Properties

Label 6240.2.a.bw.1.1
Level $6240$
Weight $2$
Character 6240.1
Self dual yes
Analytic conductor $49.827$
Analytic rank $0$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 6240 = 2^{5} \cdot 3 \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6240.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(49.8266508613\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.229.1
Defining polynomial: \( x^{3} - 4x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.86081\) of defining polynomial
Character \(\chi\) \(=\) 6240.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -1.00000 q^{5} -4.32340 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -1.00000 q^{5} -4.32340 q^{7} +1.00000 q^{9} +1.39821 q^{11} +1.00000 q^{13} +1.00000 q^{15} +5.11982 q^{17} -2.92520 q^{19} +4.32340 q^{21} -8.97021 q^{23} +1.00000 q^{25} -1.00000 q^{27} -8.36842 q^{29} -4.00000 q^{31} -1.39821 q^{33} +4.32340 q^{35} +3.39821 q^{37} -1.00000 q^{39} -0.601793 q^{41} +2.79641 q^{43} -1.00000 q^{45} +9.29362 q^{47} +11.6918 q^{49} -5.11982 q^{51} -2.19462 q^{53} -1.39821 q^{55} +2.92520 q^{57} -7.44322 q^{59} -5.24860 q^{61} -4.32340 q^{63} -1.00000 q^{65} +8.97021 q^{69} -10.0450 q^{71} -13.0152 q^{73} -1.00000 q^{75} -6.04502 q^{77} -1.95498 q^{79} +1.00000 q^{81} +17.2936 q^{83} -5.11982 q^{85} +8.36842 q^{87} +4.04502 q^{89} -4.32340 q^{91} +4.00000 q^{93} +2.92520 q^{95} +10.3234 q^{97} +1.39821 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q - 3 q^{3} - 3 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 3 q - 3 q^{3} - 3 q^{5} - 5 q^{7} + 3 q^{9} + q^{11} + 3 q^{13} + 3 q^{15} + q^{17} - 4 q^{19} + 5 q^{21} - 3 q^{23} + 3 q^{25} - 3 q^{27} + 2 q^{29} - 12 q^{31} - q^{33} + 5 q^{35} + 7 q^{37} - 3 q^{39} - 5 q^{41} + 2 q^{43} - 3 q^{45} - 4 q^{47} - q^{51} + 3 q^{53} - q^{55} + 4 q^{57} - 3 q^{61} - 5 q^{63} - 3 q^{65} + 3 q^{69} - 11 q^{71} + 4 q^{73} - 3 q^{75} + q^{77} - 25 q^{79} + 3 q^{81} + 20 q^{83} - q^{85} - 2 q^{87} - 7 q^{89} - 5 q^{91} + 12 q^{93} + 4 q^{95} + 23 q^{97} + q^{99}+O(q^{100}) \) 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
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −4.32340 −1.63409 −0.817047 0.576572i \(-0.804390\pi\)
−0.817047 + 0.576572i \(0.804390\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.39821 0.421575 0.210788 0.977532i \(-0.432397\pi\)
0.210788 + 0.977532i \(0.432397\pi\)
\(12\) 0 0
\(13\) 1.00000 0.277350
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 0 0
\(17\) 5.11982 1.24174 0.620869 0.783914i \(-0.286780\pi\)
0.620869 + 0.783914i \(0.286780\pi\)
\(18\) 0 0
\(19\) −2.92520 −0.671086 −0.335543 0.942025i \(-0.608920\pi\)
−0.335543 + 0.942025i \(0.608920\pi\)
\(20\) 0 0
\(21\) 4.32340 0.943444
\(22\) 0 0
\(23\) −8.97021 −1.87042 −0.935209 0.354095i \(-0.884789\pi\)
−0.935209 + 0.354095i \(0.884789\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −8.36842 −1.55398 −0.776988 0.629515i \(-0.783254\pi\)
−0.776988 + 0.629515i \(0.783254\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) −1.39821 −0.243397
\(34\) 0 0
\(35\) 4.32340 0.730789
\(36\) 0 0
\(37\) 3.39821 0.558662 0.279331 0.960195i \(-0.409887\pi\)
0.279331 + 0.960195i \(0.409887\pi\)
\(38\) 0 0
\(39\) −1.00000 −0.160128
\(40\) 0 0
\(41\) −0.601793 −0.0939842 −0.0469921 0.998895i \(-0.514964\pi\)
−0.0469921 + 0.998895i \(0.514964\pi\)
\(42\) 0 0
\(43\) 2.79641 0.426449 0.213225 0.977003i \(-0.431603\pi\)
0.213225 + 0.977003i \(0.431603\pi\)
\(44\) 0 0
\(45\) −1.00000 −0.149071
\(46\) 0 0
\(47\) 9.29362 1.35561 0.677807 0.735240i \(-0.262931\pi\)
0.677807 + 0.735240i \(0.262931\pi\)
\(48\) 0 0
\(49\) 11.6918 1.67026
\(50\) 0 0
\(51\) −5.11982 −0.716918
\(52\) 0 0
\(53\) −2.19462 −0.301455 −0.150727 0.988575i \(-0.548162\pi\)
−0.150727 + 0.988575i \(0.548162\pi\)
\(54\) 0 0
\(55\) −1.39821 −0.188534
\(56\) 0 0
\(57\) 2.92520 0.387452
\(58\) 0 0
\(59\) −7.44322 −0.969025 −0.484513 0.874784i \(-0.661003\pi\)
−0.484513 + 0.874784i \(0.661003\pi\)
\(60\) 0 0
\(61\) −5.24860 −0.672015 −0.336007 0.941859i \(-0.609077\pi\)
−0.336007 + 0.941859i \(0.609077\pi\)
\(62\) 0 0
\(63\) −4.32340 −0.544698
\(64\) 0 0
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 0 0
\(69\) 8.97021 1.07989
\(70\) 0 0
\(71\) −10.0450 −1.19212 −0.596062 0.802938i \(-0.703269\pi\)
−0.596062 + 0.802938i \(0.703269\pi\)
\(72\) 0 0
\(73\) −13.0152 −1.52332 −0.761659 0.647978i \(-0.775615\pi\)
−0.761659 + 0.647978i \(0.775615\pi\)
\(74\) 0 0
\(75\) −1.00000 −0.115470
\(76\) 0 0
\(77\) −6.04502 −0.688894
\(78\) 0 0
\(79\) −1.95498 −0.219953 −0.109976 0.993934i \(-0.535078\pi\)
−0.109976 + 0.993934i \(0.535078\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 17.2936 1.89822 0.949111 0.314943i \(-0.101985\pi\)
0.949111 + 0.314943i \(0.101985\pi\)
\(84\) 0 0
\(85\) −5.11982 −0.555322
\(86\) 0 0
\(87\) 8.36842 0.897189
\(88\) 0 0
\(89\) 4.04502 0.428771 0.214385 0.976749i \(-0.431225\pi\)
0.214385 + 0.976749i \(0.431225\pi\)
\(90\) 0 0
\(91\) −4.32340 −0.453216
\(92\) 0 0
\(93\) 4.00000 0.414781
\(94\) 0 0
\(95\) 2.92520 0.300119
\(96\) 0 0
\(97\) 10.3234 1.04818 0.524091 0.851662i \(-0.324405\pi\)
0.524091 + 0.851662i \(0.324405\pi\)
\(98\) 0 0
\(99\) 1.39821 0.140525
\(100\) 0 0
\(101\) −4.92520 −0.490075 −0.245038 0.969514i \(-0.578800\pi\)
−0.245038 + 0.969514i \(0.578800\pi\)
\(102\) 0 0
\(103\) 1.29362 0.127464 0.0637319 0.997967i \(-0.479700\pi\)
0.0637319 + 0.997967i \(0.479700\pi\)
\(104\) 0 0
\(105\) −4.32340 −0.421921
\(106\) 0 0
\(107\) 0.751399 0.0726405 0.0363202 0.999340i \(-0.488436\pi\)
0.0363202 + 0.999340i \(0.488436\pi\)
\(108\) 0 0
\(109\) 14.5180 1.39057 0.695287 0.718732i \(-0.255277\pi\)
0.695287 + 0.718732i \(0.255277\pi\)
\(110\) 0 0
\(111\) −3.39821 −0.322544
\(112\) 0 0
\(113\) −7.16484 −0.674011 −0.337005 0.941503i \(-0.609414\pi\)
−0.337005 + 0.941503i \(0.609414\pi\)
\(114\) 0 0
\(115\) 8.97021 0.836477
\(116\) 0 0
\(117\) 1.00000 0.0924500
\(118\) 0 0
\(119\) −22.1350 −2.02912
\(120\) 0 0
\(121\) −9.04502 −0.822274
\(122\) 0 0
\(123\) 0.601793 0.0542618
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −11.7008 −1.03828 −0.519138 0.854690i \(-0.673747\pi\)
−0.519138 + 0.854690i \(0.673747\pi\)
\(128\) 0 0
\(129\) −2.79641 −0.246211
\(130\) 0 0
\(131\) −19.0152 −1.66137 −0.830684 0.556744i \(-0.812050\pi\)
−0.830684 + 0.556744i \(0.812050\pi\)
\(132\) 0 0
\(133\) 12.6468 1.09662
\(134\) 0 0
\(135\) 1.00000 0.0860663
\(136\) 0 0
\(137\) −14.7368 −1.25905 −0.629527 0.776979i \(-0.716751\pi\)
−0.629527 + 0.776979i \(0.716751\pi\)
\(138\) 0 0
\(139\) 5.09899 0.432491 0.216246 0.976339i \(-0.430619\pi\)
0.216246 + 0.976339i \(0.430619\pi\)
\(140\) 0 0
\(141\) −9.29362 −0.782664
\(142\) 0 0
\(143\) 1.39821 0.116924
\(144\) 0 0
\(145\) 8.36842 0.694959
\(146\) 0 0
\(147\) −11.6918 −0.964325
\(148\) 0 0
\(149\) −4.69182 −0.384369 −0.192185 0.981359i \(-0.561557\pi\)
−0.192185 + 0.981359i \(0.561557\pi\)
\(150\) 0 0
\(151\) −18.8864 −1.53696 −0.768479 0.639875i \(-0.778986\pi\)
−0.768479 + 0.639875i \(0.778986\pi\)
\(152\) 0 0
\(153\) 5.11982 0.413913
\(154\) 0 0
\(155\) 4.00000 0.321288
\(156\) 0 0
\(157\) 17.1440 1.36824 0.684121 0.729369i \(-0.260186\pi\)
0.684121 + 0.729369i \(0.260186\pi\)
\(158\) 0 0
\(159\) 2.19462 0.174045
\(160\) 0 0
\(161\) 38.7819 3.05644
\(162\) 0 0
\(163\) −0.194622 −0.0152440 −0.00762200 0.999971i \(-0.502426\pi\)
−0.00762200 + 0.999971i \(0.502426\pi\)
\(164\) 0 0
\(165\) 1.39821 0.108850
\(166\) 0 0
\(167\) 11.4432 0.885503 0.442752 0.896644i \(-0.354002\pi\)
0.442752 + 0.896644i \(0.354002\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) −2.92520 −0.223695
\(172\) 0 0
\(173\) 9.44322 0.717955 0.358977 0.933346i \(-0.383125\pi\)
0.358977 + 0.933346i \(0.383125\pi\)
\(174\) 0 0
\(175\) −4.32340 −0.326819
\(176\) 0 0
\(177\) 7.44322 0.559467
\(178\) 0 0
\(179\) 6.92520 0.517614 0.258807 0.965929i \(-0.416671\pi\)
0.258807 + 0.965929i \(0.416671\pi\)
\(180\) 0 0
\(181\) 7.48824 0.556596 0.278298 0.960495i \(-0.410230\pi\)
0.278298 + 0.960495i \(0.410230\pi\)
\(182\) 0 0
\(183\) 5.24860 0.387988
\(184\) 0 0
\(185\) −3.39821 −0.249841
\(186\) 0 0
\(187\) 7.15857 0.523486
\(188\) 0 0
\(189\) 4.32340 0.314481
\(190\) 0 0
\(191\) 12.0900 0.874804 0.437402 0.899266i \(-0.355899\pi\)
0.437402 + 0.899266i \(0.355899\pi\)
\(192\) 0 0
\(193\) 24.5630 1.76809 0.884043 0.467405i \(-0.154811\pi\)
0.884043 + 0.467405i \(0.154811\pi\)
\(194\) 0 0
\(195\) 1.00000 0.0716115
\(196\) 0 0
\(197\) 17.4432 1.24278 0.621389 0.783502i \(-0.286569\pi\)
0.621389 + 0.783502i \(0.286569\pi\)
\(198\) 0 0
\(199\) 14.8864 1.05527 0.527636 0.849470i \(-0.323078\pi\)
0.527636 + 0.849470i \(0.323078\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 36.1801 2.53934
\(204\) 0 0
\(205\) 0.601793 0.0420310
\(206\) 0 0
\(207\) −8.97021 −0.623473
\(208\) 0 0
\(209\) −4.09003 −0.282913
\(210\) 0 0
\(211\) 5.29362 0.364428 0.182214 0.983259i \(-0.441674\pi\)
0.182214 + 0.983259i \(0.441674\pi\)
\(212\) 0 0
\(213\) 10.0450 0.688273
\(214\) 0 0
\(215\) −2.79641 −0.190714
\(216\) 0 0
\(217\) 17.2936 1.17397
\(218\) 0 0
\(219\) 13.0152 0.879488
\(220\) 0 0
\(221\) 5.11982 0.344396
\(222\) 0 0
\(223\) −0.427995 −0.0286606 −0.0143303 0.999897i \(-0.504562\pi\)
−0.0143303 + 0.999897i \(0.504562\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) 21.6829 1.43914 0.719571 0.694419i \(-0.244338\pi\)
0.719571 + 0.694419i \(0.244338\pi\)
\(228\) 0 0
\(229\) 5.22441 0.345239 0.172619 0.984989i \(-0.444777\pi\)
0.172619 + 0.984989i \(0.444777\pi\)
\(230\) 0 0
\(231\) 6.04502 0.397733
\(232\) 0 0
\(233\) 11.6170 0.761056 0.380528 0.924769i \(-0.375742\pi\)
0.380528 + 0.924769i \(0.375742\pi\)
\(234\) 0 0
\(235\) −9.29362 −0.606249
\(236\) 0 0
\(237\) 1.95498 0.126990
\(238\) 0 0
\(239\) 11.2486 0.727612 0.363806 0.931475i \(-0.381477\pi\)
0.363806 + 0.931475i \(0.381477\pi\)
\(240\) 0 0
\(241\) −6.38924 −0.411567 −0.205784 0.978597i \(-0.565974\pi\)
−0.205784 + 0.978597i \(0.565974\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −11.6918 −0.746963
\(246\) 0 0
\(247\) −2.92520 −0.186126
\(248\) 0 0
\(249\) −17.2936 −1.09594
\(250\) 0 0
\(251\) 25.7216 1.62353 0.811767 0.583982i \(-0.198506\pi\)
0.811767 + 0.583982i \(0.198506\pi\)
\(252\) 0 0
\(253\) −12.5422 −0.788523
\(254\) 0 0
\(255\) 5.11982 0.320616
\(256\) 0 0
\(257\) −13.2728 −0.827934 −0.413967 0.910292i \(-0.635857\pi\)
−0.413967 + 0.910292i \(0.635857\pi\)
\(258\) 0 0
\(259\) −14.6918 −0.912906
\(260\) 0 0
\(261\) −8.36842 −0.517992
\(262\) 0 0
\(263\) 28.6081 1.76405 0.882024 0.471204i \(-0.156180\pi\)
0.882024 + 0.471204i \(0.156180\pi\)
\(264\) 0 0
\(265\) 2.19462 0.134815
\(266\) 0 0
\(267\) −4.04502 −0.247551
\(268\) 0 0
\(269\) 8.66763 0.528475 0.264237 0.964458i \(-0.414880\pi\)
0.264237 + 0.964458i \(0.414880\pi\)
\(270\) 0 0
\(271\) −29.6829 −1.80311 −0.901553 0.432669i \(-0.857572\pi\)
−0.901553 + 0.432669i \(0.857572\pi\)
\(272\) 0 0
\(273\) 4.32340 0.261664
\(274\) 0 0
\(275\) 1.39821 0.0843151
\(276\) 0 0
\(277\) 13.0540 0.784338 0.392169 0.919893i \(-0.371725\pi\)
0.392169 + 0.919893i \(0.371725\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) 9.70079 0.578700 0.289350 0.957223i \(-0.406561\pi\)
0.289350 + 0.957223i \(0.406561\pi\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) −2.92520 −0.173274
\(286\) 0 0
\(287\) 2.60179 0.153579
\(288\) 0 0
\(289\) 9.21255 0.541915
\(290\) 0 0
\(291\) −10.3234 −0.605169
\(292\) 0 0
\(293\) 22.6468 1.32304 0.661520 0.749927i \(-0.269912\pi\)
0.661520 + 0.749927i \(0.269912\pi\)
\(294\) 0 0
\(295\) 7.44322 0.433361
\(296\) 0 0
\(297\) −1.39821 −0.0811322
\(298\) 0 0
\(299\) −8.97021 −0.518761
\(300\) 0 0
\(301\) −12.0900 −0.696858
\(302\) 0 0
\(303\) 4.92520 0.282945
\(304\) 0 0
\(305\) 5.24860 0.300534
\(306\) 0 0
\(307\) 14.9494 0.853207 0.426603 0.904439i \(-0.359710\pi\)
0.426603 + 0.904439i \(0.359710\pi\)
\(308\) 0 0
\(309\) −1.29362 −0.0735913
\(310\) 0 0
\(311\) 6.49720 0.368423 0.184211 0.982887i \(-0.441027\pi\)
0.184211 + 0.982887i \(0.441027\pi\)
\(312\) 0 0
\(313\) 19.0361 1.07598 0.537991 0.842951i \(-0.319184\pi\)
0.537991 + 0.842951i \(0.319184\pi\)
\(314\) 0 0
\(315\) 4.32340 0.243596
\(316\) 0 0
\(317\) 12.4072 0.696856 0.348428 0.937336i \(-0.386716\pi\)
0.348428 + 0.937336i \(0.386716\pi\)
\(318\) 0 0
\(319\) −11.7008 −0.655118
\(320\) 0 0
\(321\) −0.751399 −0.0419390
\(322\) 0 0
\(323\) −14.9765 −0.833314
\(324\) 0 0
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) −14.5180 −0.802849
\(328\) 0 0
\(329\) −40.1801 −2.21520
\(330\) 0 0
\(331\) 25.5541 1.40458 0.702290 0.711891i \(-0.252161\pi\)
0.702290 + 0.711891i \(0.252161\pi\)
\(332\) 0 0
\(333\) 3.39821 0.186221
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −20.0305 −1.09113 −0.545564 0.838069i \(-0.683685\pi\)
−0.545564 + 0.838069i \(0.683685\pi\)
\(338\) 0 0
\(339\) 7.16484 0.389140
\(340\) 0 0
\(341\) −5.59283 −0.302869
\(342\) 0 0
\(343\) −20.2847 −1.09527
\(344\) 0 0
\(345\) −8.97021 −0.482940
\(346\) 0 0
\(347\) −26.8719 −1.44256 −0.721279 0.692644i \(-0.756446\pi\)
−0.721279 + 0.692644i \(0.756446\pi\)
\(348\) 0 0
\(349\) 23.4224 1.25377 0.626886 0.779111i \(-0.284329\pi\)
0.626886 + 0.779111i \(0.284329\pi\)
\(350\) 0 0
\(351\) −1.00000 −0.0533761
\(352\) 0 0
\(353\) −17.5333 −0.933201 −0.466601 0.884468i \(-0.654521\pi\)
−0.466601 + 0.884468i \(0.654521\pi\)
\(354\) 0 0
\(355\) 10.0450 0.533134
\(356\) 0 0
\(357\) 22.1350 1.17151
\(358\) 0 0
\(359\) 13.2936 0.701610 0.350805 0.936448i \(-0.385908\pi\)
0.350805 + 0.936448i \(0.385908\pi\)
\(360\) 0 0
\(361\) −10.4432 −0.549643
\(362\) 0 0
\(363\) 9.04502 0.474740
\(364\) 0 0
\(365\) 13.0152 0.681248
\(366\) 0 0
\(367\) −12.0900 −0.631095 −0.315547 0.948910i \(-0.602188\pi\)
−0.315547 + 0.948910i \(0.602188\pi\)
\(368\) 0 0
\(369\) −0.601793 −0.0313281
\(370\) 0 0
\(371\) 9.48824 0.492605
\(372\) 0 0
\(373\) 3.55118 0.183873 0.0919366 0.995765i \(-0.470694\pi\)
0.0919366 + 0.995765i \(0.470694\pi\)
\(374\) 0 0
\(375\) 1.00000 0.0516398
\(376\) 0 0
\(377\) −8.36842 −0.430996
\(378\) 0 0
\(379\) 12.6081 0.647632 0.323816 0.946120i \(-0.395034\pi\)
0.323816 + 0.946120i \(0.395034\pi\)
\(380\) 0 0
\(381\) 11.7008 0.599449
\(382\) 0 0
\(383\) −4.94602 −0.252730 −0.126365 0.991984i \(-0.540331\pi\)
−0.126365 + 0.991984i \(0.540331\pi\)
\(384\) 0 0
\(385\) 6.04502 0.308083
\(386\) 0 0
\(387\) 2.79641 0.142150
\(388\) 0 0
\(389\) 33.3628 1.69156 0.845781 0.533530i \(-0.179135\pi\)
0.845781 + 0.533530i \(0.179135\pi\)
\(390\) 0 0
\(391\) −45.9259 −2.32257
\(392\) 0 0
\(393\) 19.0152 0.959191
\(394\) 0 0
\(395\) 1.95498 0.0983659
\(396\) 0 0
\(397\) −7.18903 −0.360807 −0.180403 0.983593i \(-0.557740\pi\)
−0.180403 + 0.983593i \(0.557740\pi\)
\(398\) 0 0
\(399\) −12.6468 −0.633132
\(400\) 0 0
\(401\) 19.0361 0.950615 0.475308 0.879820i \(-0.342337\pi\)
0.475308 + 0.879820i \(0.342337\pi\)
\(402\) 0 0
\(403\) −4.00000 −0.199254
\(404\) 0 0
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) 4.75140 0.235518
\(408\) 0 0
\(409\) −21.5333 −1.06475 −0.532375 0.846508i \(-0.678701\pi\)
−0.532375 + 0.846508i \(0.678701\pi\)
\(410\) 0 0
\(411\) 14.7368 0.726915
\(412\) 0 0
\(413\) 32.1801 1.58348
\(414\) 0 0
\(415\) −17.2936 −0.848910
\(416\) 0 0
\(417\) −5.09899 −0.249699
\(418\) 0 0
\(419\) −35.9196 −1.75479 −0.877394 0.479771i \(-0.840720\pi\)
−0.877394 + 0.479771i \(0.840720\pi\)
\(420\) 0 0
\(421\) −23.5124 −1.14593 −0.572963 0.819581i \(-0.694206\pi\)
−0.572963 + 0.819581i \(0.694206\pi\)
\(422\) 0 0
\(423\) 9.29362 0.451871
\(424\) 0 0
\(425\) 5.11982 0.248348
\(426\) 0 0
\(427\) 22.6918 1.09813
\(428\) 0 0
\(429\) −1.39821 −0.0675061
\(430\) 0 0
\(431\) −10.5872 −0.509969 −0.254985 0.966945i \(-0.582070\pi\)
−0.254985 + 0.966945i \(0.582070\pi\)
\(432\) 0 0
\(433\) −38.4376 −1.84719 −0.923597 0.383364i \(-0.874765\pi\)
−0.923597 + 0.383364i \(0.874765\pi\)
\(434\) 0 0
\(435\) −8.36842 −0.401235
\(436\) 0 0
\(437\) 26.2396 1.25521
\(438\) 0 0
\(439\) −15.6378 −0.746354 −0.373177 0.927760i \(-0.621732\pi\)
−0.373177 + 0.927760i \(0.621732\pi\)
\(440\) 0 0
\(441\) 11.6918 0.556754
\(442\) 0 0
\(443\) 17.7875 0.845107 0.422554 0.906338i \(-0.361134\pi\)
0.422554 + 0.906338i \(0.361134\pi\)
\(444\) 0 0
\(445\) −4.04502 −0.191752
\(446\) 0 0
\(447\) 4.69182 0.221916
\(448\) 0 0
\(449\) 29.7279 1.40295 0.701473 0.712696i \(-0.252526\pi\)
0.701473 + 0.712696i \(0.252526\pi\)
\(450\) 0 0
\(451\) −0.841431 −0.0396214
\(452\) 0 0
\(453\) 18.8864 0.887363
\(454\) 0 0
\(455\) 4.32340 0.202684
\(456\) 0 0
\(457\) 3.61702 0.169197 0.0845986 0.996415i \(-0.473039\pi\)
0.0845986 + 0.996415i \(0.473039\pi\)
\(458\) 0 0
\(459\) −5.11982 −0.238973
\(460\) 0 0
\(461\) 12.1350 0.565186 0.282593 0.959240i \(-0.408805\pi\)
0.282593 + 0.959240i \(0.408805\pi\)
\(462\) 0 0
\(463\) 7.11982 0.330886 0.165443 0.986219i \(-0.447095\pi\)
0.165443 + 0.986219i \(0.447095\pi\)
\(464\) 0 0
\(465\) −4.00000 −0.185496
\(466\) 0 0
\(467\) −0.542218 −0.0250909 −0.0125454 0.999921i \(-0.503993\pi\)
−0.0125454 + 0.999921i \(0.503993\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −17.1440 −0.789954
\(472\) 0 0
\(473\) 3.90997 0.179781
\(474\) 0 0
\(475\) −2.92520 −0.134217
\(476\) 0 0
\(477\) −2.19462 −0.100485
\(478\) 0 0
\(479\) 17.7458 0.810826 0.405413 0.914134i \(-0.367128\pi\)
0.405413 + 0.914134i \(0.367128\pi\)
\(480\) 0 0
\(481\) 3.39821 0.154945
\(482\) 0 0
\(483\) −38.7819 −1.76464
\(484\) 0 0
\(485\) −10.3234 −0.468762
\(486\) 0 0
\(487\) −17.5270 −0.794224 −0.397112 0.917770i \(-0.629988\pi\)
−0.397112 + 0.917770i \(0.629988\pi\)
\(488\) 0 0
\(489\) 0.194622 0.00880112
\(490\) 0 0
\(491\) −19.4045 −0.875712 −0.437856 0.899045i \(-0.644262\pi\)
−0.437856 + 0.899045i \(0.644262\pi\)
\(492\) 0 0
\(493\) −42.8448 −1.92963
\(494\) 0 0
\(495\) −1.39821 −0.0628448
\(496\) 0 0
\(497\) 43.4287 1.94804
\(498\) 0 0
\(499\) −15.6620 −0.701129 −0.350565 0.936539i \(-0.614010\pi\)
−0.350565 + 0.936539i \(0.614010\pi\)
\(500\) 0 0
\(501\) −11.4432 −0.511246
\(502\) 0 0
\(503\) 8.90727 0.397156 0.198578 0.980085i \(-0.436368\pi\)
0.198578 + 0.980085i \(0.436368\pi\)
\(504\) 0 0
\(505\) 4.92520 0.219168
\(506\) 0 0
\(507\) −1.00000 −0.0444116
\(508\) 0 0
\(509\) 40.2251 1.78295 0.891473 0.453074i \(-0.149673\pi\)
0.891473 + 0.453074i \(0.149673\pi\)
\(510\) 0 0
\(511\) 56.2701 2.48924
\(512\) 0 0
\(513\) 2.92520 0.129151
\(514\) 0 0
\(515\) −1.29362 −0.0570036
\(516\) 0 0
\(517\) 12.9944 0.571493
\(518\) 0 0
\(519\) −9.44322 −0.414512
\(520\) 0 0
\(521\) −36.0305 −1.57852 −0.789262 0.614057i \(-0.789536\pi\)
−0.789262 + 0.614057i \(0.789536\pi\)
\(522\) 0 0
\(523\) −41.3836 −1.80958 −0.904790 0.425857i \(-0.859973\pi\)
−0.904790 + 0.425857i \(0.859973\pi\)
\(524\) 0 0
\(525\) 4.32340 0.188689
\(526\) 0 0
\(527\) −20.4793 −0.892091
\(528\) 0 0
\(529\) 57.4647 2.49847
\(530\) 0 0
\(531\) −7.44322 −0.323008
\(532\) 0 0
\(533\) −0.601793 −0.0260665
\(534\) 0 0
\(535\) −0.751399 −0.0324858
\(536\) 0 0
\(537\) −6.92520 −0.298844
\(538\) 0 0
\(539\) 16.3476 0.704141
\(540\) 0 0
\(541\) −29.3144 −1.26033 −0.630163 0.776463i \(-0.717012\pi\)
−0.630163 + 0.776463i \(0.717012\pi\)
\(542\) 0 0
\(543\) −7.48824 −0.321351
\(544\) 0 0
\(545\) −14.5180 −0.621884
\(546\) 0 0
\(547\) 30.5872 1.30782 0.653908 0.756574i \(-0.273128\pi\)
0.653908 + 0.756574i \(0.273128\pi\)
\(548\) 0 0
\(549\) −5.24860 −0.224005
\(550\) 0 0
\(551\) 24.4793 1.04285
\(552\) 0 0
\(553\) 8.45219 0.359424
\(554\) 0 0
\(555\) 3.39821 0.144246
\(556\) 0 0
\(557\) 13.9100 0.589384 0.294692 0.955592i \(-0.404783\pi\)
0.294692 + 0.955592i \(0.404783\pi\)
\(558\) 0 0
\(559\) 2.79641 0.118276
\(560\) 0 0
\(561\) −7.15857 −0.302235
\(562\) 0 0
\(563\) 35.5962 1.50020 0.750100 0.661324i \(-0.230005\pi\)
0.750100 + 0.661324i \(0.230005\pi\)
\(564\) 0 0
\(565\) 7.16484 0.301427
\(566\) 0 0
\(567\) −4.32340 −0.181566
\(568\) 0 0
\(569\) −9.44322 −0.395881 −0.197940 0.980214i \(-0.563425\pi\)
−0.197940 + 0.980214i \(0.563425\pi\)
\(570\) 0 0
\(571\) 18.3026 0.765939 0.382970 0.923761i \(-0.374901\pi\)
0.382970 + 0.923761i \(0.374901\pi\)
\(572\) 0 0
\(573\) −12.0900 −0.505068
\(574\) 0 0
\(575\) −8.97021 −0.374084
\(576\) 0 0
\(577\) 4.29295 0.178718 0.0893589 0.995999i \(-0.471518\pi\)
0.0893589 + 0.995999i \(0.471518\pi\)
\(578\) 0 0
\(579\) −24.5630 −1.02081
\(580\) 0 0
\(581\) −74.7673 −3.10187
\(582\) 0 0
\(583\) −3.06854 −0.127086
\(584\) 0 0
\(585\) −1.00000 −0.0413449
\(586\) 0 0
\(587\) 30.1980 1.24640 0.623202 0.782061i \(-0.285831\pi\)
0.623202 + 0.782061i \(0.285831\pi\)
\(588\) 0 0
\(589\) 11.7008 0.482123
\(590\) 0 0
\(591\) −17.4432 −0.717518
\(592\) 0 0
\(593\) 21.7908 0.894842 0.447421 0.894324i \(-0.352343\pi\)
0.447421 + 0.894324i \(0.352343\pi\)
\(594\) 0 0
\(595\) 22.1350 0.907448
\(596\) 0 0
\(597\) −14.8864 −0.609262
\(598\) 0 0
\(599\) 4.81434 0.196709 0.0983543 0.995151i \(-0.468642\pi\)
0.0983543 + 0.995151i \(0.468642\pi\)
\(600\) 0 0
\(601\) 0.991037 0.0404252 0.0202126 0.999796i \(-0.493566\pi\)
0.0202126 + 0.999796i \(0.493566\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 9.04502 0.367732
\(606\) 0 0
\(607\) −28.0900 −1.14014 −0.570070 0.821596i \(-0.693084\pi\)
−0.570070 + 0.821596i \(0.693084\pi\)
\(608\) 0 0
\(609\) −36.1801 −1.46609
\(610\) 0 0
\(611\) 9.29362 0.375980
\(612\) 0 0
\(613\) −23.3982 −0.945045 −0.472522 0.881319i \(-0.656656\pi\)
−0.472522 + 0.881319i \(0.656656\pi\)
\(614\) 0 0
\(615\) −0.601793 −0.0242666
\(616\) 0 0
\(617\) 28.0305 1.12846 0.564232 0.825616i \(-0.309172\pi\)
0.564232 + 0.825616i \(0.309172\pi\)
\(618\) 0 0
\(619\) −27.7521 −1.11545 −0.557725 0.830026i \(-0.688326\pi\)
−0.557725 + 0.830026i \(0.688326\pi\)
\(620\) 0 0
\(621\) 8.97021 0.359962
\(622\) 0 0
\(623\) −17.4882 −0.700652
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 4.09003 0.163340
\(628\) 0 0
\(629\) 17.3982 0.693712
\(630\) 0 0
\(631\) 50.2105 1.99885 0.999425 0.0339171i \(-0.0107982\pi\)
0.999425 + 0.0339171i \(0.0107982\pi\)
\(632\) 0 0
\(633\) −5.29362 −0.210402
\(634\) 0 0
\(635\) 11.7008 0.464332
\(636\) 0 0
\(637\) 11.6918 0.463247
\(638\) 0 0
\(639\) −10.0450 −0.397375
\(640\) 0 0
\(641\) −23.2936 −0.920043 −0.460021 0.887908i \(-0.652158\pi\)
−0.460021 + 0.887908i \(0.652158\pi\)
\(642\) 0 0
\(643\) 4.54222 0.179128 0.0895638 0.995981i \(-0.471453\pi\)
0.0895638 + 0.995981i \(0.471453\pi\)
\(644\) 0 0
\(645\) 2.79641 0.110109
\(646\) 0 0
\(647\) −2.73057 −0.107350 −0.0536750 0.998558i \(-0.517093\pi\)
−0.0536750 + 0.998558i \(0.517093\pi\)
\(648\) 0 0
\(649\) −10.4072 −0.408517
\(650\) 0 0
\(651\) −17.2936 −0.677790
\(652\) 0 0
\(653\) −49.5816 −1.94028 −0.970140 0.242547i \(-0.922017\pi\)
−0.970140 + 0.242547i \(0.922017\pi\)
\(654\) 0 0
\(655\) 19.0152 0.742986
\(656\) 0 0
\(657\) −13.0152 −0.507772
\(658\) 0 0
\(659\) 20.0513 0.781087 0.390544 0.920584i \(-0.372287\pi\)
0.390544 + 0.920584i \(0.372287\pi\)
\(660\) 0 0
\(661\) −15.5415 −0.604496 −0.302248 0.953229i \(-0.597737\pi\)
−0.302248 + 0.953229i \(0.597737\pi\)
\(662\) 0 0
\(663\) −5.11982 −0.198837
\(664\) 0 0
\(665\) −12.6468 −0.490422
\(666\) 0 0
\(667\) 75.0665 2.90659
\(668\) 0 0
\(669\) 0.427995 0.0165472
\(670\) 0 0
\(671\) −7.33863 −0.283305
\(672\) 0 0
\(673\) 15.2036 0.586055 0.293028 0.956104i \(-0.405337\pi\)
0.293028 + 0.956104i \(0.405337\pi\)
\(674\) 0 0
\(675\) −1.00000 −0.0384900
\(676\) 0 0
\(677\) 26.5422 1.02010 0.510050 0.860145i \(-0.329627\pi\)
0.510050 + 0.860145i \(0.329627\pi\)
\(678\) 0 0
\(679\) −44.6323 −1.71283
\(680\) 0 0
\(681\) −21.6829 −0.830889
\(682\) 0 0
\(683\) 34.1980 1.30855 0.654275 0.756257i \(-0.272974\pi\)
0.654275 + 0.756257i \(0.272974\pi\)
\(684\) 0 0
\(685\) 14.7368 0.563066
\(686\) 0 0
\(687\) −5.22441 −0.199324
\(688\) 0 0
\(689\) −2.19462 −0.0836085
\(690\) 0 0
\(691\) −35.6204 −1.35506 −0.677532 0.735494i \(-0.736950\pi\)
−0.677532 + 0.735494i \(0.736950\pi\)
\(692\) 0 0
\(693\) −6.04502 −0.229631
\(694\) 0 0
\(695\) −5.09899 −0.193416
\(696\) 0 0
\(697\) −3.08107 −0.116704
\(698\) 0 0
\(699\) −11.6170 −0.439396
\(700\) 0 0
\(701\) −32.6260 −1.23227 −0.616133 0.787642i \(-0.711302\pi\)
−0.616133 + 0.787642i \(0.711302\pi\)
\(702\) 0 0
\(703\) −9.94043 −0.374910
\(704\) 0 0
\(705\) 9.29362 0.350018
\(706\) 0 0
\(707\) 21.2936 0.800829
\(708\) 0 0
\(709\) 42.3989 1.59232 0.796162 0.605084i \(-0.206860\pi\)
0.796162 + 0.605084i \(0.206860\pi\)
\(710\) 0 0
\(711\) −1.95498 −0.0733176
\(712\) 0 0
\(713\) 35.8809 1.34375
\(714\) 0 0
\(715\) −1.39821 −0.0522900
\(716\) 0 0
\(717\) −11.2486 −0.420087
\(718\) 0 0
\(719\) 0.855989 0.0319230 0.0159615 0.999873i \(-0.494919\pi\)
0.0159615 + 0.999873i \(0.494919\pi\)
\(720\) 0 0
\(721\) −5.59283 −0.208288
\(722\) 0 0
\(723\) 6.38924 0.237619
\(724\) 0 0
\(725\) −8.36842 −0.310795
\(726\) 0 0
\(727\) 12.3476 0.457947 0.228973 0.973433i \(-0.426463\pi\)
0.228973 + 0.973433i \(0.426463\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 14.3171 0.529538
\(732\) 0 0
\(733\) −27.4882 −1.01530 −0.507651 0.861563i \(-0.669486\pi\)
−0.507651 + 0.861563i \(0.669486\pi\)
\(734\) 0 0
\(735\) 11.6918 0.431259
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 36.3989 1.33895 0.669477 0.742833i \(-0.266518\pi\)
0.669477 + 0.742833i \(0.266518\pi\)
\(740\) 0 0
\(741\) 2.92520 0.107460
\(742\) 0 0
\(743\) −35.2340 −1.29261 −0.646306 0.763078i \(-0.723687\pi\)
−0.646306 + 0.763078i \(0.723687\pi\)
\(744\) 0 0
\(745\) 4.69182 0.171895
\(746\) 0 0
\(747\) 17.2936 0.632740
\(748\) 0 0
\(749\) −3.24860 −0.118701
\(750\) 0 0
\(751\) 3.54781 0.129462 0.0647308 0.997903i \(-0.479381\pi\)
0.0647308 + 0.997903i \(0.479381\pi\)
\(752\) 0 0
\(753\) −25.7216 −0.937348
\(754\) 0 0
\(755\) 18.8864 0.687348
\(756\) 0 0
\(757\) −22.6052 −0.821599 −0.410799 0.911726i \(-0.634750\pi\)
−0.410799 + 0.911726i \(0.634750\pi\)
\(758\) 0 0
\(759\) 12.5422 0.455254
\(760\) 0 0
\(761\) 29.6233 1.07384 0.536922 0.843632i \(-0.319587\pi\)
0.536922 + 0.843632i \(0.319587\pi\)
\(762\) 0 0
\(763\) −62.7673 −2.27233
\(764\) 0 0
\(765\) −5.11982 −0.185107
\(766\) 0 0
\(767\) −7.44322 −0.268759
\(768\) 0 0
\(769\) 3.89204 0.140351 0.0701753 0.997535i \(-0.477644\pi\)
0.0701753 + 0.997535i \(0.477644\pi\)
\(770\) 0 0
\(771\) 13.2728 0.478008
\(772\) 0 0
\(773\) −15.1261 −0.544047 −0.272024 0.962291i \(-0.587693\pi\)
−0.272024 + 0.962291i \(0.587693\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 0 0
\(777\) 14.6918 0.527066
\(778\) 0 0
\(779\) 1.76036 0.0630715
\(780\) 0 0
\(781\) −14.0450 −0.502570
\(782\) 0 0
\(783\) 8.36842 0.299063
\(784\) 0 0
\(785\) −17.1440 −0.611896
\(786\) 0 0
\(787\) −7.14401 −0.254656 −0.127328 0.991861i \(-0.540640\pi\)
−0.127328 + 0.991861i \(0.540640\pi\)
\(788\) 0 0
\(789\) −28.6081 −1.01847
\(790\) 0 0
\(791\) 30.9765 1.10140
\(792\) 0 0
\(793\) −5.24860 −0.186383
\(794\) 0 0
\(795\) −2.19462 −0.0778352
\(796\) 0 0
\(797\) −24.6918 −0.874629 −0.437315 0.899309i \(-0.644070\pi\)
−0.437315 + 0.899309i \(0.644070\pi\)
\(798\) 0 0
\(799\) 47.5816 1.68332
\(800\) 0 0
\(801\) 4.04502 0.142924
\(802\) 0 0
\(803\) −18.1980 −0.642193
\(804\) 0 0
\(805\) −38.7819 −1.36688
\(806\) 0 0
\(807\) −8.66763 −0.305115
\(808\) 0 0
\(809\) −16.5872 −0.583176 −0.291588 0.956544i \(-0.594184\pi\)
−0.291588 + 0.956544i \(0.594184\pi\)
\(810\) 0 0
\(811\) 30.3684 1.06638 0.533190 0.845996i \(-0.320993\pi\)
0.533190 + 0.845996i \(0.320993\pi\)
\(812\) 0 0
\(813\) 29.6829 1.04102
\(814\) 0 0
\(815\) 0.194622 0.00681732
\(816\) 0 0
\(817\) −8.18006 −0.286184
\(818\) 0 0
\(819\) −4.32340 −0.151072
\(820\) 0 0
\(821\) −12.9010 −0.450248 −0.225124 0.974330i \(-0.572279\pi\)
−0.225124 + 0.974330i \(0.572279\pi\)
\(822\) 0 0
\(823\) −14.7064 −0.512632 −0.256316 0.966593i \(-0.582509\pi\)
−0.256316 + 0.966593i \(0.582509\pi\)
\(824\) 0 0
\(825\) −1.39821 −0.0486793
\(826\) 0 0
\(827\) 37.5928 1.30723 0.653615 0.756827i \(-0.273251\pi\)
0.653615 + 0.756827i \(0.273251\pi\)
\(828\) 0 0
\(829\) −29.3657 −1.01991 −0.509957 0.860200i \(-0.670339\pi\)
−0.509957 + 0.860200i \(0.670339\pi\)
\(830\) 0 0
\(831\) −13.0540 −0.452838
\(832\) 0 0
\(833\) 59.8600 2.07403
\(834\) 0 0
\(835\) −11.4432 −0.396009
\(836\) 0 0
\(837\) 4.00000 0.138260
\(838\) 0 0
\(839\) −18.8594 −0.651097 −0.325549 0.945525i \(-0.605549\pi\)
−0.325549 + 0.945525i \(0.605549\pi\)
\(840\) 0 0
\(841\) 41.0305 1.41484
\(842\) 0 0
\(843\) −9.70079 −0.334113
\(844\) 0 0
\(845\) −1.00000 −0.0344010
\(846\) 0 0
\(847\) 39.1053 1.34367
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −30.4826 −1.04493
\(852\) 0 0
\(853\) −39.5783 −1.35513 −0.677567 0.735461i \(-0.736966\pi\)
−0.677567 + 0.735461i \(0.736966\pi\)
\(854\) 0 0
\(855\) 2.92520 0.100040
\(856\) 0 0
\(857\) 36.0546 1.23160 0.615802 0.787901i \(-0.288832\pi\)
0.615802 + 0.787901i \(0.288832\pi\)
\(858\) 0 0
\(859\) −8.75140 −0.298594 −0.149297 0.988792i \(-0.547701\pi\)
−0.149297 + 0.988792i \(0.547701\pi\)
\(860\) 0 0
\(861\) −2.60179 −0.0886689
\(862\) 0 0
\(863\) −35.4141 −1.20551 −0.602755 0.797926i \(-0.705930\pi\)
−0.602755 + 0.797926i \(0.705930\pi\)
\(864\) 0 0
\(865\) −9.44322 −0.321079
\(866\) 0 0
\(867\) −9.21255 −0.312875
\(868\) 0 0
\(869\) −2.73347 −0.0927267
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 10.3234 0.349394
\(874\) 0 0
\(875\) 4.32340 0.146158
\(876\) 0 0
\(877\) 53.0665 1.79193 0.895964 0.444126i \(-0.146486\pi\)
0.895964 + 0.444126i \(0.146486\pi\)
\(878\) 0 0
\(879\) −22.6468 −0.763858
\(880\) 0 0
\(881\) −38.6468 −1.30204 −0.651022 0.759059i \(-0.725659\pi\)
−0.651022 + 0.759059i \(0.725659\pi\)
\(882\) 0 0
\(883\) −20.0000 −0.673054 −0.336527 0.941674i \(-0.609252\pi\)
−0.336527 + 0.941674i \(0.609252\pi\)
\(884\) 0 0
\(885\) −7.44322 −0.250201
\(886\) 0 0
\(887\) 38.2222 1.28338 0.641688 0.766966i \(-0.278235\pi\)
0.641688 + 0.766966i \(0.278235\pi\)
\(888\) 0 0
\(889\) 50.5872 1.69664
\(890\) 0 0
\(891\) 1.39821 0.0468417
\(892\) 0 0
\(893\) −27.1857 −0.909733
\(894\) 0 0
\(895\) −6.92520 −0.231484
\(896\) 0 0
\(897\) 8.97021 0.299507
\(898\) 0 0
\(899\) 33.4737 1.11641
\(900\) 0 0
\(901\) −11.2361 −0.374328
\(902\) 0 0
\(903\) 12.0900 0.402331
\(904\) 0 0
\(905\) −7.48824 −0.248917
\(906\) 0 0
\(907\) −38.8573 −1.29024 −0.645118 0.764083i \(-0.723192\pi\)
−0.645118 + 0.764083i \(0.723192\pi\)
\(908\) 0 0
\(909\) −4.92520 −0.163358
\(910\) 0 0
\(911\) 32.8269 1.08760 0.543801 0.839214i \(-0.316984\pi\)
0.543801 + 0.839214i \(0.316984\pi\)
\(912\) 0 0
\(913\) 24.1801 0.800243
\(914\) 0 0
\(915\) −5.24860 −0.173513
\(916\) 0 0
\(917\) 82.2105 2.71483
\(918\) 0 0
\(919\) −46.3151 −1.52779 −0.763897 0.645338i \(-0.776717\pi\)
−0.763897 + 0.645338i \(0.776717\pi\)
\(920\) 0 0
\(921\) −14.9494 −0.492599
\(922\) 0 0
\(923\) −10.0450 −0.330636
\(924\) 0 0
\(925\) 3.39821 0.111732
\(926\) 0 0
\(927\) 1.29362 0.0424880
\(928\) 0 0
\(929\) −24.4343 −0.801662 −0.400831 0.916152i \(-0.631279\pi\)
−0.400831 + 0.916152i \(0.631279\pi\)
\(930\) 0 0
\(931\) −34.2009 −1.12089
\(932\) 0 0
\(933\) −6.49720 −0.212709
\(934\) 0 0
\(935\) −7.15857 −0.234110
\(936\) 0 0
\(937\) 14.6885 0.479851 0.239925 0.970791i \(-0.422877\pi\)
0.239925 + 0.970791i \(0.422877\pi\)
\(938\) 0 0
\(939\) −19.0361 −0.621218
\(940\) 0 0
\(941\) 12.0034 0.391299 0.195649 0.980674i \(-0.437319\pi\)
0.195649 + 0.980674i \(0.437319\pi\)
\(942\) 0 0
\(943\) 5.39821 0.175790
\(944\) 0 0
\(945\) −4.32340 −0.140640
\(946\) 0 0
\(947\) 35.7008 1.16012 0.580060 0.814574i \(-0.303029\pi\)
0.580060 + 0.814574i \(0.303029\pi\)
\(948\) 0 0
\(949\) −13.0152 −0.422492
\(950\) 0 0
\(951\) −12.4072 −0.402330
\(952\) 0 0
\(953\) −28.1738 −0.912639 −0.456319 0.889816i \(-0.650833\pi\)
−0.456319 + 0.889816i \(0.650833\pi\)
\(954\) 0 0
\(955\) −12.0900 −0.391224
\(956\) 0 0
\(957\) 11.7008 0.378233
\(958\) 0 0
\(959\) 63.7133 2.05741
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 0 0
\(963\) 0.751399 0.0242135
\(964\) 0 0
\(965\) −24.5630 −0.790712
\(966\) 0 0
\(967\) −0.685559 −0.0220461 −0.0110230 0.999939i \(-0.503509\pi\)
−0.0110230 + 0.999939i \(0.503509\pi\)
\(968\) 0 0
\(969\) 14.9765 0.481114
\(970\) 0 0
\(971\) 33.6925 1.08124 0.540622 0.841266i \(-0.318189\pi\)
0.540622 + 0.841266i \(0.318189\pi\)
\(972\) 0 0
\(973\) −22.0450 −0.706731
\(974\) 0 0
\(975\) −1.00000 −0.0320256
\(976\) 0 0
\(977\) −38.4793 −1.23106 −0.615531 0.788113i \(-0.711058\pi\)
−0.615531 + 0.788113i \(0.711058\pi\)
\(978\) 0 0
\(979\) 5.65577 0.180759
\(980\) 0 0
\(981\) 14.5180 0.463525
\(982\) 0 0
\(983\) −33.7312 −1.07586 −0.537930 0.842990i \(-0.680793\pi\)
−0.537930 + 0.842990i \(0.680793\pi\)
\(984\) 0 0
\(985\) −17.4432 −0.555787
\(986\) 0 0
\(987\) 40.1801 1.27895
\(988\) 0 0
\(989\) −25.0844 −0.797639
\(990\) 0 0
\(991\) 33.5366 1.06533 0.532663 0.846327i \(-0.321191\pi\)
0.532663 + 0.846327i \(0.321191\pi\)
\(992\) 0 0
\(993\) −25.5541 −0.810934
\(994\) 0 0
\(995\) −14.8864 −0.471932
\(996\) 0 0
\(997\) −54.2284 −1.71743 −0.858716 0.512452i \(-0.828737\pi\)
−0.858716 + 0.512452i \(0.828737\pi\)
\(998\) 0 0
\(999\) −3.39821 −0.107515
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 6240.2.a.bw.1.1 3
4.3 odd 2 6240.2.a.cb.1.3 yes 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6240.2.a.bw.1.1 3 1.1 even 1 trivial
6240.2.a.cb.1.3 yes 3 4.3 odd 2