Properties

Label 260.2.a.b.1.1
Level $260$
Weight $2$
Character 260.1
Self dual yes
Analytic conductor $2.076$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 260.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(2.07611045255\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.564.1
Defining polynomial: \( x^{3} - x^{2} - 5x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0.571993\) of defining polynomial
Character \(\chi\) \(=\) 260.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.67282 q^{3} +1.00000 q^{5} -1.14399 q^{7} +4.14399 q^{9} +O(q^{10})\) \(q-2.67282 q^{3} +1.00000 q^{5} -1.14399 q^{7} +4.14399 q^{9} +3.81681 q^{11} +1.00000 q^{13} -2.67282 q^{15} +7.34565 q^{17} +5.52884 q^{19} +3.05767 q^{21} -6.67282 q^{23} +1.00000 q^{25} -3.05767 q^{27} +2.85601 q^{29} -0.183190 q^{31} -10.2017 q^{33} -1.14399 q^{35} +6.48963 q^{37} -2.67282 q^{39} -7.34565 q^{41} +2.67282 q^{43} +4.14399 q^{45} -2.85601 q^{47} -5.69129 q^{49} -19.6336 q^{51} -13.6336 q^{53} +3.81681 q^{55} -14.7776 q^{57} +5.16246 q^{59} +5.14399 q^{61} -4.74066 q^{63} +1.00000 q^{65} -2.48963 q^{67} +17.8353 q^{69} +3.81681 q^{71} +12.7776 q^{73} -2.67282 q^{75} -4.36638 q^{77} +9.34565 q^{79} -4.25934 q^{81} +11.8353 q^{83} +7.34565 q^{85} -7.63362 q^{87} -14.9793 q^{89} -1.14399 q^{91} +0.489634 q^{93} +5.52884 q^{95} +7.71203 q^{97} +15.8168 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + 2 q^{3} + 3 q^{5} - 2 q^{7} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + 2 q^{3} + 3 q^{5} - 2 q^{7} + 11 q^{9} + 3 q^{13} + 2 q^{15} + 2 q^{17} + 8 q^{19} - 8 q^{21} - 10 q^{23} + 3 q^{25} + 8 q^{27} + 10 q^{29} - 12 q^{31} - 12 q^{33} - 2 q^{35} - 2 q^{37} + 2 q^{39} - 2 q^{41} - 2 q^{43} + 11 q^{45} - 10 q^{47} + 23 q^{49} - 36 q^{51} - 18 q^{53} - 20 q^{57} - 16 q^{59} + 14 q^{61} - 50 q^{63} + 3 q^{65} + 14 q^{67} + 12 q^{69} + 14 q^{73} + 2 q^{75} - 36 q^{77} + 8 q^{79} + 23 q^{81} - 6 q^{83} + 2 q^{85} - 2 q^{89} - 2 q^{91} - 20 q^{93} + 8 q^{95} + 26 q^{97} + 36 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.67282 −1.54316 −0.771578 0.636135i \(-0.780532\pi\)
−0.771578 + 0.636135i \(0.780532\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) −1.14399 −0.432386 −0.216193 0.976351i \(-0.569364\pi\)
−0.216193 + 0.976351i \(0.569364\pi\)
\(8\) 0 0
\(9\) 4.14399 1.38133
\(10\) 0 0
\(11\) 3.81681 1.15081 0.575406 0.817868i \(-0.304844\pi\)
0.575406 + 0.817868i \(0.304844\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) −2.67282 −0.690120
\(16\) 0 0
\(17\) 7.34565 1.78158 0.890791 0.454414i \(-0.150151\pi\)
0.890791 + 0.454414i \(0.150151\pi\)
\(18\) 0 0
\(19\) 5.52884 1.26840 0.634201 0.773168i \(-0.281329\pi\)
0.634201 + 0.773168i \(0.281329\pi\)
\(20\) 0 0
\(21\) 3.05767 0.667239
\(22\) 0 0
\(23\) −6.67282 −1.39138 −0.695690 0.718342i \(-0.744901\pi\)
−0.695690 + 0.718342i \(0.744901\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −3.05767 −0.588450
\(28\) 0 0
\(29\) 2.85601 0.530348 0.265174 0.964201i \(-0.414571\pi\)
0.265174 + 0.964201i \(0.414571\pi\)
\(30\) 0 0
\(31\) −0.183190 −0.0329019 −0.0164509 0.999865i \(-0.505237\pi\)
−0.0164509 + 0.999865i \(0.505237\pi\)
\(32\) 0 0
\(33\) −10.2017 −1.77588
\(34\) 0 0
\(35\) −1.14399 −0.193369
\(36\) 0 0
\(37\) 6.48963 1.06689 0.533445 0.845835i \(-0.320897\pi\)
0.533445 + 0.845835i \(0.320897\pi\)
\(38\) 0 0
\(39\) −2.67282 −0.427994
\(40\) 0 0
\(41\) −7.34565 −1.14720 −0.573599 0.819136i \(-0.694453\pi\)
−0.573599 + 0.819136i \(0.694453\pi\)
\(42\) 0 0
\(43\) 2.67282 0.407602 0.203801 0.979012i \(-0.434670\pi\)
0.203801 + 0.979012i \(0.434670\pi\)
\(44\) 0 0
\(45\) 4.14399 0.617749
\(46\) 0 0
\(47\) −2.85601 −0.416592 −0.208296 0.978066i \(-0.566792\pi\)
−0.208296 + 0.978066i \(0.566792\pi\)
\(48\) 0 0
\(49\) −5.69129 −0.813042
\(50\) 0 0
\(51\) −19.6336 −2.74926
\(52\) 0 0
\(53\) −13.6336 −1.87272 −0.936361 0.351039i \(-0.885829\pi\)
−0.936361 + 0.351039i \(0.885829\pi\)
\(54\) 0 0
\(55\) 3.81681 0.514659
\(56\) 0 0
\(57\) −14.7776 −1.95734
\(58\) 0 0
\(59\) 5.16246 0.672095 0.336047 0.941845i \(-0.390910\pi\)
0.336047 + 0.941845i \(0.390910\pi\)
\(60\) 0 0
\(61\) 5.14399 0.658620 0.329310 0.944222i \(-0.393184\pi\)
0.329310 + 0.944222i \(0.393184\pi\)
\(62\) 0 0
\(63\) −4.74066 −0.597268
\(64\) 0 0
\(65\) 1.00000 0.124035
\(66\) 0 0
\(67\) −2.48963 −0.304157 −0.152079 0.988368i \(-0.548597\pi\)
−0.152079 + 0.988368i \(0.548597\pi\)
\(68\) 0 0
\(69\) 17.8353 2.14712
\(70\) 0 0
\(71\) 3.81681 0.452972 0.226486 0.974014i \(-0.427276\pi\)
0.226486 + 0.974014i \(0.427276\pi\)
\(72\) 0 0
\(73\) 12.7776 1.49551 0.747753 0.663977i \(-0.231133\pi\)
0.747753 + 0.663977i \(0.231133\pi\)
\(74\) 0 0
\(75\) −2.67282 −0.308631
\(76\) 0 0
\(77\) −4.36638 −0.497595
\(78\) 0 0
\(79\) 9.34565 1.05147 0.525734 0.850649i \(-0.323791\pi\)
0.525734 + 0.850649i \(0.323791\pi\)
\(80\) 0 0
\(81\) −4.25934 −0.473259
\(82\) 0 0
\(83\) 11.8353 1.29909 0.649545 0.760323i \(-0.274959\pi\)
0.649545 + 0.760323i \(0.274959\pi\)
\(84\) 0 0
\(85\) 7.34565 0.796747
\(86\) 0 0
\(87\) −7.63362 −0.818410
\(88\) 0 0
\(89\) −14.9793 −1.58780 −0.793900 0.608049i \(-0.791952\pi\)
−0.793900 + 0.608049i \(0.791952\pi\)
\(90\) 0 0
\(91\) −1.14399 −0.119922
\(92\) 0 0
\(93\) 0.489634 0.0507727
\(94\) 0 0
\(95\) 5.52884 0.567247
\(96\) 0 0
\(97\) 7.71203 0.783038 0.391519 0.920170i \(-0.371950\pi\)
0.391519 + 0.920170i \(0.371950\pi\)
\(98\) 0 0
\(99\) 15.8168 1.58965
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) −4.38485 −0.432052 −0.216026 0.976388i \(-0.569310\pi\)
−0.216026 + 0.976388i \(0.569310\pi\)
\(104\) 0 0
\(105\) 3.05767 0.298398
\(106\) 0 0
\(107\) 0.384851 0.0372049 0.0186025 0.999827i \(-0.494078\pi\)
0.0186025 + 0.999827i \(0.494078\pi\)
\(108\) 0 0
\(109\) −12.6913 −1.21561 −0.607803 0.794088i \(-0.707949\pi\)
−0.607803 + 0.794088i \(0.707949\pi\)
\(110\) 0 0
\(111\) −17.3456 −1.64638
\(112\) 0 0
\(113\) 1.05767 0.0994976 0.0497488 0.998762i \(-0.484158\pi\)
0.0497488 + 0.998762i \(0.484158\pi\)
\(114\) 0 0
\(115\) −6.67282 −0.622244
\(116\) 0 0
\(117\) 4.14399 0.383112
\(118\) 0 0
\(119\) −8.40332 −0.770331
\(120\) 0 0
\(121\) 3.56804 0.324367
\(122\) 0 0
\(123\) 19.6336 1.77030
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 8.96080 0.795142 0.397571 0.917571i \(-0.369853\pi\)
0.397571 + 0.917571i \(0.369853\pi\)
\(128\) 0 0
\(129\) −7.14399 −0.628993
\(130\) 0 0
\(131\) −8.97927 −0.784522 −0.392261 0.919854i \(-0.628307\pi\)
−0.392261 + 0.919854i \(0.628307\pi\)
\(132\) 0 0
\(133\) −6.32492 −0.548440
\(134\) 0 0
\(135\) −3.05767 −0.263163
\(136\) 0 0
\(137\) −14.4033 −1.23056 −0.615279 0.788309i \(-0.710957\pi\)
−0.615279 + 0.788309i \(0.710957\pi\)
\(138\) 0 0
\(139\) 21.3456 1.81051 0.905257 0.424864i \(-0.139678\pi\)
0.905257 + 0.424864i \(0.139678\pi\)
\(140\) 0 0
\(141\) 7.63362 0.642867
\(142\) 0 0
\(143\) 3.81681 0.319178
\(144\) 0 0
\(145\) 2.85601 0.237179
\(146\) 0 0
\(147\) 15.2118 1.25465
\(148\) 0 0
\(149\) −14.4033 −1.17997 −0.589983 0.807416i \(-0.700866\pi\)
−0.589983 + 0.807416i \(0.700866\pi\)
\(150\) 0 0
\(151\) −22.5081 −1.83168 −0.915842 0.401539i \(-0.868475\pi\)
−0.915842 + 0.401539i \(0.868475\pi\)
\(152\) 0 0
\(153\) 30.4403 2.46095
\(154\) 0 0
\(155\) −0.183190 −0.0147142
\(156\) 0 0
\(157\) 16.6913 1.33211 0.666055 0.745902i \(-0.267982\pi\)
0.666055 + 0.745902i \(0.267982\pi\)
\(158\) 0 0
\(159\) 36.4403 2.88990
\(160\) 0 0
\(161\) 7.63362 0.601614
\(162\) 0 0
\(163\) −23.4689 −1.83823 −0.919113 0.393994i \(-0.871093\pi\)
−0.919113 + 0.393994i \(0.871093\pi\)
\(164\) 0 0
\(165\) −10.2017 −0.794198
\(166\) 0 0
\(167\) −9.14399 −0.707583 −0.353791 0.935324i \(-0.615108\pi\)
−0.353791 + 0.935324i \(0.615108\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 22.9114 1.75208
\(172\) 0 0
\(173\) −10.0369 −0.763095 −0.381547 0.924349i \(-0.624609\pi\)
−0.381547 + 0.924349i \(0.624609\pi\)
\(174\) 0 0
\(175\) −1.14399 −0.0864773
\(176\) 0 0
\(177\) −13.7983 −1.03715
\(178\) 0 0
\(179\) −20.9793 −1.56806 −0.784032 0.620720i \(-0.786840\pi\)
−0.784032 + 0.620720i \(0.786840\pi\)
\(180\) 0 0
\(181\) 13.5473 1.00696 0.503482 0.864006i \(-0.332052\pi\)
0.503482 + 0.864006i \(0.332052\pi\)
\(182\) 0 0
\(183\) −13.7490 −1.01635
\(184\) 0 0
\(185\) 6.48963 0.477127
\(186\) 0 0
\(187\) 28.0369 2.05026
\(188\) 0 0
\(189\) 3.49794 0.254438
\(190\) 0 0
\(191\) 12.0000 0.868290 0.434145 0.900843i \(-0.357051\pi\)
0.434145 + 0.900843i \(0.357051\pi\)
\(192\) 0 0
\(193\) −3.71203 −0.267198 −0.133599 0.991036i \(-0.542653\pi\)
−0.133599 + 0.991036i \(0.542653\pi\)
\(194\) 0 0
\(195\) −2.67282 −0.191405
\(196\) 0 0
\(197\) 8.69129 0.619229 0.309615 0.950862i \(-0.399800\pi\)
0.309615 + 0.950862i \(0.399800\pi\)
\(198\) 0 0
\(199\) −24.9793 −1.77073 −0.885367 0.464893i \(-0.846093\pi\)
−0.885367 + 0.464893i \(0.846093\pi\)
\(200\) 0 0
\(201\) 6.65435 0.469362
\(202\) 0 0
\(203\) −3.26724 −0.229315
\(204\) 0 0
\(205\) −7.34565 −0.513042
\(206\) 0 0
\(207\) −27.6521 −1.92195
\(208\) 0 0
\(209\) 21.1025 1.45969
\(210\) 0 0
\(211\) 16.9793 1.16890 0.584451 0.811429i \(-0.301310\pi\)
0.584451 + 0.811429i \(0.301310\pi\)
\(212\) 0 0
\(213\) −10.2017 −0.699006
\(214\) 0 0
\(215\) 2.67282 0.182285
\(216\) 0 0
\(217\) 0.209567 0.0142263
\(218\) 0 0
\(219\) −34.1523 −2.30780
\(220\) 0 0
\(221\) 7.34565 0.494122
\(222\) 0 0
\(223\) 13.5473 0.907195 0.453597 0.891207i \(-0.350140\pi\)
0.453597 + 0.891207i \(0.350140\pi\)
\(224\) 0 0
\(225\) 4.14399 0.276266
\(226\) 0 0
\(227\) 9.91369 0.657995 0.328997 0.944331i \(-0.393289\pi\)
0.328997 + 0.944331i \(0.393289\pi\)
\(228\) 0 0
\(229\) −14.0369 −0.927587 −0.463794 0.885943i \(-0.653512\pi\)
−0.463794 + 0.885943i \(0.653512\pi\)
\(230\) 0 0
\(231\) 11.6706 0.767867
\(232\) 0 0
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) −2.85601 −0.186306
\(236\) 0 0
\(237\) −24.9793 −1.62258
\(238\) 0 0
\(239\) −10.1048 −0.653624 −0.326812 0.945089i \(-0.605974\pi\)
−0.326812 + 0.945089i \(0.605974\pi\)
\(240\) 0 0
\(241\) −26.0369 −1.67719 −0.838593 0.544758i \(-0.816622\pi\)
−0.838593 + 0.544758i \(0.816622\pi\)
\(242\) 0 0
\(243\) 20.5575 1.31876
\(244\) 0 0
\(245\) −5.69129 −0.363603
\(246\) 0 0
\(247\) 5.52884 0.351791
\(248\) 0 0
\(249\) −31.6336 −2.00470
\(250\) 0 0
\(251\) 4.94233 0.311957 0.155978 0.987760i \(-0.450147\pi\)
0.155978 + 0.987760i \(0.450147\pi\)
\(252\) 0 0
\(253\) −25.4689 −1.60122
\(254\) 0 0
\(255\) −19.6336 −1.22951
\(256\) 0 0
\(257\) −12.2880 −0.766503 −0.383251 0.923644i \(-0.625196\pi\)
−0.383251 + 0.923644i \(0.625196\pi\)
\(258\) 0 0
\(259\) −7.42405 −0.461308
\(260\) 0 0
\(261\) 11.8353 0.732586
\(262\) 0 0
\(263\) −7.44252 −0.458926 −0.229463 0.973317i \(-0.573697\pi\)
−0.229463 + 0.973317i \(0.573697\pi\)
\(264\) 0 0
\(265\) −13.6336 −0.837507
\(266\) 0 0
\(267\) 40.0369 2.45022
\(268\) 0 0
\(269\) −21.2672 −1.29669 −0.648343 0.761348i \(-0.724538\pi\)
−0.648343 + 0.761348i \(0.724538\pi\)
\(270\) 0 0
\(271\) −19.8168 −1.20379 −0.601893 0.798577i \(-0.705587\pi\)
−0.601893 + 0.798577i \(0.705587\pi\)
\(272\) 0 0
\(273\) 3.05767 0.185059
\(274\) 0 0
\(275\) 3.81681 0.230162
\(276\) 0 0
\(277\) −11.9216 −0.716299 −0.358150 0.933664i \(-0.616592\pi\)
−0.358150 + 0.933664i \(0.616592\pi\)
\(278\) 0 0
\(279\) −0.759136 −0.0454483
\(280\) 0 0
\(281\) 19.3456 1.15406 0.577032 0.816721i \(-0.304211\pi\)
0.577032 + 0.816721i \(0.304211\pi\)
\(282\) 0 0
\(283\) 29.3641 1.74552 0.872758 0.488153i \(-0.162329\pi\)
0.872758 + 0.488153i \(0.162329\pi\)
\(284\) 0 0
\(285\) −14.7776 −0.875350
\(286\) 0 0
\(287\) 8.40332 0.496032
\(288\) 0 0
\(289\) 36.9585 2.17403
\(290\) 0 0
\(291\) −20.6129 −1.20835
\(292\) 0 0
\(293\) −24.6050 −1.43744 −0.718719 0.695300i \(-0.755271\pi\)
−0.718719 + 0.695300i \(0.755271\pi\)
\(294\) 0 0
\(295\) 5.16246 0.300570
\(296\) 0 0
\(297\) −11.6706 −0.677195
\(298\) 0 0
\(299\) −6.67282 −0.385899
\(300\) 0 0
\(301\) −3.05767 −0.176241
\(302\) 0 0
\(303\) −16.0369 −0.921298
\(304\) 0 0
\(305\) 5.14399 0.294544
\(306\) 0 0
\(307\) −15.2593 −0.870896 −0.435448 0.900214i \(-0.643410\pi\)
−0.435448 + 0.900214i \(0.643410\pi\)
\(308\) 0 0
\(309\) 11.7199 0.666724
\(310\) 0 0
\(311\) 16.0369 0.909372 0.454686 0.890652i \(-0.349752\pi\)
0.454686 + 0.890652i \(0.349752\pi\)
\(312\) 0 0
\(313\) 27.9216 1.57822 0.789111 0.614251i \(-0.210542\pi\)
0.789111 + 0.614251i \(0.210542\pi\)
\(314\) 0 0
\(315\) −4.74066 −0.267106
\(316\) 0 0
\(317\) −21.9137 −1.23080 −0.615398 0.788217i \(-0.711005\pi\)
−0.615398 + 0.788217i \(0.711005\pi\)
\(318\) 0 0
\(319\) 10.9009 0.610331
\(320\) 0 0
\(321\) −1.02864 −0.0574130
\(322\) 0 0
\(323\) 40.6129 2.25976
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) 33.9216 1.87587
\(328\) 0 0
\(329\) 3.26724 0.180129
\(330\) 0 0
\(331\) −7.24086 −0.397994 −0.198997 0.980000i \(-0.563768\pi\)
−0.198997 + 0.980000i \(0.563768\pi\)
\(332\) 0 0
\(333\) 26.8930 1.47372
\(334\) 0 0
\(335\) −2.48963 −0.136023
\(336\) 0 0
\(337\) 9.05767 0.493403 0.246701 0.969092i \(-0.420653\pi\)
0.246701 + 0.969092i \(0.420653\pi\)
\(338\) 0 0
\(339\) −2.82698 −0.153540
\(340\) 0 0
\(341\) −0.699201 −0.0378638
\(342\) 0 0
\(343\) 14.5187 0.783935
\(344\) 0 0
\(345\) 17.8353 0.960219
\(346\) 0 0
\(347\) −2.63588 −0.141502 −0.0707508 0.997494i \(-0.522539\pi\)
−0.0707508 + 0.997494i \(0.522539\pi\)
\(348\) 0 0
\(349\) −17.6336 −0.943906 −0.471953 0.881624i \(-0.656451\pi\)
−0.471953 + 0.881624i \(0.656451\pi\)
\(350\) 0 0
\(351\) −3.05767 −0.163207
\(352\) 0 0
\(353\) 12.6050 0.670896 0.335448 0.942059i \(-0.391112\pi\)
0.335448 + 0.942059i \(0.391112\pi\)
\(354\) 0 0
\(355\) 3.81681 0.202575
\(356\) 0 0
\(357\) 22.4606 1.18874
\(358\) 0 0
\(359\) 6.83754 0.360872 0.180436 0.983587i \(-0.442249\pi\)
0.180436 + 0.983587i \(0.442249\pi\)
\(360\) 0 0
\(361\) 11.5680 0.608844
\(362\) 0 0
\(363\) −9.53674 −0.500549
\(364\) 0 0
\(365\) 12.7776 0.668811
\(366\) 0 0
\(367\) −10.0969 −0.527053 −0.263526 0.964652i \(-0.584886\pi\)
−0.263526 + 0.964652i \(0.584886\pi\)
\(368\) 0 0
\(369\) −30.4403 −1.58466
\(370\) 0 0
\(371\) 15.5967 0.809739
\(372\) 0 0
\(373\) 1.42405 0.0737347 0.0368674 0.999320i \(-0.488262\pi\)
0.0368674 + 0.999320i \(0.488262\pi\)
\(374\) 0 0
\(375\) −2.67282 −0.138024
\(376\) 0 0
\(377\) 2.85601 0.147092
\(378\) 0 0
\(379\) −24.4297 −1.25487 −0.627435 0.778669i \(-0.715895\pi\)
−0.627435 + 0.778669i \(0.715895\pi\)
\(380\) 0 0
\(381\) −23.9506 −1.22703
\(382\) 0 0
\(383\) 5.54731 0.283454 0.141727 0.989906i \(-0.454734\pi\)
0.141727 + 0.989906i \(0.454734\pi\)
\(384\) 0 0
\(385\) −4.36638 −0.222531
\(386\) 0 0
\(387\) 11.0761 0.563032
\(388\) 0 0
\(389\) 34.8066 1.76477 0.882383 0.470531i \(-0.155938\pi\)
0.882383 + 0.470531i \(0.155938\pi\)
\(390\) 0 0
\(391\) −49.0162 −2.47886
\(392\) 0 0
\(393\) 24.0000 1.21064
\(394\) 0 0
\(395\) 9.34565 0.470231
\(396\) 0 0
\(397\) 15.2224 0.763990 0.381995 0.924164i \(-0.375237\pi\)
0.381995 + 0.924164i \(0.375237\pi\)
\(398\) 0 0
\(399\) 16.9054 0.846328
\(400\) 0 0
\(401\) −0.863919 −0.0431421 −0.0215710 0.999767i \(-0.506867\pi\)
−0.0215710 + 0.999767i \(0.506867\pi\)
\(402\) 0 0
\(403\) −0.183190 −0.00912533
\(404\) 0 0
\(405\) −4.25934 −0.211648
\(406\) 0 0
\(407\) 24.7697 1.22779
\(408\) 0 0
\(409\) 6.03694 0.298508 0.149254 0.988799i \(-0.452313\pi\)
0.149254 + 0.988799i \(0.452313\pi\)
\(410\) 0 0
\(411\) 38.4975 1.89894
\(412\) 0 0
\(413\) −5.90578 −0.290605
\(414\) 0 0
\(415\) 11.8353 0.580971
\(416\) 0 0
\(417\) −57.0532 −2.79390
\(418\) 0 0
\(419\) −4.36638 −0.213312 −0.106656 0.994296i \(-0.534014\pi\)
−0.106656 + 0.994296i \(0.534014\pi\)
\(420\) 0 0
\(421\) 34.6498 1.68873 0.844365 0.535769i \(-0.179978\pi\)
0.844365 + 0.535769i \(0.179978\pi\)
\(422\) 0 0
\(423\) −11.8353 −0.575451
\(424\) 0 0
\(425\) 7.34565 0.356316
\(426\) 0 0
\(427\) −5.88465 −0.284778
\(428\) 0 0
\(429\) −10.2017 −0.492541
\(430\) 0 0
\(431\) 15.8168 0.761869 0.380934 0.924602i \(-0.375602\pi\)
0.380934 + 0.924602i \(0.375602\pi\)
\(432\) 0 0
\(433\) 7.38259 0.354785 0.177392 0.984140i \(-0.443234\pi\)
0.177392 + 0.984140i \(0.443234\pi\)
\(434\) 0 0
\(435\) −7.63362 −0.366004
\(436\) 0 0
\(437\) −36.8930 −1.76483
\(438\) 0 0
\(439\) −21.3826 −1.02054 −0.510268 0.860016i \(-0.670454\pi\)
−0.510268 + 0.860016i \(0.670454\pi\)
\(440\) 0 0
\(441\) −23.5846 −1.12308
\(442\) 0 0
\(443\) −7.24877 −0.344399 −0.172200 0.985062i \(-0.555087\pi\)
−0.172200 + 0.985062i \(0.555087\pi\)
\(444\) 0 0
\(445\) −14.9793 −0.710085
\(446\) 0 0
\(447\) 38.4975 1.82087
\(448\) 0 0
\(449\) −28.9009 −1.36392 −0.681958 0.731391i \(-0.738871\pi\)
−0.681958 + 0.731391i \(0.738871\pi\)
\(450\) 0 0
\(451\) −28.0369 −1.32021
\(452\) 0 0
\(453\) 60.1602 2.82657
\(454\) 0 0
\(455\) −1.14399 −0.0536309
\(456\) 0 0
\(457\) 22.9793 1.07492 0.537462 0.843288i \(-0.319383\pi\)
0.537462 + 0.843288i \(0.319383\pi\)
\(458\) 0 0
\(459\) −22.4606 −1.04837
\(460\) 0 0
\(461\) 12.4817 0.581332 0.290666 0.956825i \(-0.406123\pi\)
0.290666 + 0.956825i \(0.406123\pi\)
\(462\) 0 0
\(463\) −32.2017 −1.49654 −0.748269 0.663395i \(-0.769115\pi\)
−0.748269 + 0.663395i \(0.769115\pi\)
\(464\) 0 0
\(465\) 0.489634 0.0227062
\(466\) 0 0
\(467\) −27.0761 −1.25293 −0.626467 0.779448i \(-0.715500\pi\)
−0.626467 + 0.779448i \(0.715500\pi\)
\(468\) 0 0
\(469\) 2.84811 0.131513
\(470\) 0 0
\(471\) −44.6129 −2.05565
\(472\) 0 0
\(473\) 10.2017 0.469073
\(474\) 0 0
\(475\) 5.52884 0.253680
\(476\) 0 0
\(477\) −56.4975 −2.58684
\(478\) 0 0
\(479\) 24.7961 1.13296 0.566481 0.824075i \(-0.308305\pi\)
0.566481 + 0.824075i \(0.308305\pi\)
\(480\) 0 0
\(481\) 6.48963 0.295902
\(482\) 0 0
\(483\) −20.4033 −0.928383
\(484\) 0 0
\(485\) 7.71203 0.350185
\(486\) 0 0
\(487\) −7.62571 −0.345554 −0.172777 0.984961i \(-0.555274\pi\)
−0.172777 + 0.984961i \(0.555274\pi\)
\(488\) 0 0
\(489\) 62.7282 2.83667
\(490\) 0 0
\(491\) −34.3249 −1.54906 −0.774531 0.632536i \(-0.782014\pi\)
−0.774531 + 0.632536i \(0.782014\pi\)
\(492\) 0 0
\(493\) 20.9793 0.944859
\(494\) 0 0
\(495\) 15.8168 0.710913
\(496\) 0 0
\(497\) −4.36638 −0.195859
\(498\) 0 0
\(499\) −8.58651 −0.384385 −0.192193 0.981357i \(-0.561560\pi\)
−0.192193 + 0.981357i \(0.561560\pi\)
\(500\) 0 0
\(501\) 24.4403 1.09191
\(502\) 0 0
\(503\) 40.2280 1.79368 0.896840 0.442356i \(-0.145857\pi\)
0.896840 + 0.442356i \(0.145857\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) −2.67282 −0.118704
\(508\) 0 0
\(509\) −10.3664 −0.459482 −0.229741 0.973252i \(-0.573788\pi\)
−0.229741 + 0.973252i \(0.573788\pi\)
\(510\) 0 0
\(511\) −14.6174 −0.646636
\(512\) 0 0
\(513\) −16.9054 −0.746391
\(514\) 0 0
\(515\) −4.38485 −0.193220
\(516\) 0 0
\(517\) −10.9009 −0.479419
\(518\) 0 0
\(519\) 26.8270 1.17757
\(520\) 0 0
\(521\) 32.8145 1.43763 0.718816 0.695201i \(-0.244684\pi\)
0.718816 + 0.695201i \(0.244684\pi\)
\(522\) 0 0
\(523\) −25.9401 −1.13428 −0.567140 0.823621i \(-0.691950\pi\)
−0.567140 + 0.823621i \(0.691950\pi\)
\(524\) 0 0
\(525\) 3.05767 0.133448
\(526\) 0 0
\(527\) −1.34565 −0.0586173
\(528\) 0 0
\(529\) 21.5266 0.935938
\(530\) 0 0
\(531\) 21.3932 0.928384
\(532\) 0 0
\(533\) −7.34565 −0.318175
\(534\) 0 0
\(535\) 0.384851 0.0166385
\(536\) 0 0
\(537\) 56.0739 2.41977
\(538\) 0 0
\(539\) −21.7226 −0.935658
\(540\) 0 0
\(541\) 6.61289 0.284310 0.142155 0.989844i \(-0.454597\pi\)
0.142155 + 0.989844i \(0.454597\pi\)
\(542\) 0 0
\(543\) −36.2096 −1.55390
\(544\) 0 0
\(545\) −12.6913 −0.543635
\(546\) 0 0
\(547\) 8.38485 0.358510 0.179255 0.983803i \(-0.442631\pi\)
0.179255 + 0.983803i \(0.442631\pi\)
\(548\) 0 0
\(549\) 21.3166 0.909771
\(550\) 0 0
\(551\) 15.7904 0.672695
\(552\) 0 0
\(553\) −10.6913 −0.454640
\(554\) 0 0
\(555\) −17.3456 −0.736282
\(556\) 0 0
\(557\) 40.4482 1.71384 0.856922 0.515446i \(-0.172374\pi\)
0.856922 + 0.515446i \(0.172374\pi\)
\(558\) 0 0
\(559\) 2.67282 0.113048
\(560\) 0 0
\(561\) −74.9378 −3.16388
\(562\) 0 0
\(563\) −16.7512 −0.705980 −0.352990 0.935627i \(-0.614835\pi\)
−0.352990 + 0.935627i \(0.614835\pi\)
\(564\) 0 0
\(565\) 1.05767 0.0444967
\(566\) 0 0
\(567\) 4.87262 0.204631
\(568\) 0 0
\(569\) −12.4112 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(570\) 0 0
\(571\) 12.0369 0.503730 0.251865 0.967762i \(-0.418956\pi\)
0.251865 + 0.967762i \(0.418956\pi\)
\(572\) 0 0
\(573\) −32.0739 −1.33991
\(574\) 0 0
\(575\) −6.67282 −0.278276
\(576\) 0 0
\(577\) −16.6050 −0.691274 −0.345637 0.938368i \(-0.612337\pi\)
−0.345637 + 0.938368i \(0.612337\pi\)
\(578\) 0 0
\(579\) 9.92159 0.412327
\(580\) 0 0
\(581\) −13.5394 −0.561709
\(582\) 0 0
\(583\) −52.0369 −2.15515
\(584\) 0 0
\(585\) 4.14399 0.171333
\(586\) 0 0
\(587\) −24.8515 −1.02573 −0.512865 0.858469i \(-0.671416\pi\)
−0.512865 + 0.858469i \(0.671416\pi\)
\(588\) 0 0
\(589\) −1.01283 −0.0417328
\(590\) 0 0
\(591\) −23.2303 −0.955567
\(592\) 0 0
\(593\) −15.5552 −0.638776 −0.319388 0.947624i \(-0.603477\pi\)
−0.319388 + 0.947624i \(0.603477\pi\)
\(594\) 0 0
\(595\) −8.40332 −0.344503
\(596\) 0 0
\(597\) 66.7652 2.73252
\(598\) 0 0
\(599\) −0.193755 −0.00791662 −0.00395831 0.999992i \(-0.501260\pi\)
−0.00395831 + 0.999992i \(0.501260\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) −10.3170 −0.420141
\(604\) 0 0
\(605\) 3.56804 0.145061
\(606\) 0 0
\(607\) −16.9608 −0.688418 −0.344209 0.938893i \(-0.611853\pi\)
−0.344209 + 0.938893i \(0.611853\pi\)
\(608\) 0 0
\(609\) 8.73276 0.353869
\(610\) 0 0
\(611\) −2.85601 −0.115542
\(612\) 0 0
\(613\) −26.8066 −1.08271 −0.541355 0.840794i \(-0.682089\pi\)
−0.541355 + 0.840794i \(0.682089\pi\)
\(614\) 0 0
\(615\) 19.6336 0.791704
\(616\) 0 0
\(617\) −0.287973 −0.0115934 −0.00579668 0.999983i \(-0.501845\pi\)
−0.00579668 + 0.999983i \(0.501845\pi\)
\(618\) 0 0
\(619\) 12.0106 0.482745 0.241373 0.970432i \(-0.422402\pi\)
0.241373 + 0.970432i \(0.422402\pi\)
\(620\) 0 0
\(621\) 20.4033 0.818757
\(622\) 0 0
\(623\) 17.1361 0.686543
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −56.4033 −2.25253
\(628\) 0 0
\(629\) 47.6706 1.90075
\(630\) 0 0
\(631\) −20.3928 −0.811823 −0.405911 0.913912i \(-0.633046\pi\)
−0.405911 + 0.913912i \(0.633046\pi\)
\(632\) 0 0
\(633\) −45.3826 −1.80380
\(634\) 0 0
\(635\) 8.96080 0.355598
\(636\) 0 0
\(637\) −5.69129 −0.225497
\(638\) 0 0
\(639\) 15.8168 0.625703
\(640\) 0 0
\(641\) 21.2672 0.840006 0.420003 0.907523i \(-0.362029\pi\)
0.420003 + 0.907523i \(0.362029\pi\)
\(642\) 0 0
\(643\) −23.6627 −0.933164 −0.466582 0.884478i \(-0.654515\pi\)
−0.466582 + 0.884478i \(0.654515\pi\)
\(644\) 0 0
\(645\) −7.14399 −0.281294
\(646\) 0 0
\(647\) −39.8458 −1.56650 −0.783251 0.621706i \(-0.786440\pi\)
−0.783251 + 0.621706i \(0.786440\pi\)
\(648\) 0 0
\(649\) 19.7041 0.773454
\(650\) 0 0
\(651\) −0.560135 −0.0219534
\(652\) 0 0
\(653\) −11.7120 −0.458327 −0.229164 0.973388i \(-0.573599\pi\)
−0.229164 + 0.973388i \(0.573599\pi\)
\(654\) 0 0
\(655\) −8.97927 −0.350849
\(656\) 0 0
\(657\) 52.9502 2.06579
\(658\) 0 0
\(659\) 21.1730 0.824784 0.412392 0.911007i \(-0.364693\pi\)
0.412392 + 0.911007i \(0.364693\pi\)
\(660\) 0 0
\(661\) 2.57595 0.100193 0.0500963 0.998744i \(-0.484047\pi\)
0.0500963 + 0.998744i \(0.484047\pi\)
\(662\) 0 0
\(663\) −19.6336 −0.762507
\(664\) 0 0
\(665\) −6.32492 −0.245270
\(666\) 0 0
\(667\) −19.0577 −0.737916
\(668\) 0 0
\(669\) −36.2096 −1.39994
\(670\) 0 0
\(671\) 19.6336 0.757948
\(672\) 0 0
\(673\) −16.7282 −0.644826 −0.322413 0.946599i \(-0.604494\pi\)
−0.322413 + 0.946599i \(0.604494\pi\)
\(674\) 0 0
\(675\) −3.05767 −0.117690
\(676\) 0 0
\(677\) −10.9423 −0.420548 −0.210274 0.977643i \(-0.567436\pi\)
−0.210274 + 0.977643i \(0.567436\pi\)
\(678\) 0 0
\(679\) −8.82245 −0.338575
\(680\) 0 0
\(681\) −26.4975 −1.01539
\(682\) 0 0
\(683\) 6.89296 0.263752 0.131876 0.991266i \(-0.457900\pi\)
0.131876 + 0.991266i \(0.457900\pi\)
\(684\) 0 0
\(685\) −14.4033 −0.550323
\(686\) 0 0
\(687\) 37.5183 1.43141
\(688\) 0 0
\(689\) −13.6336 −0.519400
\(690\) 0 0
\(691\) 43.4504 1.65293 0.826466 0.562986i \(-0.190348\pi\)
0.826466 + 0.562986i \(0.190348\pi\)
\(692\) 0 0
\(693\) −18.0942 −0.687343
\(694\) 0 0
\(695\) 21.3456 0.809687
\(696\) 0 0
\(697\) −53.9585 −2.04383
\(698\) 0 0
\(699\) 16.0369 0.606573
\(700\) 0 0
\(701\) 32.1153 1.21298 0.606490 0.795091i \(-0.292577\pi\)
0.606490 + 0.795091i \(0.292577\pi\)
\(702\) 0 0
\(703\) 35.8801 1.35324
\(704\) 0 0
\(705\) 7.63362 0.287499
\(706\) 0 0
\(707\) −6.86392 −0.258144
\(708\) 0 0
\(709\) 1.23030 0.0462048 0.0231024 0.999733i \(-0.492646\pi\)
0.0231024 + 0.999733i \(0.492646\pi\)
\(710\) 0 0
\(711\) 38.7282 1.45242
\(712\) 0 0
\(713\) 1.22239 0.0457790
\(714\) 0 0
\(715\) 3.81681 0.142741
\(716\) 0 0
\(717\) 27.0083 1.00864
\(718\) 0 0
\(719\) 7.82738 0.291912 0.145956 0.989291i \(-0.453374\pi\)
0.145956 + 0.989291i \(0.453374\pi\)
\(720\) 0 0
\(721\) 5.01621 0.186813
\(722\) 0 0
\(723\) 69.5922 2.58816
\(724\) 0 0
\(725\) 2.85601 0.106070
\(726\) 0 0
\(727\) −27.2857 −1.01197 −0.505986 0.862542i \(-0.668871\pi\)
−0.505986 + 0.862542i \(0.668871\pi\)
\(728\) 0 0
\(729\) −42.1685 −1.56180
\(730\) 0 0
\(731\) 19.6336 0.726176
\(732\) 0 0
\(733\) −10.0000 −0.369358 −0.184679 0.982799i \(-0.559125\pi\)
−0.184679 + 0.982799i \(0.559125\pi\)
\(734\) 0 0
\(735\) 15.2118 0.561097
\(736\) 0 0
\(737\) −9.50246 −0.350028
\(738\) 0 0
\(739\) 30.5450 1.12362 0.561809 0.827267i \(-0.310106\pi\)
0.561809 + 0.827267i \(0.310106\pi\)
\(740\) 0 0
\(741\) −14.7776 −0.542869
\(742\) 0 0
\(743\) −36.4112 −1.33580 −0.667899 0.744252i \(-0.732806\pi\)
−0.667899 + 0.744252i \(0.732806\pi\)
\(744\) 0 0
\(745\) −14.4033 −0.527697
\(746\) 0 0
\(747\) 49.0452 1.79447
\(748\) 0 0
\(749\) −0.440264 −0.0160869
\(750\) 0 0
\(751\) −13.1730 −0.480690 −0.240345 0.970687i \(-0.577261\pi\)
−0.240345 + 0.970687i \(0.577261\pi\)
\(752\) 0 0
\(753\) −13.2100 −0.481398
\(754\) 0 0
\(755\) −22.5081 −0.819154
\(756\) 0 0
\(757\) 33.8801 1.23139 0.615697 0.787983i \(-0.288874\pi\)
0.615697 + 0.787983i \(0.288874\pi\)
\(758\) 0 0
\(759\) 68.0739 2.47093
\(760\) 0 0
\(761\) 33.2672 1.20594 0.602968 0.797765i \(-0.293985\pi\)
0.602968 + 0.797765i \(0.293985\pi\)
\(762\) 0 0
\(763\) 14.5187 0.525611
\(764\) 0 0
\(765\) 30.4403 1.10057
\(766\) 0 0
\(767\) 5.16246 0.186406
\(768\) 0 0
\(769\) 29.8432 1.07617 0.538086 0.842890i \(-0.319147\pi\)
0.538086 + 0.842890i \(0.319147\pi\)
\(770\) 0 0
\(771\) 32.8436 1.18283
\(772\) 0 0
\(773\) −16.7776 −0.603449 −0.301724 0.953395i \(-0.597562\pi\)
−0.301724 + 0.953395i \(0.597562\pi\)
\(774\) 0 0
\(775\) −0.183190 −0.00658037
\(776\) 0 0
\(777\) 19.8432 0.711870
\(778\) 0 0
\(779\) −40.6129 −1.45511
\(780\) 0 0
\(781\) 14.5680 0.521285
\(782\) 0 0
\(783\) −8.73276 −0.312083
\(784\) 0 0
\(785\) 16.6913 0.595738
\(786\) 0 0
\(787\) 20.1647 0.718795 0.359397 0.933185i \(-0.382982\pi\)
0.359397 + 0.933185i \(0.382982\pi\)
\(788\) 0 0
\(789\) 19.8926 0.708194
\(790\) 0 0
\(791\) −1.20997 −0.0430214
\(792\) 0 0
\(793\) 5.14399 0.182668
\(794\) 0 0
\(795\) 36.4403 1.29240
\(796\) 0 0
\(797\) 3.30871 0.117200 0.0586002 0.998282i \(-0.481336\pi\)
0.0586002 + 0.998282i \(0.481336\pi\)
\(798\) 0 0
\(799\) −20.9793 −0.742193
\(800\) 0 0
\(801\) −62.0739 −2.19327
\(802\) 0 0
\(803\) 48.7697 1.72105
\(804\) 0 0
\(805\) 7.63362 0.269050
\(806\) 0 0
\(807\) 56.8436 2.00099
\(808\) 0 0
\(809\) 22.6834 0.797505 0.398753 0.917058i \(-0.369443\pi\)
0.398753 + 0.917058i \(0.369443\pi\)
\(810\) 0 0
\(811\) −9.93216 −0.348765 −0.174383 0.984678i \(-0.555793\pi\)
−0.174383 + 0.984678i \(0.555793\pi\)
\(812\) 0 0
\(813\) 52.9668 1.85763
\(814\) 0 0
\(815\) −23.4689 −0.822080
\(816\) 0 0
\(817\) 14.7776 0.517003
\(818\) 0 0
\(819\) −4.74066 −0.165652
\(820\) 0 0
\(821\) −38.4033 −1.34029 −0.670143 0.742232i \(-0.733767\pi\)
−0.670143 + 0.742232i \(0.733767\pi\)
\(822\) 0 0
\(823\) −13.1176 −0.457251 −0.228626 0.973514i \(-0.573423\pi\)
−0.228626 + 0.973514i \(0.573423\pi\)
\(824\) 0 0
\(825\) −10.2017 −0.355176
\(826\) 0 0
\(827\) −16.9714 −0.590152 −0.295076 0.955474i \(-0.595345\pi\)
−0.295076 + 0.955474i \(0.595345\pi\)
\(828\) 0 0
\(829\) 31.8353 1.10569 0.552843 0.833286i \(-0.313543\pi\)
0.552843 + 0.833286i \(0.313543\pi\)
\(830\) 0 0
\(831\) 31.8643 1.10536
\(832\) 0 0
\(833\) −41.8062 −1.44850
\(834\) 0 0
\(835\) −9.14399 −0.316441
\(836\) 0 0
\(837\) 0.560135 0.0193611
\(838\) 0 0
\(839\) −3.62306 −0.125082 −0.0625409 0.998042i \(-0.519920\pi\)
−0.0625409 + 0.998042i \(0.519920\pi\)
\(840\) 0 0
\(841\) −20.8432 −0.718731
\(842\) 0 0
\(843\) −51.7075 −1.78090
\(844\) 0 0
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) −4.08179 −0.140252
\(848\) 0 0
\(849\) −78.4851 −2.69360
\(850\) 0 0
\(851\) −43.3042 −1.48445
\(852\) 0 0
\(853\) 21.5104 0.736501 0.368250 0.929727i \(-0.379957\pi\)
0.368250 + 0.929727i \(0.379957\pi\)
\(854\) 0 0
\(855\) 22.9114 0.783554
\(856\) 0 0
\(857\) −17.6706 −0.603615 −0.301807 0.953369i \(-0.597590\pi\)
−0.301807 + 0.953369i \(0.597590\pi\)
\(858\) 0 0
\(859\) 3.63362 0.123978 0.0619888 0.998077i \(-0.480256\pi\)
0.0619888 + 0.998077i \(0.480256\pi\)
\(860\) 0 0
\(861\) −22.4606 −0.765455
\(862\) 0 0
\(863\) −13.9506 −0.474885 −0.237442 0.971402i \(-0.576309\pi\)
−0.237442 + 0.971402i \(0.576309\pi\)
\(864\) 0 0
\(865\) −10.0369 −0.341266
\(866\) 0 0
\(867\) −98.7837 −3.35487
\(868\) 0 0
\(869\) 35.6706 1.21004
\(870\) 0 0
\(871\) −2.48963 −0.0843580
\(872\) 0 0
\(873\) 31.9585 1.08163
\(874\) 0 0
\(875\) −1.14399 −0.0386738
\(876\) 0 0
\(877\) −10.0000 −0.337676 −0.168838 0.985644i \(-0.554001\pi\)
−0.168838 + 0.985644i \(0.554001\pi\)
\(878\) 0 0
\(879\) 65.7648 2.21819
\(880\) 0 0
\(881\) −16.3954 −0.552376 −0.276188 0.961104i \(-0.589071\pi\)
−0.276188 + 0.961104i \(0.589071\pi\)
\(882\) 0 0
\(883\) 44.6314 1.50196 0.750982 0.660322i \(-0.229580\pi\)
0.750982 + 0.660322i \(0.229580\pi\)
\(884\) 0 0
\(885\) −13.7983 −0.463826
\(886\) 0 0
\(887\) −47.4795 −1.59420 −0.797102 0.603844i \(-0.793635\pi\)
−0.797102 + 0.603844i \(0.793635\pi\)
\(888\) 0 0
\(889\) −10.2510 −0.343809
\(890\) 0 0
\(891\) −16.2571 −0.544632
\(892\) 0 0
\(893\) −15.7904 −0.528407
\(894\) 0 0
\(895\) −20.9793 −0.701260
\(896\) 0 0
\(897\) 17.8353 0.595503
\(898\) 0 0
\(899\) −0.523192 −0.0174494
\(900\) 0 0
\(901\) −100.148 −3.33641
\(902\) 0 0
\(903\) 8.17262 0.271968
\(904\) 0 0
\(905\) 13.5473 0.450328
\(906\) 0 0
\(907\) 22.8824 0.759797 0.379899 0.925028i \(-0.375959\pi\)
0.379899 + 0.925028i \(0.375959\pi\)
\(908\) 0 0
\(909\) 24.8639 0.824684
\(910\) 0 0
\(911\) 0.329437 0.0109147 0.00545737 0.999985i \(-0.498263\pi\)
0.00545737 + 0.999985i \(0.498263\pi\)
\(912\) 0 0
\(913\) 45.1730 1.49501
\(914\) 0 0
\(915\) −13.7490 −0.454527
\(916\) 0 0
\(917\) 10.2722 0.339217
\(918\) 0 0
\(919\) 36.0369 1.18875 0.594375 0.804188i \(-0.297400\pi\)
0.594375 + 0.804188i \(0.297400\pi\)
\(920\) 0 0
\(921\) 40.7855 1.34393
\(922\) 0 0
\(923\) 3.81681 0.125632
\(924\) 0 0
\(925\) 6.48963 0.213378
\(926\) 0 0
\(927\) −18.1708 −0.596806
\(928\) 0 0
\(929\) 26.7855 0.878804 0.439402 0.898290i \(-0.355190\pi\)
0.439402 + 0.898290i \(0.355190\pi\)
\(930\) 0 0
\(931\) −31.4662 −1.03126
\(932\) 0 0
\(933\) −42.8639 −1.40330
\(934\) 0 0
\(935\) 28.0369 0.916906
\(936\) 0 0
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 0 0
\(939\) −74.6295 −2.43544
\(940\) 0 0
\(941\) −13.9631 −0.455183 −0.227591 0.973757i \(-0.573085\pi\)
−0.227591 + 0.973757i \(0.573085\pi\)
\(942\) 0 0
\(943\) 49.0162 1.59619
\(944\) 0 0
\(945\) 3.49794 0.113788
\(946\) 0 0
\(947\) −18.1233 −0.588927 −0.294463 0.955663i \(-0.595141\pi\)
−0.294463 + 0.955663i \(0.595141\pi\)
\(948\) 0 0
\(949\) 12.7776 0.414779
\(950\) 0 0
\(951\) 58.5714 1.89931
\(952\) 0 0
\(953\) 2.97927 0.0965080 0.0482540 0.998835i \(-0.484634\pi\)
0.0482540 + 0.998835i \(0.484634\pi\)
\(954\) 0 0
\(955\) 12.0000 0.388311
\(956\) 0 0
\(957\) −29.1361 −0.941836
\(958\) 0 0
\(959\) 16.4772 0.532077
\(960\) 0 0
\(961\) −30.9664 −0.998917
\(962\) 0 0
\(963\) 1.59482 0.0513922
\(964\) 0 0
\(965\) −3.71203 −0.119494
\(966\) 0 0
\(967\) 6.48963 0.208693 0.104346 0.994541i \(-0.466725\pi\)
0.104346 + 0.994541i \(0.466725\pi\)
\(968\) 0 0
\(969\) −108.551 −3.48716
\(970\) 0 0
\(971\) 32.9793 1.05836 0.529178 0.848511i \(-0.322501\pi\)
0.529178 + 0.848511i \(0.322501\pi\)
\(972\) 0 0
\(973\) −24.4191 −0.782841
\(974\) 0 0
\(975\) −2.67282 −0.0855989
\(976\) 0 0
\(977\) −31.7983 −1.01732 −0.508659 0.860968i \(-0.669859\pi\)
−0.508659 + 0.860968i \(0.669859\pi\)
\(978\) 0 0
\(979\) −57.1730 −1.82726
\(980\) 0 0
\(981\) −52.5926 −1.67915
\(982\) 0 0
\(983\) 23.0656 0.735678 0.367839 0.929890i \(-0.380098\pi\)
0.367839 + 0.929890i \(0.380098\pi\)
\(984\) 0 0
\(985\) 8.69129 0.276928
\(986\) 0 0
\(987\) −8.73276 −0.277967
\(988\) 0 0
\(989\) −17.8353 −0.567129
\(990\) 0 0
\(991\) 52.0739 1.65418 0.827091 0.562068i \(-0.189994\pi\)
0.827091 + 0.562068i \(0.189994\pi\)
\(992\) 0 0
\(993\) 19.3536 0.614166
\(994\) 0 0
\(995\) −24.9793 −0.791896
\(996\) 0 0
\(997\) −6.78551 −0.214899 −0.107450 0.994211i \(-0.534268\pi\)
−0.107450 + 0.994211i \(0.534268\pi\)
\(998\) 0 0
\(999\) −19.8432 −0.627811
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 260.2.a.b.1.1 3
3.2 odd 2 2340.2.a.n.1.2 3
4.3 odd 2 1040.2.a.o.1.3 3
5.2 odd 4 1300.2.c.f.1249.5 6
5.3 odd 4 1300.2.c.f.1249.2 6
5.4 even 2 1300.2.a.i.1.3 3
8.3 odd 2 4160.2.a.br.1.1 3
8.5 even 2 4160.2.a.bo.1.3 3
12.11 even 2 9360.2.a.da.1.2 3
13.5 odd 4 3380.2.f.h.3041.1 6
13.8 odd 4 3380.2.f.h.3041.2 6
13.12 even 2 3380.2.a.o.1.1 3
20.19 odd 2 5200.2.a.ci.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
260.2.a.b.1.1 3 1.1 even 1 trivial
1040.2.a.o.1.3 3 4.3 odd 2
1300.2.a.i.1.3 3 5.4 even 2
1300.2.c.f.1249.2 6 5.3 odd 4
1300.2.c.f.1249.5 6 5.2 odd 4
2340.2.a.n.1.2 3 3.2 odd 2
3380.2.a.o.1.1 3 13.12 even 2
3380.2.f.h.3041.1 6 13.5 odd 4
3380.2.f.h.3041.2 6 13.8 odd 4
4160.2.a.bo.1.3 3 8.5 even 2
4160.2.a.br.1.1 3 8.3 odd 2
5200.2.a.ci.1.1 3 20.19 odd 2
9360.2.a.da.1.2 3 12.11 even 2