Properties

Label 7600.2.a.bi.1.2
Level $7600$
Weight $2$
Character 7600.1
Self dual yes
Analytic conductor $60.686$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.6863055362\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.568.1
Defining polynomial: \(x^{3} - x^{2} - 6 x - 2\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-0.363328\) of defining polynomial
Character \(\chi\) \(=\) 7600.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.36333 q^{3} -0.636672 q^{7} -1.14134 q^{9} +O(q^{10})\) \(q-1.36333 q^{3} -0.636672 q^{7} -1.14134 q^{9} -3.50466 q^{11} -0.141336 q^{13} +2.14134 q^{17} -1.00000 q^{19} +0.867993 q^{21} -4.91934 q^{23} +5.64600 q^{27} +7.15066 q^{29} +7.78734 q^{31} +4.77801 q^{33} +3.27334 q^{37} +0.192688 q^{39} -4.23132 q^{41} -2.49534 q^{43} +10.2827 q^{47} -6.59465 q^{49} -2.91934 q^{51} +8.14134 q^{53} +1.36333 q^{57} +5.64600 q^{59} -6.49534 q^{61} +0.726656 q^{63} -8.37266 q^{67} +6.70668 q^{69} +8.95798 q^{71} -3.69735 q^{73} +2.23132 q^{77} +4.17997 q^{79} -4.27334 q^{81} +9.00933 q^{83} -9.74870 q^{87} -6.77801 q^{89} +0.0899847 q^{91} -10.6167 q^{93} +14.5653 q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 2q^{3} - 4q^{7} + 5q^{9} + O(q^{10}) \) \( 3q - 2q^{3} - 4q^{7} + 5q^{9} + 8q^{13} - 2q^{17} - 3q^{19} - 10q^{21} - 2q^{27} - 8q^{29} - 4q^{31} + 8q^{33} + 14q^{37} - 10q^{39} + 2q^{41} - 18q^{43} + 14q^{47} - 3q^{49} + 6q^{51} + 16q^{53} + 2q^{57} - 2q^{59} - 30q^{61} - 2q^{63} - 2q^{67} - 22q^{69} + 8q^{71} + 10q^{73} - 8q^{77} - 17q^{81} + 6q^{83} - 6q^{87} - 14q^{89} - 6q^{91} + 4q^{93} + 10q^{97} + 12q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.36333 −0.787118 −0.393559 0.919299i \(-0.628756\pi\)
−0.393559 + 0.919299i \(0.628756\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −0.636672 −0.240639 −0.120320 0.992735i \(-0.538392\pi\)
−0.120320 + 0.992735i \(0.538392\pi\)
\(8\) 0 0
\(9\) −1.14134 −0.380445
\(10\) 0 0
\(11\) −3.50466 −1.05670 −0.528348 0.849028i \(-0.677188\pi\)
−0.528348 + 0.849028i \(0.677188\pi\)
\(12\) 0 0
\(13\) −0.141336 −0.0391996 −0.0195998 0.999808i \(-0.506239\pi\)
−0.0195998 + 0.999808i \(0.506239\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.14134 0.519350 0.259675 0.965696i \(-0.416385\pi\)
0.259675 + 0.965696i \(0.416385\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0.867993 0.189412
\(22\) 0 0
\(23\) −4.91934 −1.02575 −0.512877 0.858462i \(-0.671420\pi\)
−0.512877 + 0.858462i \(0.671420\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.64600 1.08657
\(28\) 0 0
\(29\) 7.15066 1.32785 0.663923 0.747801i \(-0.268890\pi\)
0.663923 + 0.747801i \(0.268890\pi\)
\(30\) 0 0
\(31\) 7.78734 1.39865 0.699323 0.714805i \(-0.253485\pi\)
0.699323 + 0.714805i \(0.253485\pi\)
\(32\) 0 0
\(33\) 4.77801 0.831744
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.27334 0.538134 0.269067 0.963121i \(-0.413285\pi\)
0.269067 + 0.963121i \(0.413285\pi\)
\(38\) 0 0
\(39\) 0.192688 0.0308547
\(40\) 0 0
\(41\) −4.23132 −0.660821 −0.330411 0.943837i \(-0.607187\pi\)
−0.330411 + 0.943837i \(0.607187\pi\)
\(42\) 0 0
\(43\) −2.49534 −0.380535 −0.190268 0.981732i \(-0.560936\pi\)
−0.190268 + 0.981732i \(0.560936\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 10.2827 1.49988 0.749941 0.661505i \(-0.230082\pi\)
0.749941 + 0.661505i \(0.230082\pi\)
\(48\) 0 0
\(49\) −6.59465 −0.942093
\(50\) 0 0
\(51\) −2.91934 −0.408790
\(52\) 0 0
\(53\) 8.14134 1.11830 0.559149 0.829067i \(-0.311128\pi\)
0.559149 + 0.829067i \(0.311128\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.36333 0.180577
\(58\) 0 0
\(59\) 5.64600 0.735047 0.367523 0.930014i \(-0.380206\pi\)
0.367523 + 0.930014i \(0.380206\pi\)
\(60\) 0 0
\(61\) −6.49534 −0.831643 −0.415821 0.909446i \(-0.636506\pi\)
−0.415821 + 0.909446i \(0.636506\pi\)
\(62\) 0 0
\(63\) 0.726656 0.0915501
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −8.37266 −1.02288 −0.511441 0.859318i \(-0.670888\pi\)
−0.511441 + 0.859318i \(0.670888\pi\)
\(68\) 0 0
\(69\) 6.70668 0.807389
\(70\) 0 0
\(71\) 8.95798 1.06312 0.531558 0.847022i \(-0.321607\pi\)
0.531558 + 0.847022i \(0.321607\pi\)
\(72\) 0 0
\(73\) −3.69735 −0.432742 −0.216371 0.976311i \(-0.569422\pi\)
−0.216371 + 0.976311i \(0.569422\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.23132 0.254283
\(78\) 0 0
\(79\) 4.17997 0.470283 0.235142 0.971961i \(-0.424445\pi\)
0.235142 + 0.971961i \(0.424445\pi\)
\(80\) 0 0
\(81\) −4.27334 −0.474816
\(82\) 0 0
\(83\) 9.00933 0.988902 0.494451 0.869205i \(-0.335369\pi\)
0.494451 + 0.869205i \(0.335369\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −9.74870 −1.04517
\(88\) 0 0
\(89\) −6.77801 −0.718467 −0.359234 0.933248i \(-0.616962\pi\)
−0.359234 + 0.933248i \(0.616962\pi\)
\(90\) 0 0
\(91\) 0.0899847 0.00943296
\(92\) 0 0
\(93\) −10.6167 −1.10090
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 14.5653 1.47889 0.739443 0.673219i \(-0.235089\pi\)
0.739443 + 0.673219i \(0.235089\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −16.6167 −1.65342 −0.826712 0.562626i \(-0.809791\pi\)
−0.826712 + 0.562626i \(0.809791\pi\)
\(102\) 0 0
\(103\) −9.06068 −0.892775 −0.446388 0.894840i \(-0.647290\pi\)
−0.446388 + 0.894840i \(0.647290\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.0899847 −0.00869915 −0.00434958 0.999991i \(-0.501385\pi\)
−0.00434958 + 0.999991i \(0.501385\pi\)
\(108\) 0 0
\(109\) −13.5946 −1.30213 −0.651066 0.759021i \(-0.725678\pi\)
−0.651066 + 0.759021i \(0.725678\pi\)
\(110\) 0 0
\(111\) −4.46264 −0.423575
\(112\) 0 0
\(113\) 11.5233 1.08402 0.542011 0.840371i \(-0.317663\pi\)
0.542011 + 0.840371i \(0.317663\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.161312 0.0149133
\(118\) 0 0
\(119\) −1.36333 −0.124976
\(120\) 0 0
\(121\) 1.28267 0.116607
\(122\) 0 0
\(123\) 5.76868 0.520144
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 3.29200 0.292118 0.146059 0.989276i \(-0.453341\pi\)
0.146059 + 0.989276i \(0.453341\pi\)
\(128\) 0 0
\(129\) 3.40196 0.299526
\(130\) 0 0
\(131\) −18.0187 −1.57430 −0.787149 0.616763i \(-0.788444\pi\)
−0.787149 + 0.616763i \(0.788444\pi\)
\(132\) 0 0
\(133\) 0.636672 0.0552064
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −14.4240 −1.23233 −0.616163 0.787619i \(-0.711314\pi\)
−0.616163 + 0.787619i \(0.711314\pi\)
\(138\) 0 0
\(139\) −15.4720 −1.31232 −0.656158 0.754624i \(-0.727819\pi\)
−0.656158 + 0.754624i \(0.727819\pi\)
\(140\) 0 0
\(141\) −14.0187 −1.18058
\(142\) 0 0
\(143\) 0.495336 0.0414220
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 8.99067 0.741538
\(148\) 0 0
\(149\) −17.1893 −1.40820 −0.704101 0.710100i \(-0.748650\pi\)
−0.704101 + 0.710100i \(0.748650\pi\)
\(150\) 0 0
\(151\) −3.29200 −0.267899 −0.133950 0.990988i \(-0.542766\pi\)
−0.133950 + 0.990988i \(0.542766\pi\)
\(152\) 0 0
\(153\) −2.44398 −0.197584
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 15.1893 1.21224 0.606119 0.795374i \(-0.292726\pi\)
0.606119 + 0.795374i \(0.292726\pi\)
\(158\) 0 0
\(159\) −11.0993 −0.880233
\(160\) 0 0
\(161\) 3.13201 0.246837
\(162\) 0 0
\(163\) 14.0700 1.10205 0.551024 0.834489i \(-0.314237\pi\)
0.551024 + 0.834489i \(0.314237\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 14.7967 1.14500 0.572500 0.819905i \(-0.305974\pi\)
0.572500 + 0.819905i \(0.305974\pi\)
\(168\) 0 0
\(169\) −12.9800 −0.998463
\(170\) 0 0
\(171\) 1.14134 0.0872802
\(172\) 0 0
\(173\) −17.2920 −1.31469 −0.657343 0.753591i \(-0.728320\pi\)
−0.657343 + 0.753591i \(0.728320\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −7.69735 −0.578568
\(178\) 0 0
\(179\) −17.7360 −1.32565 −0.662825 0.748774i \(-0.730643\pi\)
−0.662825 + 0.748774i \(0.730643\pi\)
\(180\) 0 0
\(181\) 6.17997 0.459354 0.229677 0.973267i \(-0.426233\pi\)
0.229677 + 0.973267i \(0.426233\pi\)
\(182\) 0 0
\(183\) 8.85527 0.654601
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −7.50466 −0.548795
\(188\) 0 0
\(189\) −3.59465 −0.261472
\(190\) 0 0
\(191\) −14.6367 −1.05907 −0.529536 0.848287i \(-0.677634\pi\)
−0.529536 + 0.848287i \(0.677634\pi\)
\(192\) 0 0
\(193\) 20.0187 1.44097 0.720487 0.693468i \(-0.243918\pi\)
0.720487 + 0.693468i \(0.243918\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −9.94865 −0.708812 −0.354406 0.935092i \(-0.615317\pi\)
−0.354406 + 0.935092i \(0.615317\pi\)
\(198\) 0 0
\(199\) −9.74870 −0.691067 −0.345534 0.938406i \(-0.612302\pi\)
−0.345534 + 0.938406i \(0.612302\pi\)
\(200\) 0 0
\(201\) 11.4147 0.805129
\(202\) 0 0
\(203\) −4.55263 −0.319532
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 5.61462 0.390243
\(208\) 0 0
\(209\) 3.50466 0.242423
\(210\) 0 0
\(211\) 20.7580 1.42904 0.714521 0.699614i \(-0.246645\pi\)
0.714521 + 0.699614i \(0.246645\pi\)
\(212\) 0 0
\(213\) −12.2127 −0.836798
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −4.95798 −0.336569
\(218\) 0 0
\(219\) 5.04070 0.340619
\(220\) 0 0
\(221\) −0.302648 −0.0203583
\(222\) 0 0
\(223\) 10.7267 0.718310 0.359155 0.933278i \(-0.383065\pi\)
0.359155 + 0.933278i \(0.383065\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −12.5526 −0.833147 −0.416574 0.909102i \(-0.636769\pi\)
−0.416574 + 0.909102i \(0.636769\pi\)
\(228\) 0 0
\(229\) 25.4720 1.68324 0.841618 0.540074i \(-0.181604\pi\)
0.841618 + 0.540074i \(0.181604\pi\)
\(230\) 0 0
\(231\) −3.04202 −0.200150
\(232\) 0 0
\(233\) −3.11203 −0.203876 −0.101938 0.994791i \(-0.532504\pi\)
−0.101938 + 0.994791i \(0.532504\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −5.69867 −0.370168
\(238\) 0 0
\(239\) 1.54330 0.0998276 0.0499138 0.998754i \(-0.484105\pi\)
0.0499138 + 0.998754i \(0.484105\pi\)
\(240\) 0 0
\(241\) 10.2827 0.662365 0.331183 0.943567i \(-0.392552\pi\)
0.331183 + 0.943567i \(0.392552\pi\)
\(242\) 0 0
\(243\) −11.1120 −0.712837
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.141336 0.00899300
\(248\) 0 0
\(249\) −12.2827 −0.778383
\(250\) 0 0
\(251\) 2.51399 0.158682 0.0793409 0.996848i \(-0.474718\pi\)
0.0793409 + 0.996848i \(0.474718\pi\)
\(252\) 0 0
\(253\) 17.2406 1.08391
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −24.7967 −1.54677 −0.773387 0.633934i \(-0.781439\pi\)
−0.773387 + 0.633934i \(0.781439\pi\)
\(258\) 0 0
\(259\) −2.08405 −0.129496
\(260\) 0 0
\(261\) −8.16131 −0.505173
\(262\) 0 0
\(263\) 22.5653 1.39144 0.695719 0.718314i \(-0.255086\pi\)
0.695719 + 0.718314i \(0.255086\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 9.24065 0.565519
\(268\) 0 0
\(269\) −26.5653 −1.61972 −0.809859 0.586625i \(-0.800456\pi\)
−0.809859 + 0.586625i \(0.800456\pi\)
\(270\) 0 0
\(271\) 24.9380 1.51488 0.757438 0.652907i \(-0.226451\pi\)
0.757438 + 0.652907i \(0.226451\pi\)
\(272\) 0 0
\(273\) −0.122679 −0.00742485
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 18.5467 1.11436 0.557181 0.830391i \(-0.311883\pi\)
0.557181 + 0.830391i \(0.311883\pi\)
\(278\) 0 0
\(279\) −8.88797 −0.532109
\(280\) 0 0
\(281\) 24.7967 1.47925 0.739623 0.673022i \(-0.235004\pi\)
0.739623 + 0.673022i \(0.235004\pi\)
\(282\) 0 0
\(283\) −13.5747 −0.806931 −0.403465 0.914995i \(-0.632194\pi\)
−0.403465 + 0.914995i \(0.632194\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.69396 0.159020
\(288\) 0 0
\(289\) −12.4147 −0.730275
\(290\) 0 0
\(291\) −19.8573 −1.16406
\(292\) 0 0
\(293\) −15.6133 −0.912139 −0.456070 0.889944i \(-0.650743\pi\)
−0.456070 + 0.889944i \(0.650743\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −19.7873 −1.14818
\(298\) 0 0
\(299\) 0.695281 0.0402091
\(300\) 0 0
\(301\) 1.58871 0.0915717
\(302\) 0 0
\(303\) 22.6540 1.30144
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −34.0187 −1.94155 −0.970774 0.239997i \(-0.922854\pi\)
−0.970774 + 0.239997i \(0.922854\pi\)
\(308\) 0 0
\(309\) 12.3527 0.702719
\(310\) 0 0
\(311\) −8.93800 −0.506828 −0.253414 0.967358i \(-0.581553\pi\)
−0.253414 + 0.967358i \(0.581553\pi\)
\(312\) 0 0
\(313\) −18.4240 −1.04139 −0.520693 0.853744i \(-0.674326\pi\)
−0.520693 + 0.853744i \(0.674326\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 33.5547 1.88462 0.942310 0.334742i \(-0.108649\pi\)
0.942310 + 0.334742i \(0.108649\pi\)
\(318\) 0 0
\(319\) −25.0607 −1.40313
\(320\) 0 0
\(321\) 0.122679 0.00684726
\(322\) 0 0
\(323\) −2.14134 −0.119147
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 18.5340 1.02493
\(328\) 0 0
\(329\) −6.54669 −0.360931
\(330\) 0 0
\(331\) −2.25130 −0.123742 −0.0618712 0.998084i \(-0.519707\pi\)
−0.0618712 + 0.998084i \(0.519707\pi\)
\(332\) 0 0
\(333\) −3.73599 −0.204731
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −21.3620 −1.16366 −0.581831 0.813309i \(-0.697664\pi\)
−0.581831 + 0.813309i \(0.697664\pi\)
\(338\) 0 0
\(339\) −15.7101 −0.853254
\(340\) 0 0
\(341\) −27.2920 −1.47794
\(342\) 0 0
\(343\) 8.65533 0.467344
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −11.5560 −0.620359 −0.310180 0.950678i \(-0.600389\pi\)
−0.310180 + 0.950678i \(0.600389\pi\)
\(348\) 0 0
\(349\) −17.1120 −0.915986 −0.457993 0.888956i \(-0.651432\pi\)
−0.457993 + 0.888956i \(0.651432\pi\)
\(350\) 0 0
\(351\) −0.797984 −0.0425932
\(352\) 0 0
\(353\) 11.6974 0.622587 0.311294 0.950314i \(-0.399238\pi\)
0.311294 + 0.950314i \(0.399238\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.85866 0.0983709
\(358\) 0 0
\(359\) 4.47536 0.236200 0.118100 0.993002i \(-0.462320\pi\)
0.118100 + 0.993002i \(0.462320\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −1.74870 −0.0917831
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −18.7453 −0.978497 −0.489249 0.872144i \(-0.662729\pi\)
−0.489249 + 0.872144i \(0.662729\pi\)
\(368\) 0 0
\(369\) 4.82936 0.251406
\(370\) 0 0
\(371\) −5.18336 −0.269107
\(372\) 0 0
\(373\) 1.69735 0.0878855 0.0439428 0.999034i \(-0.486008\pi\)
0.0439428 + 0.999034i \(0.486008\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.01065 −0.0520510
\(378\) 0 0
\(379\) −2.63667 −0.135437 −0.0677184 0.997704i \(-0.521572\pi\)
−0.0677184 + 0.997704i \(0.521572\pi\)
\(380\) 0 0
\(381\) −4.48808 −0.229931
\(382\) 0 0
\(383\) −12.4953 −0.638482 −0.319241 0.947674i \(-0.603428\pi\)
−0.319241 + 0.947674i \(0.603428\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 2.84802 0.144773
\(388\) 0 0
\(389\) −4.51399 −0.228869 −0.114434 0.993431i \(-0.536506\pi\)
−0.114434 + 0.993431i \(0.536506\pi\)
\(390\) 0 0
\(391\) −10.5340 −0.532726
\(392\) 0 0
\(393\) 24.5653 1.23916
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −35.6774 −1.79060 −0.895298 0.445468i \(-0.853037\pi\)
−0.895298 + 0.445468i \(0.853037\pi\)
\(398\) 0 0
\(399\) −0.867993 −0.0434540
\(400\) 0 0
\(401\) 15.3434 0.766210 0.383105 0.923705i \(-0.374855\pi\)
0.383105 + 0.923705i \(0.374855\pi\)
\(402\) 0 0
\(403\) −1.10063 −0.0548264
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −11.4720 −0.568644
\(408\) 0 0
\(409\) 29.3620 1.45186 0.725929 0.687770i \(-0.241410\pi\)
0.725929 + 0.687770i \(0.241410\pi\)
\(410\) 0 0
\(411\) 19.6647 0.969986
\(412\) 0 0
\(413\) −3.59465 −0.176881
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 21.0934 1.03295
\(418\) 0 0
\(419\) −25.1379 −1.22807 −0.614035 0.789279i \(-0.710454\pi\)
−0.614035 + 0.789279i \(0.710454\pi\)
\(420\) 0 0
\(421\) 14.5454 0.708898 0.354449 0.935075i \(-0.384668\pi\)
0.354449 + 0.935075i \(0.384668\pi\)
\(422\) 0 0
\(423\) −11.7360 −0.570623
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.13540 0.200126
\(428\) 0 0
\(429\) −0.675305 −0.0326040
\(430\) 0 0
\(431\) −19.4020 −0.934560 −0.467280 0.884109i \(-0.654766\pi\)
−0.467280 + 0.884109i \(0.654766\pi\)
\(432\) 0 0
\(433\) 5.50466 0.264537 0.132269 0.991214i \(-0.457774\pi\)
0.132269 + 0.991214i \(0.457774\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.91934 0.235324
\(438\) 0 0
\(439\) −12.2500 −0.584660 −0.292330 0.956318i \(-0.594430\pi\)
−0.292330 + 0.956318i \(0.594430\pi\)
\(440\) 0 0
\(441\) 7.52671 0.358415
\(442\) 0 0
\(443\) −31.6006 −1.50139 −0.750695 0.660649i \(-0.770281\pi\)
−0.750695 + 0.660649i \(0.770281\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 23.4347 1.10842
\(448\) 0 0
\(449\) −36.0187 −1.69983 −0.849913 0.526923i \(-0.823345\pi\)
−0.849913 + 0.526923i \(0.823345\pi\)
\(450\) 0 0
\(451\) 14.8294 0.698287
\(452\) 0 0
\(453\) 4.48808 0.210868
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 22.1413 1.03573 0.517864 0.855463i \(-0.326727\pi\)
0.517864 + 0.855463i \(0.326727\pi\)
\(458\) 0 0
\(459\) 12.0900 0.564312
\(460\) 0 0
\(461\) −2.31537 −0.107837 −0.0539187 0.998545i \(-0.517171\pi\)
−0.0539187 + 0.998545i \(0.517171\pi\)
\(462\) 0 0
\(463\) −15.8387 −0.736086 −0.368043 0.929809i \(-0.619972\pi\)
−0.368043 + 0.929809i \(0.619972\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −23.1379 −1.07070 −0.535348 0.844631i \(-0.679820\pi\)
−0.535348 + 0.844631i \(0.679820\pi\)
\(468\) 0 0
\(469\) 5.33063 0.246146
\(470\) 0 0
\(471\) −20.7080 −0.954174
\(472\) 0 0
\(473\) 8.74531 0.402110
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −9.29200 −0.425451
\(478\) 0 0
\(479\) 10.1214 0.462457 0.231228 0.972900i \(-0.425726\pi\)
0.231228 + 0.972900i \(0.425726\pi\)
\(480\) 0 0
\(481\) −0.462642 −0.0210946
\(482\) 0 0
\(483\) −4.26995 −0.194290
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −20.3854 −0.923750 −0.461875 0.886945i \(-0.652823\pi\)
−0.461875 + 0.886945i \(0.652823\pi\)
\(488\) 0 0
\(489\) −19.1820 −0.867442
\(490\) 0 0
\(491\) 7.78734 0.351438 0.175719 0.984440i \(-0.443775\pi\)
0.175719 + 0.984440i \(0.443775\pi\)
\(492\) 0 0
\(493\) 15.3120 0.689617
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −5.70329 −0.255828
\(498\) 0 0
\(499\) −4.31537 −0.193182 −0.0965912 0.995324i \(-0.530794\pi\)
−0.0965912 + 0.995324i \(0.530794\pi\)
\(500\) 0 0
\(501\) −20.1727 −0.901250
\(502\) 0 0
\(503\) −18.5526 −0.827221 −0.413610 0.910454i \(-0.635732\pi\)
−0.413610 + 0.910454i \(0.635732\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 17.6960 0.785908
\(508\) 0 0
\(509\) −7.73599 −0.342892 −0.171446 0.985194i \(-0.554844\pi\)
−0.171446 + 0.985194i \(0.554844\pi\)
\(510\) 0 0
\(511\) 2.35400 0.104135
\(512\) 0 0
\(513\) −5.64600 −0.249277
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −36.0373 −1.58492
\(518\) 0 0
\(519\) 23.5747 1.03481
\(520\) 0 0
\(521\) 15.2080 0.666273 0.333136 0.942879i \(-0.391893\pi\)
0.333136 + 0.942879i \(0.391893\pi\)
\(522\) 0 0
\(523\) 18.2113 0.796327 0.398163 0.917315i \(-0.369648\pi\)
0.398163 + 0.917315i \(0.369648\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 16.6753 0.726388
\(528\) 0 0
\(529\) 1.19995 0.0521715
\(530\) 0 0
\(531\) −6.44398 −0.279645
\(532\) 0 0
\(533\) 0.598038 0.0259039
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 24.1800 1.04344
\(538\) 0 0
\(539\) 23.1120 0.995506
\(540\) 0 0
\(541\) 16.5140 0.709992 0.354996 0.934868i \(-0.384482\pi\)
0.354996 + 0.934868i \(0.384482\pi\)
\(542\) 0 0
\(543\) −8.42533 −0.361565
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −16.2827 −0.696197 −0.348098 0.937458i \(-0.613172\pi\)
−0.348098 + 0.937458i \(0.613172\pi\)
\(548\) 0 0
\(549\) 7.41336 0.316395
\(550\) 0 0
\(551\) −7.15066 −0.304629
\(552\) 0 0
\(553\) −2.66127 −0.113169
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 37.4533 1.58695 0.793474 0.608604i \(-0.208270\pi\)
0.793474 + 0.608604i \(0.208270\pi\)
\(558\) 0 0
\(559\) 0.352681 0.0149168
\(560\) 0 0
\(561\) 10.2313 0.431967
\(562\) 0 0
\(563\) 29.1307 1.22771 0.613856 0.789418i \(-0.289618\pi\)
0.613856 + 0.789418i \(0.289618\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 2.72072 0.114259
\(568\) 0 0
\(569\) 14.8480 0.622461 0.311231 0.950334i \(-0.399259\pi\)
0.311231 + 0.950334i \(0.399259\pi\)
\(570\) 0 0
\(571\) −41.9087 −1.75382 −0.876912 0.480651i \(-0.840401\pi\)
−0.876912 + 0.480651i \(0.840401\pi\)
\(572\) 0 0
\(573\) 19.9546 0.833615
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 16.4427 0.684517 0.342259 0.939606i \(-0.388808\pi\)
0.342259 + 0.939606i \(0.388808\pi\)
\(578\) 0 0
\(579\) −27.2920 −1.13422
\(580\) 0 0
\(581\) −5.73599 −0.237969
\(582\) 0 0
\(583\) −28.5327 −1.18170
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 42.5327 1.75551 0.877755 0.479109i \(-0.159040\pi\)
0.877755 + 0.479109i \(0.159040\pi\)
\(588\) 0 0
\(589\) −7.78734 −0.320872
\(590\) 0 0
\(591\) 13.5633 0.557919
\(592\) 0 0
\(593\) 3.92273 0.161087 0.0805437 0.996751i \(-0.474334\pi\)
0.0805437 + 0.996751i \(0.474334\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 13.2907 0.543951
\(598\) 0 0
\(599\) 10.7594 0.439615 0.219808 0.975543i \(-0.429457\pi\)
0.219808 + 0.975543i \(0.429457\pi\)
\(600\) 0 0
\(601\) 25.2220 1.02883 0.514413 0.857542i \(-0.328010\pi\)
0.514413 + 0.857542i \(0.328010\pi\)
\(602\) 0 0
\(603\) 9.55602 0.389151
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −39.2920 −1.59481 −0.797407 0.603442i \(-0.793795\pi\)
−0.797407 + 0.603442i \(0.793795\pi\)
\(608\) 0 0
\(609\) 6.20672 0.251509
\(610\) 0 0
\(611\) −1.45331 −0.0587947
\(612\) 0 0
\(613\) 9.80599 0.396060 0.198030 0.980196i \(-0.436546\pi\)
0.198030 + 0.980196i \(0.436546\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −35.0093 −1.40942 −0.704711 0.709494i \(-0.748923\pi\)
−0.704711 + 0.709494i \(0.748923\pi\)
\(618\) 0 0
\(619\) −13.4206 −0.539420 −0.269710 0.962942i \(-0.586928\pi\)
−0.269710 + 0.962942i \(0.586928\pi\)
\(620\) 0 0
\(621\) −27.7746 −1.11456
\(622\) 0 0
\(623\) 4.31537 0.172891
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −4.77801 −0.190815
\(628\) 0 0
\(629\) 7.00933 0.279480
\(630\) 0 0
\(631\) −40.5254 −1.61329 −0.806645 0.591036i \(-0.798719\pi\)
−0.806645 + 0.591036i \(0.798719\pi\)
\(632\) 0 0
\(633\) −28.3000 −1.12482
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0.932062 0.0369296
\(638\) 0 0
\(639\) −10.2241 −0.404458
\(640\) 0 0
\(641\) −26.0700 −1.02970 −0.514852 0.857279i \(-0.672153\pi\)
−0.514852 + 0.857279i \(0.672153\pi\)
\(642\) 0 0
\(643\) −30.1400 −1.18861 −0.594303 0.804241i \(-0.702572\pi\)
−0.594303 + 0.804241i \(0.702572\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 20.1086 0.790552 0.395276 0.918562i \(-0.370649\pi\)
0.395276 + 0.918562i \(0.370649\pi\)
\(648\) 0 0
\(649\) −19.7873 −0.776721
\(650\) 0 0
\(651\) 6.75935 0.264920
\(652\) 0 0
\(653\) −28.0373 −1.09718 −0.548592 0.836090i \(-0.684836\pi\)
−0.548592 + 0.836090i \(0.684836\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 4.21992 0.164635
\(658\) 0 0
\(659\) −4.90069 −0.190904 −0.0954518 0.995434i \(-0.530430\pi\)
−0.0954518 + 0.995434i \(0.530430\pi\)
\(660\) 0 0
\(661\) −8.03863 −0.312667 −0.156333 0.987704i \(-0.549967\pi\)
−0.156333 + 0.987704i \(0.549967\pi\)
\(662\) 0 0
\(663\) 0.412609 0.0160244
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −35.1766 −1.36204
\(668\) 0 0
\(669\) −14.6240 −0.565395
\(670\) 0 0
\(671\) 22.7640 0.878793
\(672\) 0 0
\(673\) −4.82936 −0.186158 −0.0930791 0.995659i \(-0.529671\pi\)
−0.0930791 + 0.995659i \(0.529671\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 12.8094 0.492305 0.246152 0.969231i \(-0.420834\pi\)
0.246152 + 0.969231i \(0.420834\pi\)
\(678\) 0 0
\(679\) −9.27334 −0.355878
\(680\) 0 0
\(681\) 17.1133 0.655785
\(682\) 0 0
\(683\) −37.1307 −1.42077 −0.710383 0.703815i \(-0.751478\pi\)
−0.710383 + 0.703815i \(0.751478\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −34.7267 −1.32490
\(688\) 0 0
\(689\) −1.15066 −0.0438368
\(690\) 0 0
\(691\) 18.1986 0.692308 0.346154 0.938178i \(-0.387487\pi\)
0.346154 + 0.938178i \(0.387487\pi\)
\(692\) 0 0
\(693\) −2.54669 −0.0967406
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −9.06068 −0.343198
\(698\) 0 0
\(699\) 4.24272 0.160474
\(700\) 0 0
\(701\) −26.2827 −0.992683 −0.496341 0.868127i \(-0.665324\pi\)
−0.496341 + 0.868127i \(0.665324\pi\)
\(702\) 0 0
\(703\) −3.27334 −0.123456
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 10.5794 0.397879
\(708\) 0 0
\(709\) −14.9253 −0.560531 −0.280265 0.959923i \(-0.590422\pi\)
−0.280265 + 0.959923i \(0.590422\pi\)
\(710\) 0 0
\(711\) −4.77075 −0.178917
\(712\) 0 0
\(713\) −38.3086 −1.43467
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −2.10402 −0.0785761
\(718\) 0 0
\(719\) −32.3327 −1.20581 −0.602903 0.797814i \(-0.705989\pi\)
−0.602903 + 0.797814i \(0.705989\pi\)
\(720\) 0 0
\(721\) 5.76868 0.214837
\(722\) 0 0
\(723\) −14.0187 −0.521359
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 42.0246 1.55861 0.779303 0.626647i \(-0.215573\pi\)
0.779303 + 0.626647i \(0.215573\pi\)
\(728\) 0 0
\(729\) 27.9694 1.03590
\(730\) 0 0
\(731\) −5.34335 −0.197631
\(732\) 0 0
\(733\) 26.5840 0.981903 0.490951 0.871187i \(-0.336649\pi\)
0.490951 + 0.871187i \(0.336649\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 29.3434 1.08088
\(738\) 0 0
\(739\) −8.14728 −0.299702 −0.149851 0.988709i \(-0.547879\pi\)
−0.149851 + 0.988709i \(0.547879\pi\)
\(740\) 0 0
\(741\) −0.192688 −0.00707855
\(742\) 0 0
\(743\) −35.8247 −1.31428 −0.657139 0.753769i \(-0.728234\pi\)
−0.657139 + 0.753769i \(0.728234\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −10.2827 −0.376223
\(748\) 0 0
\(749\) 0.0572907 0.00209336
\(750\) 0 0
\(751\) 14.8994 0.543686 0.271843 0.962342i \(-0.412367\pi\)
0.271843 + 0.962342i \(0.412367\pi\)
\(752\) 0 0
\(753\) −3.42740 −0.124901
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −47.7920 −1.73703 −0.868514 0.495664i \(-0.834925\pi\)
−0.868514 + 0.495664i \(0.834925\pi\)
\(758\) 0 0
\(759\) −23.5047 −0.853165
\(760\) 0 0
\(761\) −38.9053 −1.41032 −0.705158 0.709050i \(-0.749124\pi\)
−0.705158 + 0.709050i \(0.749124\pi\)
\(762\) 0 0
\(763\) 8.65533 0.313344
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −0.797984 −0.0288135
\(768\) 0 0
\(769\) 8.74663 0.315412 0.157706 0.987486i \(-0.449590\pi\)
0.157706 + 0.987486i \(0.449590\pi\)
\(770\) 0 0
\(771\) 33.8060 1.21749
\(772\) 0 0
\(773\) −23.4707 −0.844181 −0.422090 0.906554i \(-0.638703\pi\)
−0.422090 + 0.906554i \(0.638703\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 2.84124 0.101929
\(778\) 0 0
\(779\) 4.23132 0.151603
\(780\) 0 0
\(781\) −31.3947 −1.12339
\(782\) 0 0
\(783\) 40.3727 1.44280
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −1.26063 −0.0449364 −0.0224682 0.999748i \(-0.507152\pi\)
−0.0224682 + 0.999748i \(0.507152\pi\)
\(788\) 0 0
\(789\) −30.7640 −1.09523
\(790\) 0 0
\(791\) −7.33657 −0.260859
\(792\) 0 0
\(793\) 0.918026 0.0326000
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −38.6481 −1.36898 −0.684492 0.729020i \(-0.739976\pi\)
−0.684492 + 0.729020i \(0.739976\pi\)
\(798\) 0 0
\(799\) 22.0187 0.778964
\(800\) 0 0
\(801\) 7.73599 0.273338
\(802\) 0 0
\(803\) 12.9580 0.457277
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 36.2173 1.27491
\(808\) 0 0
\(809\) 51.6506 1.81594 0.907970 0.419036i \(-0.137632\pi\)
0.907970 + 0.419036i \(0.137632\pi\)
\(810\) 0 0
\(811\) −8.19269 −0.287684 −0.143842 0.989601i \(-0.545946\pi\)
−0.143842 + 0.989601i \(0.545946\pi\)
\(812\) 0 0
\(813\) −33.9987 −1.19239
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 2.49534 0.0873007
\(818\) 0 0
\(819\) −0.102703 −0.00358873
\(820\) 0 0
\(821\) −49.9600 −1.74362 −0.871809 0.489846i \(-0.837053\pi\)
−0.871809 + 0.489846i \(0.837053\pi\)
\(822\) 0 0
\(823\) 16.8421 0.587078 0.293539 0.955947i \(-0.405167\pi\)
0.293539 + 0.955947i \(0.405167\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 41.7487 1.45174 0.725872 0.687829i \(-0.241436\pi\)
0.725872 + 0.687829i \(0.241436\pi\)
\(828\) 0 0
\(829\) −5.98002 −0.207695 −0.103847 0.994593i \(-0.533115\pi\)
−0.103847 + 0.994593i \(0.533115\pi\)
\(830\) 0 0
\(831\) −25.2852 −0.877135
\(832\) 0 0
\(833\) −14.1214 −0.489276
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 43.9673 1.51973
\(838\) 0 0
\(839\) −32.0373 −1.10605 −0.553025 0.833164i \(-0.686527\pi\)
−0.553025 + 0.833164i \(0.686527\pi\)
\(840\) 0 0
\(841\) 22.1320 0.763173
\(842\) 0 0
\(843\) −33.8060 −1.16434
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −0.816641 −0.0280601
\(848\) 0 0
\(849\) 18.5067 0.635150
\(850\) 0 0
\(851\) −16.1027 −0.551994
\(852\) 0 0
\(853\) −40.8480 −1.39861 −0.699305 0.714824i \(-0.746507\pi\)
−0.699305 + 0.714824i \(0.746507\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 28.8667 0.986067 0.493033 0.870010i \(-0.335888\pi\)
0.493033 + 0.870010i \(0.335888\pi\)
\(858\) 0 0
\(859\) 11.5047 0.392534 0.196267 0.980550i \(-0.437118\pi\)
0.196267 + 0.980550i \(0.437118\pi\)
\(860\) 0 0
\(861\) −3.67276 −0.125167
\(862\) 0 0
\(863\) 31.6074 1.07593 0.537964 0.842968i \(-0.319194\pi\)
0.537964 + 0.842968i \(0.319194\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 16.9253 0.574813
\(868\) 0 0
\(869\) −14.6494 −0.496947
\(870\) 0 0
\(871\) 1.18336 0.0400966
\(872\) 0 0
\(873\) −16.6240 −0.562636
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 12.0641 0.407375 0.203687 0.979036i \(-0.434707\pi\)
0.203687 + 0.979036i \(0.434707\pi\)
\(878\) 0 0
\(879\) 21.2861 0.717961
\(880\) 0 0
\(881\) −22.8480 −0.769769 −0.384885 0.922965i \(-0.625759\pi\)
−0.384885 + 0.922965i \(0.625759\pi\)
\(882\) 0 0
\(883\) 34.1773 1.15016 0.575079 0.818098i \(-0.304971\pi\)
0.575079 + 0.818098i \(0.304971\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −26.6167 −0.893701 −0.446851 0.894609i \(-0.647454\pi\)
−0.446851 + 0.894609i \(0.647454\pi\)
\(888\) 0 0
\(889\) −2.09592 −0.0702950
\(890\) 0 0
\(891\) 14.9766 0.501736
\(892\) 0 0
\(893\) −10.2827 −0.344097
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −0.947896 −0.0316493
\(898\) 0 0
\(899\) 55.6846 1.85719
\(900\) 0 0
\(901\) 17.4333 0.580789
\(902\) 0 0
\(903\) −2.16593 −0.0720777
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −13.1434 −0.436420 −0.218210 0.975902i \(-0.570022\pi\)
−0.218210 + 0.975902i \(0.570022\pi\)
\(908\) 0 0
\(909\) 18.9652 0.629037
\(910\) 0 0
\(911\) 32.9253 1.09086 0.545432 0.838155i \(-0.316366\pi\)
0.545432 + 0.838155i \(0.316366\pi\)
\(912\) 0 0
\(913\) −31.5747 −1.04497
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 11.4720 0.378838
\(918\) 0 0
\(919\) 24.1273 0.795886 0.397943 0.917410i \(-0.369724\pi\)
0.397943 + 0.917410i \(0.369724\pi\)
\(920\) 0 0
\(921\) 46.3786 1.52823
\(922\) 0 0
\(923\) −1.26609 −0.0416737
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 10.3413 0.339652
\(928\) 0 0
\(929\) −15.9359 −0.522841 −0.261420 0.965225i \(-0.584191\pi\)
−0.261420 + 0.965225i \(0.584191\pi\)
\(930\) 0 0
\(931\) 6.59465 0.216131
\(932\) 0 0
\(933\) 12.1854 0.398933
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 23.5547 0.769498 0.384749 0.923021i \(-0.374288\pi\)
0.384749 + 0.923021i \(0.374288\pi\)
\(938\) 0 0
\(939\) 25.1180 0.819694
\(940\) 0 0
\(941\) −25.6974 −0.837710 −0.418855 0.908053i \(-0.637568\pi\)
−0.418855 + 0.908053i \(0.637568\pi\)
\(942\) 0 0
\(943\) 20.8153 0.677840
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 16.3013 0.529722 0.264861 0.964287i \(-0.414674\pi\)
0.264861 + 0.964287i \(0.414674\pi\)
\(948\) 0 0
\(949\) 0.522569 0.0169633
\(950\) 0 0
\(951\) −45.7461 −1.48342
\(952\) 0 0
\(953\) 10.2754 0.332853 0.166427 0.986054i \(-0.446777\pi\)
0.166427 + 0.986054i \(0.446777\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 34.1659 1.10443
\(958\) 0 0
\(959\) 9.18336 0.296546
\(960\) 0 0
\(961\) 29.6426 0.956213
\(962\) 0 0
\(963\) 0.102703 0.00330955
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 53.2920 1.71376 0.856878 0.515520i \(-0.172401\pi\)
0.856878 + 0.515520i \(0.172401\pi\)
\(968\) 0 0
\(969\) 2.91934 0.0937828
\(970\) 0 0
\(971\) −2.54669 −0.0817271 −0.0408635 0.999165i \(-0.513011\pi\)
−0.0408635 + 0.999165i \(0.513011\pi\)
\(972\) 0 0
\(973\) 9.85057 0.315795
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −49.2966 −1.57714 −0.788569 0.614946i \(-0.789178\pi\)
−0.788569 + 0.614946i \(0.789178\pi\)
\(978\) 0 0
\(979\) 23.7546 0.759202
\(980\) 0 0
\(981\) 15.5161 0.495390
\(982\) 0 0
\(983\) 36.7453 1.17199 0.585997 0.810313i \(-0.300703\pi\)
0.585997 + 0.810313i \(0.300703\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 8.92528 0.284095
\(988\) 0 0
\(989\) 12.2754 0.390335
\(990\) 0 0
\(991\) 35.5674 1.12984 0.564918 0.825147i \(-0.308908\pi\)
0.564918 + 0.825147i \(0.308908\pi\)
\(992\) 0 0
\(993\) 3.06926 0.0973999
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −48.4299 −1.53379 −0.766896 0.641771i \(-0.778200\pi\)
−0.766896 + 0.641771i \(0.778200\pi\)
\(998\) 0 0
\(999\) 18.4813 0.584722
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 7600.2.a.bi.1.2 3
4.3 odd 2 950.2.a.n.1.2 3
5.2 odd 4 1520.2.d.j.609.4 6
5.3 odd 4 1520.2.d.j.609.3 6
5.4 even 2 7600.2.a.cd.1.2 3
12.11 even 2 8550.2.a.ck.1.2 3
20.3 even 4 190.2.b.b.39.2 6
20.7 even 4 190.2.b.b.39.5 yes 6
20.19 odd 2 950.2.a.i.1.2 3
60.23 odd 4 1710.2.d.d.1369.5 6
60.47 odd 4 1710.2.d.d.1369.2 6
60.59 even 2 8550.2.a.cl.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.b.b.39.2 6 20.3 even 4
190.2.b.b.39.5 yes 6 20.7 even 4
950.2.a.i.1.2 3 20.19 odd 2
950.2.a.n.1.2 3 4.3 odd 2
1520.2.d.j.609.3 6 5.3 odd 4
1520.2.d.j.609.4 6 5.2 odd 4
1710.2.d.d.1369.2 6 60.47 odd 4
1710.2.d.d.1369.5 6 60.23 odd 4
7600.2.a.bi.1.2 3 1.1 even 1 trivial
7600.2.a.cd.1.2 3 5.4 even 2
8550.2.a.ck.1.2 3 12.11 even 2
8550.2.a.cl.1.2 3 60.59 even 2