0.142639 0.0713195 0.997454i \(-0.477279\pi\)
0.0713195 + 0.997454i \(0.477279\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) −89.4427 −2.84699
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 13.4164 0.426186 0.213093 0.977032i \(-0.431646\pi\)
0.213093 + 0.977032i \(0.431646\pi\)
\(992\) 0 0
\(993\) −25.0000 −0.793351
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −52.0000 −1.64686 −0.823428 0.567420i \(-0.807941\pi\)
−0.823428 + 0.567420i \(0.807941\pi\)
\(998\) 0 0
\(999\) −4.47214 −0.141492
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 1600.2.a.bb.1.2 2
4.3 odd 2 inner 1600.2.a.bb.1.1 2
5.2 odd 4 1600.2.c.o.449.1 4
5.3 odd 4 1600.2.c.o.449.3 4
5.4 even 2 1600.2.a.ba.1.1 2
8.3 odd 2 800.2.a.k.1.2 yes 2
8.5 even 2 800.2.a.k.1.1 2
20.3 even 4 1600.2.c.o.449.2 4
20.7 even 4 1600.2.c.o.449.4 4
20.19 odd 2 1600.2.a.ba.1.2 2
24.5 odd 2 7200.2.a.cf.1.1 2
24.11 even 2 7200.2.a.cf.1.2 2
40.3 even 4 800.2.c.g.449.3 4
40.13 odd 4 800.2.c.g.449.2 4
40.19 odd 2 800.2.a.l.1.1 yes 2
40.27 even 4 800.2.c.g.449.1 4
40.29 even 2 800.2.a.l.1.2 yes 2
40.37 odd 4 800.2.c.g.449.4 4
120.29 odd 2 7200.2.a.cn.1.2 2
120.53 even 4 7200.2.f.bg.6049.3 4
120.59 even 2 7200.2.a.cn.1.1 2
120.77 even 4 7200.2.f.bg.6049.1 4
120.83 odd 4 7200.2.f.bg.6049.2 4
120.107 odd 4 7200.2.f.bg.6049.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
800.2.a.k.1.1 2 8.5 even 2
800.2.a.k.1.2 yes 2 8.3 odd 2
800.2.a.l.1.1 yes 2 40.19 odd 2
800.2.a.l.1.2 yes 2 40.29 even 2
800.2.c.g.449.1 4 40.27 even 4
800.2.c.g.449.2 4 40.13 odd 4
800.2.c.g.449.3 4 40.3 even 4
800.2.c.g.449.4 4 40.37 odd 4
1600.2.a.ba.1.1 2 5.4 even 2
1600.2.a.ba.1.2 2 20.19 odd 2
1600.2.a.bb.1.1 2 4.3 odd 2 inner
1600.2.a.bb.1.2 2 1.1 even 1 trivial
1600.2.c.o.449.1 4 5.2 odd 4
1600.2.c.o.449.2 4 20.3 even 4
1600.2.c.o.449.3 4 5.3 odd 4
1600.2.c.o.449.4 4 20.7 even 4
7200.2.a.cf.1.1 2 24.5 odd 2
7200.2.a.cf.1.2 2 24.11 even 2
7200.2.a.cn.1.1 2 120.59 even 2
7200.2.a.cn.1.2 2 120.29 odd 2
7200.2.f.bg.6049.1 4 120.77 even 4
7200.2.f.bg.6049.2 4 120.83 odd 4
7200.2.f.bg.6049.3 4 120.53 even 4
7200.2.f.bg.6049.4 4 120.107 odd 4