Properties

Label 7623.2.a.ck.1.1
Level 7623
Weight 2
Character 7623.1
Self dual yes
Analytic conductor 60.870
Analytic rank 1
Dimension 4
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 7623 = 3^{2} \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 7623.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.8699614608\)
Analytic rank: \(1\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{7})\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.57794\)
Character \(\chi\) = 7623.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.41421 q^{2} -2.64575 q^{5} +1.00000 q^{7} +2.82843 q^{8} +O(q^{10})\) \(q-1.41421 q^{2} -2.64575 q^{5} +1.00000 q^{7} +2.82843 q^{8} +3.74166 q^{10} +1.74166 q^{13} -1.41421 q^{14} -4.00000 q^{16} -0.182676 q^{17} -1.74166 q^{19} +6.70572 q^{23} +2.00000 q^{25} -2.46308 q^{26} +6.70572 q^{29} -9.48331 q^{31} +0.258343 q^{34} -2.64575 q^{35} -11.4833 q^{37} +2.46308 q^{38} -7.48331 q^{40} +5.65685 q^{41} -1.00000 q^{43} -9.48331 q^{46} -0.182676 q^{47} +1.00000 q^{49} -2.82843 q^{50} -7.75458 q^{53} +2.82843 q^{56} -9.48331 q^{58} +3.01110 q^{59} -5.74166 q^{61} +13.4114 q^{62} +8.00000 q^{64} -4.60799 q^{65} +8.48331 q^{67} +3.74166 q^{70} -1.41421 q^{71} -8.25834 q^{73} +16.2399 q^{74} +1.48331 q^{79} +10.5830 q^{80} -8.00000 q^{82} -5.83953 q^{83} +0.483315 q^{85} +1.41421 q^{86} +11.1310 q^{89} +1.74166 q^{91} +0.258343 q^{94} +4.60799 q^{95} +15.2250 q^{97} -1.41421 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{7} + O(q^{10}) \) \( 4q + 4q^{7} - 8q^{13} - 16q^{16} + 8q^{19} + 8q^{25} - 8q^{31} + 16q^{34} - 16q^{37} - 4q^{43} - 8q^{46} + 4q^{49} - 8q^{58} - 8q^{61} + 32q^{64} + 4q^{67} - 48q^{73} - 24q^{79} - 32q^{82} - 28q^{85} - 8q^{91} + 16q^{94} + 16q^{97} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.41421 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(3\) 0 0
\(4\) 0 0
\(5\) −2.64575 −1.18322 −0.591608 0.806226i \(-0.701507\pi\)
−0.591608 + 0.806226i \(0.701507\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 2.82843 1.00000
\(9\) 0 0
\(10\) 3.74166 1.18322
\(11\) 0 0
\(12\) 0 0
\(13\) 1.74166 0.483049 0.241524 0.970395i \(-0.422353\pi\)
0.241524 + 0.970395i \(0.422353\pi\)
\(14\) −1.41421 −0.377964
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) −0.182676 −0.0443054 −0.0221527 0.999755i \(-0.507052\pi\)
−0.0221527 + 0.999755i \(0.507052\pi\)
\(18\) 0 0
\(19\) −1.74166 −0.399564 −0.199782 0.979840i \(-0.564023\pi\)
−0.199782 + 0.979840i \(0.564023\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.70572 1.39824 0.699119 0.715005i \(-0.253576\pi\)
0.699119 + 0.715005i \(0.253576\pi\)
\(24\) 0 0
\(25\) 2.00000 0.400000
\(26\) −2.46308 −0.483049
\(27\) 0 0
\(28\) 0 0
\(29\) 6.70572 1.24522 0.622610 0.782532i \(-0.286072\pi\)
0.622610 + 0.782532i \(0.286072\pi\)
\(30\) 0 0
\(31\) −9.48331 −1.70325 −0.851627 0.524149i \(-0.824384\pi\)
−0.851627 + 0.524149i \(0.824384\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0.258343 0.0443054
\(35\) −2.64575 −0.447214
\(36\) 0 0
\(37\) −11.4833 −1.88785 −0.943923 0.330167i \(-0.892895\pi\)
−0.943923 + 0.330167i \(0.892895\pi\)
\(38\) 2.46308 0.399564
\(39\) 0 0
\(40\) −7.48331 −1.18322
\(41\) 5.65685 0.883452 0.441726 0.897150i \(-0.354366\pi\)
0.441726 + 0.897150i \(0.354366\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −9.48331 −1.39824
\(47\) −0.182676 −0.0266460 −0.0133230 0.999911i \(-0.504241\pi\)
−0.0133230 + 0.999911i \(0.504241\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −2.82843 −0.400000
\(51\) 0 0
\(52\) 0 0
\(53\) −7.75458 −1.06517 −0.532587 0.846376i \(-0.678780\pi\)
−0.532587 + 0.846376i \(0.678780\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 2.82843 0.377964
\(57\) 0 0
\(58\) −9.48331 −1.24522
\(59\) 3.01110 0.392012 0.196006 0.980603i \(-0.437203\pi\)
0.196006 + 0.980603i \(0.437203\pi\)
\(60\) 0 0
\(61\) −5.74166 −0.735144 −0.367572 0.929995i \(-0.619811\pi\)
−0.367572 + 0.929995i \(0.619811\pi\)
\(62\) 13.4114 1.70325
\(63\) 0 0
\(64\) 8.00000 1.00000
\(65\) −4.60799 −0.571551
\(66\) 0 0
\(67\) 8.48331 1.03640 0.518201 0.855259i \(-0.326602\pi\)
0.518201 + 0.855259i \(0.326602\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 3.74166 0.447214
\(71\) −1.41421 −0.167836 −0.0839181 0.996473i \(-0.526743\pi\)
−0.0839181 + 0.996473i \(0.526743\pi\)
\(72\) 0 0
\(73\) −8.25834 −0.966566 −0.483283 0.875464i \(-0.660556\pi\)
−0.483283 + 0.875464i \(0.660556\pi\)
\(74\) 16.2399 1.88785
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 1.48331 0.166886 0.0834430 0.996513i \(-0.473408\pi\)
0.0834430 + 0.996513i \(0.473408\pi\)
\(80\) 10.5830 1.18322
\(81\) 0 0
\(82\) −8.00000 −0.883452
\(83\) −5.83953 −0.640972 −0.320486 0.947253i \(-0.603846\pi\)
−0.320486 + 0.947253i \(0.603846\pi\)
\(84\) 0 0
\(85\) 0.483315 0.0524228
\(86\) 1.41421 0.152499
\(87\) 0 0
\(88\) 0 0
\(89\) 11.1310 1.17989 0.589944 0.807444i \(-0.299150\pi\)
0.589944 + 0.807444i \(0.299150\pi\)
\(90\) 0 0
\(91\) 1.74166 0.182575
\(92\) 0 0
\(93\) 0 0
\(94\) 0.258343 0.0266460
\(95\) 4.60799 0.472770
\(96\) 0 0
\(97\) 15.2250 1.54586 0.772931 0.634490i \(-0.218790\pi\)
0.772931 + 0.634490i \(0.218790\pi\)
\(98\) −1.41421 −0.142857
\(99\) 0 0
\(100\) 0 0
\(101\) 13.9595 1.38902 0.694509 0.719484i \(-0.255622\pi\)
0.694509 + 0.719484i \(0.255622\pi\)
\(102\) 0 0
\(103\) 9.22497 0.908964 0.454482 0.890756i \(-0.349824\pi\)
0.454482 + 0.890756i \(0.349824\pi\)
\(104\) 4.92615 0.483049
\(105\) 0 0
\(106\) 10.9666 1.06517
\(107\) −1.04886 −0.101397 −0.0506987 0.998714i \(-0.516145\pi\)
−0.0506987 + 0.998714i \(0.516145\pi\)
\(108\) 0 0
\(109\) 1.51669 0.145272 0.0726360 0.997359i \(-0.476859\pi\)
0.0726360 + 0.997359i \(0.476859\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −4.00000 −0.377964
\(113\) −5.29150 −0.497783 −0.248891 0.968531i \(-0.580066\pi\)
−0.248891 + 0.968531i \(0.580066\pi\)
\(114\) 0 0
\(115\) −17.7417 −1.65442
\(116\) 0 0
\(117\) 0 0
\(118\) −4.25834 −0.392012
\(119\) −0.182676 −0.0167459
\(120\) 0 0
\(121\) 0 0
\(122\) 8.11993 0.735144
\(123\) 0 0
\(124\) 0 0
\(125\) 7.93725 0.709930
\(126\) 0 0
\(127\) −1.51669 −0.134584 −0.0672920 0.997733i \(-0.521436\pi\)
−0.0672920 + 0.997733i \(0.521436\pi\)
\(128\) −11.3137 −1.00000
\(129\) 0 0
\(130\) 6.51669 0.571551
\(131\) −13.9595 −1.21964 −0.609822 0.792539i \(-0.708759\pi\)
−0.609822 + 0.792539i \(0.708759\pi\)
\(132\) 0 0
\(133\) −1.74166 −0.151021
\(134\) −11.9972 −1.03640
\(135\) 0 0
\(136\) −0.516685 −0.0443054
\(137\) −22.9456 −1.96037 −0.980186 0.198077i \(-0.936530\pi\)
−0.980186 + 0.198077i \(0.936530\pi\)
\(138\) 0 0
\(139\) −3.74166 −0.317363 −0.158682 0.987330i \(-0.550724\pi\)
−0.158682 + 0.987330i \(0.550724\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 2.00000 0.167836
\(143\) 0 0
\(144\) 0 0
\(145\) −17.7417 −1.47336
\(146\) 11.6791 0.966566
\(147\) 0 0
\(148\) 0 0
\(149\) −2.14492 −0.175718 −0.0878592 0.996133i \(-0.528003\pi\)
−0.0878592 + 0.996133i \(0.528003\pi\)
\(150\) 0 0
\(151\) −22.4833 −1.82967 −0.914833 0.403832i \(-0.867678\pi\)
−0.914833 + 0.403832i \(0.867678\pi\)
\(152\) −4.92615 −0.399564
\(153\) 0 0
\(154\) 0 0
\(155\) 25.0905 2.01532
\(156\) 0 0
\(157\) 16.9666 1.35408 0.677042 0.735944i \(-0.263261\pi\)
0.677042 + 0.735944i \(0.263261\pi\)
\(158\) −2.09772 −0.166886
\(159\) 0 0
\(160\) 0 0
\(161\) 6.70572 0.528484
\(162\) 0 0
\(163\) 20.4499 1.60176 0.800882 0.598823i \(-0.204365\pi\)
0.800882 + 0.598823i \(0.204365\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 8.25834 0.640972
\(167\) 13.9595 1.08022 0.540108 0.841596i \(-0.318383\pi\)
0.540108 + 0.841596i \(0.318383\pi\)
\(168\) 0 0
\(169\) −9.96663 −0.766664
\(170\) −0.683510 −0.0524228
\(171\) 0 0
\(172\) 0 0
\(173\) 10.7657 0.818500 0.409250 0.912422i \(-0.365790\pi\)
0.409250 + 0.912422i \(0.365790\pi\)
\(174\) 0 0
\(175\) 2.00000 0.151186
\(176\) 0 0
\(177\) 0 0
\(178\) −15.7417 −1.17989
\(179\) 14.1421 1.05703 0.528516 0.848923i \(-0.322748\pi\)
0.528516 + 0.848923i \(0.322748\pi\)
\(180\) 0 0
\(181\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(182\) −2.46308 −0.182575
\(183\) 0 0
\(184\) 18.9666 1.39824
\(185\) 30.3820 2.23373
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) −6.51669 −0.472770
\(191\) −1.41421 −0.102329 −0.0511645 0.998690i \(-0.516293\pi\)
−0.0511645 + 0.998690i \(0.516293\pi\)
\(192\) 0 0
\(193\) −1.51669 −0.109173 −0.0545867 0.998509i \(-0.517384\pi\)
−0.0545867 + 0.998509i \(0.517384\pi\)
\(194\) −21.5314 −1.54586
\(195\) 0 0
\(196\) 0 0
\(197\) −11.6791 −0.832099 −0.416049 0.909342i \(-0.636586\pi\)
−0.416049 + 0.909342i \(0.636586\pi\)
\(198\) 0 0
\(199\) 9.74166 0.690568 0.345284 0.938498i \(-0.387783\pi\)
0.345284 + 0.938498i \(0.387783\pi\)
\(200\) 5.65685 0.400000
\(201\) 0 0
\(202\) −19.7417 −1.38902
\(203\) 6.70572 0.470649
\(204\) 0 0
\(205\) −14.9666 −1.04531
\(206\) −13.0461 −0.908964
\(207\) 0 0
\(208\) −6.96663 −0.483049
\(209\) 0 0
\(210\) 0 0
\(211\) −24.4833 −1.68550 −0.842750 0.538304i \(-0.819065\pi\)
−0.842750 + 0.538304i \(0.819065\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 1.48331 0.101397
\(215\) 2.64575 0.180439
\(216\) 0 0
\(217\) −9.48331 −0.643769
\(218\) −2.14492 −0.145272
\(219\) 0 0
\(220\) 0 0
\(221\) −0.318159 −0.0214017
\(222\) 0 0
\(223\) 2.51669 0.168530 0.0842649 0.996443i \(-0.473146\pi\)
0.0842649 + 0.996443i \(0.473146\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 7.48331 0.497783
\(227\) −11.8617 −0.787291 −0.393646 0.919262i \(-0.628786\pi\)
−0.393646 + 0.919262i \(0.628786\pi\)
\(228\) 0 0
\(229\) −1.48331 −0.0980202 −0.0490101 0.998798i \(-0.515607\pi\)
−0.0490101 + 0.998798i \(0.515607\pi\)
\(230\) 25.0905 1.65442
\(231\) 0 0
\(232\) 18.9666 1.24522
\(233\) 14.8256 0.971260 0.485630 0.874164i \(-0.338590\pi\)
0.485630 + 0.874164i \(0.338590\pi\)
\(234\) 0 0
\(235\) 0.483315 0.0315280
\(236\) 0 0
\(237\) 0 0
\(238\) 0.258343 0.0167459
\(239\) −2.46308 −0.159323 −0.0796616 0.996822i \(-0.525384\pi\)
−0.0796616 + 0.996822i \(0.525384\pi\)
\(240\) 0 0
\(241\) −19.2250 −1.23839 −0.619195 0.785238i \(-0.712541\pi\)
−0.619195 + 0.785238i \(0.712541\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.64575 −0.169031
\(246\) 0 0
\(247\) −3.03337 −0.193009
\(248\) −26.8229 −1.70325
\(249\) 0 0
\(250\) −11.2250 −0.709930
\(251\) 19.0683 1.20358 0.601790 0.798655i \(-0.294455\pi\)
0.601790 + 0.798655i \(0.294455\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 2.14492 0.134584
\(255\) 0 0
\(256\) 0 0
\(257\) 16.4225 1.02441 0.512205 0.858863i \(-0.328829\pi\)
0.512205 + 0.858863i \(0.328829\pi\)
\(258\) 0 0
\(259\) −11.4833 −0.713538
\(260\) 0 0
\(261\) 0 0
\(262\) 19.7417 1.21964
\(263\) −11.6319 −0.717252 −0.358626 0.933481i \(-0.616755\pi\)
−0.358626 + 0.933481i \(0.616755\pi\)
\(264\) 0 0
\(265\) 20.5167 1.26033
\(266\) 2.46308 0.151021
\(267\) 0 0
\(268\) 0 0
\(269\) 7.38923 0.450529 0.225265 0.974298i \(-0.427675\pi\)
0.225265 + 0.974298i \(0.427675\pi\)
\(270\) 0 0
\(271\) 20.9666 1.27363 0.636816 0.771016i \(-0.280251\pi\)
0.636816 + 0.771016i \(0.280251\pi\)
\(272\) 0.730703 0.0443054
\(273\) 0 0
\(274\) 32.4499 1.96037
\(275\) 0 0
\(276\) 0 0
\(277\) 9.96663 0.598837 0.299418 0.954122i \(-0.403207\pi\)
0.299418 + 0.954122i \(0.403207\pi\)
\(278\) 5.29150 0.317363
\(279\) 0 0
\(280\) −7.48331 −0.447214
\(281\) −4.92615 −0.293870 −0.146935 0.989146i \(-0.546941\pi\)
−0.146935 + 0.989146i \(0.546941\pi\)
\(282\) 0 0
\(283\) −20.9666 −1.24634 −0.623168 0.782088i \(-0.714155\pi\)
−0.623168 + 0.782088i \(0.714155\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 5.65685 0.333914
\(288\) 0 0
\(289\) −16.9666 −0.998037
\(290\) 25.0905 1.47336
\(291\) 0 0
\(292\) 0 0
\(293\) 22.8101 1.33258 0.666290 0.745693i \(-0.267881\pi\)
0.666290 + 0.745693i \(0.267881\pi\)
\(294\) 0 0
\(295\) −7.96663 −0.463835
\(296\) −32.4797 −1.88785
\(297\) 0 0
\(298\) 3.03337 0.175718
\(299\) 11.6791 0.675417
\(300\) 0 0
\(301\) −1.00000 −0.0576390
\(302\) 31.7962 1.82967
\(303\) 0 0
\(304\) 6.96663 0.399564
\(305\) 15.1910 0.869834
\(306\) 0 0
\(307\) 30.7083 1.75261 0.876307 0.481753i \(-0.160000\pi\)
0.876307 + 0.481753i \(0.160000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −35.4833 −2.01532
\(311\) −32.2970 −1.83140 −0.915699 0.401866i \(-0.868362\pi\)
−0.915699 + 0.401866i \(0.868362\pi\)
\(312\) 0 0
\(313\) −19.4833 −1.10126 −0.550631 0.834749i \(-0.685613\pi\)
−0.550631 + 0.834749i \(0.685613\pi\)
\(314\) −23.9944 −1.35408
\(315\) 0 0
\(316\) 0 0
\(317\) −1.04886 −0.0589100 −0.0294550 0.999566i \(-0.509377\pi\)
−0.0294550 + 0.999566i \(0.509377\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −21.1660 −1.18322
\(321\) 0 0
\(322\) −9.48331 −0.528484
\(323\) 0.318159 0.0177028
\(324\) 0 0
\(325\) 3.48331 0.193220
\(326\) −28.9206 −1.60176
\(327\) 0 0
\(328\) 16.0000 0.883452
\(329\) −0.182676 −0.0100712
\(330\) 0 0
\(331\) 5.51669 0.303224 0.151612 0.988440i \(-0.451554\pi\)
0.151612 + 0.988440i \(0.451554\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −19.7417 −1.08022
\(335\) −22.4447 −1.22629
\(336\) 0 0
\(337\) −6.96663 −0.379496 −0.189748 0.981833i \(-0.560767\pi\)
−0.189748 + 0.981833i \(0.560767\pi\)
\(338\) 14.0949 0.766664
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −2.82843 −0.152499
\(345\) 0 0
\(346\) −15.2250 −0.818500
\(347\) 30.3348 1.62846 0.814229 0.580544i \(-0.197160\pi\)
0.814229 + 0.580544i \(0.197160\pi\)
\(348\) 0 0
\(349\) −18.5167 −0.991175 −0.495588 0.868558i \(-0.665047\pi\)
−0.495588 + 0.868558i \(0.665047\pi\)
\(350\) −2.82843 −0.151186
\(351\) 0 0
\(352\) 0 0
\(353\) −33.5758 −1.78706 −0.893529 0.449005i \(-0.851778\pi\)
−0.893529 + 0.449005i \(0.851778\pi\)
\(354\) 0 0
\(355\) 3.74166 0.198587
\(356\) 0 0
\(357\) 0 0
\(358\) −20.0000 −1.05703
\(359\) −28.2371 −1.49030 −0.745148 0.666899i \(-0.767621\pi\)
−0.745148 + 0.666899i \(0.767621\pi\)
\(360\) 0 0
\(361\) −15.9666 −0.840349
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 21.8495 1.14366
\(366\) 0 0
\(367\) −5.22497 −0.272741 −0.136371 0.990658i \(-0.543544\pi\)
−0.136371 + 0.990658i \(0.543544\pi\)
\(368\) −26.8229 −1.39824
\(369\) 0 0
\(370\) −42.9666 −2.23373
\(371\) −7.75458 −0.402598
\(372\) 0 0
\(373\) 25.4499 1.31775 0.658874 0.752253i \(-0.271033\pi\)
0.658874 + 0.752253i \(0.271033\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −0.516685 −0.0266460
\(377\) 11.6791 0.601502
\(378\) 0 0
\(379\) −19.5167 −1.00250 −0.501252 0.865301i \(-0.667127\pi\)
−0.501252 + 0.865301i \(0.667127\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 2.00000 0.102329
\(383\) 15.6918 0.801815 0.400908 0.916119i \(-0.368695\pi\)
0.400908 + 0.916119i \(0.368695\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 2.14492 0.109173
\(387\) 0 0
\(388\) 0 0
\(389\) −22.9928 −1.16578 −0.582890 0.812551i \(-0.698078\pi\)
−0.582890 + 0.812551i \(0.698078\pi\)
\(390\) 0 0
\(391\) −1.22497 −0.0619495
\(392\) 2.82843 0.142857
\(393\) 0 0
\(394\) 16.5167 0.832099
\(395\) −3.92448 −0.197462
\(396\) 0 0
\(397\) −13.4833 −0.676708 −0.338354 0.941019i \(-0.609870\pi\)
−0.338354 + 0.941019i \(0.609870\pi\)
\(398\) −13.7768 −0.690568
\(399\) 0 0
\(400\) −8.00000 −0.400000
\(401\) −2.46308 −0.123000 −0.0615001 0.998107i \(-0.519588\pi\)
−0.0615001 + 0.998107i \(0.519588\pi\)
\(402\) 0 0
\(403\) −16.5167 −0.822755
\(404\) 0 0
\(405\) 0 0
\(406\) −9.48331 −0.470649
\(407\) 0 0
\(408\) 0 0
\(409\) −13.2250 −0.653933 −0.326966 0.945036i \(-0.606026\pi\)
−0.326966 + 0.945036i \(0.606026\pi\)
\(410\) 21.1660 1.04531
\(411\) 0 0
\(412\) 0 0
\(413\) 3.01110 0.148167
\(414\) 0 0
\(415\) 15.4499 0.758408
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 18.1549 0.886925 0.443463 0.896293i \(-0.353750\pi\)
0.443463 + 0.896293i \(0.353750\pi\)
\(420\) 0 0
\(421\) −22.4833 −1.09577 −0.547885 0.836554i \(-0.684567\pi\)
−0.547885 + 0.836554i \(0.684567\pi\)
\(422\) 34.6246 1.68550
\(423\) 0 0
\(424\) −21.9333 −1.06517
\(425\) −0.365352 −0.0177222
\(426\) 0 0
\(427\) −5.74166 −0.277858
\(428\) 0 0
\(429\) 0 0
\(430\) −3.74166 −0.180439
\(431\) −15.8745 −0.764648 −0.382324 0.924028i \(-0.624876\pi\)
−0.382324 + 0.924028i \(0.624876\pi\)
\(432\) 0 0
\(433\) 5.74166 0.275926 0.137963 0.990437i \(-0.455944\pi\)
0.137963 + 0.990437i \(0.455944\pi\)
\(434\) 13.4114 0.643769
\(435\) 0 0
\(436\) 0 0
\(437\) −11.6791 −0.558685
\(438\) 0 0
\(439\) −4.51669 −0.215570 −0.107785 0.994174i \(-0.534376\pi\)
−0.107785 + 0.994174i \(0.534376\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0.449944 0.0214017
\(443\) −37.8184 −1.79681 −0.898404 0.439171i \(-0.855272\pi\)
−0.898404 + 0.439171i \(0.855272\pi\)
\(444\) 0 0
\(445\) −29.4499 −1.39606
\(446\) −3.55913 −0.168530
\(447\) 0 0
\(448\) 8.00000 0.377964
\(449\) −21.5314 −1.01613 −0.508064 0.861319i \(-0.669639\pi\)
−0.508064 + 0.861319i \(0.669639\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 16.7750 0.787291
\(455\) −4.60799 −0.216026
\(456\) 0 0
\(457\) −23.0000 −1.07589 −0.537947 0.842978i \(-0.680800\pi\)
−0.537947 + 0.842978i \(0.680800\pi\)
\(458\) 2.09772 0.0980202
\(459\) 0 0
\(460\) 0 0
\(461\) 29.8340 1.38951 0.694753 0.719248i \(-0.255514\pi\)
0.694753 + 0.719248i \(0.255514\pi\)
\(462\) 0 0
\(463\) −2.51669 −0.116960 −0.0584801 0.998289i \(-0.518625\pi\)
−0.0584801 + 0.998289i \(0.518625\pi\)
\(464\) −26.8229 −1.24522
\(465\) 0 0
\(466\) −20.9666 −0.971260
\(467\) −32.1144 −1.48608 −0.743038 0.669249i \(-0.766616\pi\)
−0.743038 + 0.669249i \(0.766616\pi\)
\(468\) 0 0
\(469\) 8.48331 0.391723
\(470\) −0.683510 −0.0315280
\(471\) 0 0
\(472\) 8.51669 0.392012
\(473\) 0 0
\(474\) 0 0
\(475\) −3.48331 −0.159825
\(476\) 0 0
\(477\) 0 0
\(478\) 3.48331 0.159323
\(479\) −39.0500 −1.78424 −0.892119 0.451801i \(-0.850782\pi\)
−0.892119 + 0.451801i \(0.850782\pi\)
\(480\) 0 0
\(481\) −20.0000 −0.911922
\(482\) 27.1882 1.23839
\(483\) 0 0
\(484\) 0 0
\(485\) −40.2815 −1.82909
\(486\) 0 0
\(487\) 20.4833 0.928188 0.464094 0.885786i \(-0.346380\pi\)
0.464094 + 0.885786i \(0.346380\pi\)
\(488\) −16.2399 −0.735144
\(489\) 0 0
\(490\) 3.74166 0.169031
\(491\) 29.6985 1.34027 0.670137 0.742237i \(-0.266235\pi\)
0.670137 + 0.742237i \(0.266235\pi\)
\(492\) 0 0
\(493\) −1.22497 −0.0551700
\(494\) 4.28983 0.193009
\(495\) 0 0
\(496\) 37.9333 1.70325
\(497\) −1.41421 −0.0634361
\(498\) 0 0
\(499\) 11.9666 0.535700 0.267850 0.963461i \(-0.413687\pi\)
0.267850 + 0.963461i \(0.413687\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −26.9666 −1.20358
\(503\) −34.3948 −1.53359 −0.766793 0.641894i \(-0.778149\pi\)
−0.766793 + 0.641894i \(0.778149\pi\)
\(504\) 0 0
\(505\) −36.9333 −1.64351
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −27.7362 −1.22939 −0.614694 0.788766i \(-0.710720\pi\)
−0.614694 + 0.788766i \(0.710720\pi\)
\(510\) 0 0
\(511\) −8.25834 −0.365328
\(512\) 22.6274 1.00000
\(513\) 0 0
\(514\) −23.2250 −1.02441
\(515\) −24.4070 −1.07550
\(516\) 0 0
\(517\) 0 0
\(518\) 16.2399 0.713538
\(519\) 0 0
\(520\) −13.0334 −0.571551
\(521\) 29.8340 1.30705 0.653525 0.756905i \(-0.273289\pi\)
0.653525 + 0.756905i \(0.273289\pi\)
\(522\) 0 0
\(523\) −15.2250 −0.665742 −0.332871 0.942972i \(-0.608017\pi\)
−0.332871 + 0.942972i \(0.608017\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 16.4499 0.717252
\(527\) 1.73237 0.0754633
\(528\) 0 0
\(529\) 21.9666 0.955071
\(530\) −29.0150 −1.26033
\(531\) 0 0
\(532\) 0 0
\(533\) 9.85230 0.426751
\(534\) 0 0
\(535\) 2.77503 0.119975
\(536\) 23.9944 1.03640
\(537\) 0 0
\(538\) −10.4499 −0.450529
\(539\) 0 0
\(540\) 0 0
\(541\) −15.0000 −0.644900 −0.322450 0.946586i \(-0.604506\pi\)
−0.322450 + 0.946586i \(0.604506\pi\)
\(542\) −29.6513 −1.27363
\(543\) 0 0
\(544\) 0 0
\(545\) −4.01277 −0.171888
\(546\) 0 0
\(547\) 10.0000 0.427569 0.213785 0.976881i \(-0.431421\pi\)
0.213785 + 0.976881i \(0.431421\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −11.6791 −0.497545
\(552\) 0 0
\(553\) 1.48331 0.0630770
\(554\) −14.0949 −0.598837
\(555\) 0 0
\(556\) 0 0
\(557\) 15.2382 0.645663 0.322831 0.946456i \(-0.395365\pi\)
0.322831 + 0.946456i \(0.395365\pi\)
\(558\) 0 0
\(559\) −1.74166 −0.0736643
\(560\) 10.5830 0.447214
\(561\) 0 0
\(562\) 6.96663 0.293870
\(563\) −13.2288 −0.557526 −0.278763 0.960360i \(-0.589924\pi\)
−0.278763 + 0.960360i \(0.589924\pi\)
\(564\) 0 0
\(565\) 14.0000 0.588984
\(566\) 29.6513 1.24634
\(567\) 0 0
\(568\) −4.00000 −0.167836
\(569\) −18.3848 −0.770730 −0.385365 0.922764i \(-0.625924\pi\)
−0.385365 + 0.922764i \(0.625924\pi\)
\(570\) 0 0
\(571\) 2.96663 0.124150 0.0620748 0.998072i \(-0.480228\pi\)
0.0620748 + 0.998072i \(0.480228\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) −8.00000 −0.333914
\(575\) 13.4114 0.559295
\(576\) 0 0
\(577\) 18.7083 0.778836 0.389418 0.921061i \(-0.372676\pi\)
0.389418 + 0.921061i \(0.372676\pi\)
\(578\) 23.9944 0.998037
\(579\) 0 0
\(580\) 0 0
\(581\) −5.83953 −0.242265
\(582\) 0 0
\(583\) 0 0
\(584\) −23.3581 −0.966566
\(585\) 0 0
\(586\) −32.2583 −1.33258
\(587\) −35.4908 −1.46486 −0.732431 0.680841i \(-0.761615\pi\)
−0.732431 + 0.680841i \(0.761615\pi\)
\(588\) 0 0
\(589\) 16.5167 0.680558
\(590\) 11.2665 0.463835
\(591\) 0 0
\(592\) 45.9333 1.88785
\(593\) −39.6863 −1.62972 −0.814860 0.579658i \(-0.803186\pi\)
−0.814860 + 0.579658i \(0.803186\pi\)
\(594\) 0 0
\(595\) 0.483315 0.0198140
\(596\) 0 0
\(597\) 0 0
\(598\) −16.5167 −0.675417
\(599\) −12.6807 −0.518121 −0.259060 0.965861i \(-0.583413\pi\)
−0.259060 + 0.965861i \(0.583413\pi\)
\(600\) 0 0
\(601\) −14.7750 −0.602686 −0.301343 0.953516i \(-0.597435\pi\)
−0.301343 + 0.953516i \(0.597435\pi\)
\(602\) 1.41421 0.0576390
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −28.2583 −1.14697 −0.573485 0.819216i \(-0.694409\pi\)
−0.573485 + 0.819216i \(0.694409\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −21.4833 −0.869834
\(611\) −0.318159 −0.0128713
\(612\) 0 0
\(613\) −11.5167 −0.465155 −0.232577 0.972578i \(-0.574716\pi\)
−0.232577 + 0.972578i \(0.574716\pi\)
\(614\) −43.4281 −1.75261
\(615\) 0 0
\(616\) 0 0
\(617\) 19.0683 0.767660 0.383830 0.923404i \(-0.374605\pi\)
0.383830 + 0.923404i \(0.374605\pi\)
\(618\) 0 0
\(619\) −10.4499 −0.420019 −0.210009 0.977699i \(-0.567349\pi\)
−0.210009 + 0.977699i \(0.567349\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 45.6749 1.83140
\(623\) 11.1310 0.445955
\(624\) 0 0
\(625\) −31.0000 −1.24000
\(626\) 27.5536 1.10126
\(627\) 0 0
\(628\) 0 0
\(629\) 2.09772 0.0836417
\(630\) 0 0
\(631\) 19.4499 0.774290 0.387145 0.922019i \(-0.373461\pi\)
0.387145 + 0.922019i \(0.373461\pi\)
\(632\) 4.19545 0.166886
\(633\) 0 0
\(634\) 1.48331 0.0589100
\(635\) 4.01277 0.159242
\(636\) 0 0
\(637\) 1.74166 0.0690070
\(638\) 0 0
\(639\) 0 0
\(640\) 29.9333 1.18322
\(641\) 31.0655 1.22701 0.613507 0.789689i \(-0.289758\pi\)
0.613507 + 0.789689i \(0.289758\pi\)
\(642\) 0 0
\(643\) 4.44994 0.175489 0.0877443 0.996143i \(-0.472034\pi\)
0.0877443 + 0.996143i \(0.472034\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.449944 −0.0177028
\(647\) 42.6091 1.67514 0.837568 0.546333i \(-0.183977\pi\)
0.837568 + 0.546333i \(0.183977\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) −4.92615 −0.193220
\(651\) 0 0
\(652\) 0 0
\(653\) −25.0433 −0.980020 −0.490010 0.871717i \(-0.663007\pi\)
−0.490010 + 0.871717i \(0.663007\pi\)
\(654\) 0 0
\(655\) 36.9333 1.44310
\(656\) −22.6274 −0.883452
\(657\) 0 0
\(658\) 0.258343 0.0100712
\(659\) 32.5269 1.26707 0.633534 0.773715i \(-0.281604\pi\)
0.633534 + 0.773715i \(0.281604\pi\)
\(660\) 0 0
\(661\) 40.0000 1.55582 0.777910 0.628376i \(-0.216280\pi\)
0.777910 + 0.628376i \(0.216280\pi\)
\(662\) −7.80177 −0.303224
\(663\) 0 0
\(664\) −16.5167 −0.640972
\(665\) 4.60799 0.178690
\(666\) 0 0
\(667\) 44.9666 1.74111
\(668\) 0 0
\(669\) 0 0
\(670\) 31.7417 1.22629
\(671\) 0 0
\(672\) 0 0
\(673\) −39.4499 −1.52068 −0.760342 0.649523i \(-0.774969\pi\)
−0.760342 + 0.649523i \(0.774969\pi\)
\(674\) 9.85230 0.379496
\(675\) 0 0
\(676\) 0 0
\(677\) 32.2970 1.24128 0.620638 0.784097i \(-0.286874\pi\)
0.620638 + 0.784097i \(0.286874\pi\)
\(678\) 0 0
\(679\) 15.2250 0.584281
\(680\) 1.36702 0.0524228
\(681\) 0 0
\(682\) 0 0
\(683\) −14.1421 −0.541134 −0.270567 0.962701i \(-0.587211\pi\)
−0.270567 + 0.962701i \(0.587211\pi\)
\(684\) 0 0
\(685\) 60.7083 2.31954
\(686\) −1.41421 −0.0539949
\(687\) 0 0
\(688\) 4.00000 0.152499
\(689\) −13.5058 −0.514531
\(690\) 0 0
\(691\) 34.4499 1.31054 0.655269 0.755396i \(-0.272555\pi\)
0.655269 + 0.755396i \(0.272555\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −42.8999 −1.62846
\(695\) 9.89949 0.375509
\(696\) 0 0
\(697\) −1.03337 −0.0391417
\(698\) 26.1865 0.991175
\(699\) 0 0
\(700\) 0 0
\(701\) −26.1394 −0.987270 −0.493635 0.869669i \(-0.664332\pi\)
−0.493635 + 0.869669i \(0.664332\pi\)
\(702\) 0 0
\(703\) 20.0000 0.754314
\(704\) 0 0
\(705\) 0 0
\(706\) 47.4833 1.78706
\(707\) 13.9595 0.525000
\(708\) 0 0
\(709\) −34.4166 −1.29254 −0.646271 0.763108i \(-0.723672\pi\)
−0.646271 + 0.763108i \(0.723672\pi\)
\(710\) −5.29150 −0.198587
\(711\) 0 0
\(712\) 31.4833 1.17989
\(713\) −63.5924 −2.38155
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 39.9333 1.49030
\(719\) −2.82843 −0.105483 −0.0527413 0.998608i \(-0.516796\pi\)
−0.0527413 + 0.998608i \(0.516796\pi\)
\(720\) 0 0
\(721\) 9.22497 0.343556
\(722\) 22.5802 0.840349
\(723\) 0 0
\(724\) 0 0
\(725\) 13.4114 0.498088
\(726\) 0 0
\(727\) −42.1916 −1.56480 −0.782400 0.622776i \(-0.786005\pi\)
−0.782400 + 0.622776i \(0.786005\pi\)
\(728\) 4.92615 0.182575
\(729\) 0 0
\(730\) −30.8999 −1.14366
\(731\) 0.182676 0.00675651
\(732\) 0 0
\(733\) 38.7083 1.42972 0.714862 0.699266i \(-0.246490\pi\)
0.714862 + 0.699266i \(0.246490\pi\)
\(734\) 7.38923 0.272741
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −31.9333 −1.17468 −0.587342 0.809339i \(-0.699826\pi\)
−0.587342 + 0.809339i \(0.699826\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 10.9666 0.402598
\(743\) 21.5786 0.791640 0.395820 0.918328i \(-0.370460\pi\)
0.395820 + 0.918328i \(0.370460\pi\)
\(744\) 0 0
\(745\) 5.67492 0.207913
\(746\) −35.9917 −1.31775
\(747\) 0 0
\(748\) 0 0
\(749\) −1.04886 −0.0383246
\(750\) 0 0
\(751\) −2.03337 −0.0741987 −0.0370994 0.999312i \(-0.511812\pi\)
−0.0370994 + 0.999312i \(0.511812\pi\)
\(752\) 0.730703 0.0266460
\(753\) 0 0
\(754\) −16.5167 −0.601502
\(755\) 59.4853 2.16489
\(756\) 0 0
\(757\) −9.51669 −0.345890 −0.172945 0.984932i \(-0.555328\pi\)
−0.172945 + 0.984932i \(0.555328\pi\)
\(758\) 27.6008 1.00250
\(759\) 0 0
\(760\) 13.0334 0.472770
\(761\) 15.0555 0.545762 0.272881 0.962048i \(-0.412023\pi\)
0.272881 + 0.962048i \(0.412023\pi\)
\(762\) 0 0
\(763\) 1.51669 0.0549077
\(764\) 0 0
\(765\) 0 0
\(766\) −22.1916 −0.801815
\(767\) 5.24431 0.189361
\(768\) 0 0
\(769\) −48.4499 −1.74715 −0.873575 0.486690i \(-0.838204\pi\)
−0.873575 + 0.486690i \(0.838204\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −9.76401 −0.351187 −0.175594 0.984463i \(-0.556184\pi\)
−0.175594 + 0.984463i \(0.556184\pi\)
\(774\) 0 0
\(775\) −18.9666 −0.681301
\(776\) 43.0627 1.54586
\(777\) 0 0
\(778\) 32.5167 1.16578
\(779\) −9.85230 −0.352995
\(780\) 0 0
\(781\) 0 0
\(782\) 1.73237 0.0619495
\(783\) 0 0
\(784\) −4.00000 −0.142857
\(785\) −44.8895 −1.60217
\(786\) 0 0
\(787\) −52.4499 −1.86964 −0.934819 0.355124i \(-0.884439\pi\)
−0.934819 + 0.355124i \(0.884439\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 5.55006 0.197462
\(791\) −5.29150 −0.188144
\(792\) 0 0
\(793\) −10.0000 −0.355110
\(794\) 19.0683 0.676708
\(795\) 0 0
\(796\) 0 0
\(797\) 53.8284 1.90670 0.953350 0.301867i \(-0.0976099\pi\)
0.953350 + 0.301867i \(0.0976099\pi\)
\(798\) 0 0
\(799\) 0.0333705 0.00118056
\(800\) 0 0
\(801\) 0 0
\(802\) 3.48331 0.123000
\(803\) 0 0
\(804\) 0 0
\(805\) −17.7417 −0.625311
\(806\) 23.3581 0.822755
\(807\) 0 0
\(808\) 39.4833 1.38902
\(809\) 42.7446 1.50282 0.751409 0.659836i \(-0.229374\pi\)
0.751409 + 0.659836i \(0.229374\pi\)
\(810\) 0 0
\(811\) −49.2250 −1.72852 −0.864261 0.503043i \(-0.832214\pi\)
−0.864261 + 0.503043i \(0.832214\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −54.1055 −1.89523
\(816\) 0 0
\(817\) 1.74166 0.0609329
\(818\) 18.7029 0.653933
\(819\) 0 0
\(820\) 0 0
\(821\) −33.9411 −1.18455 −0.592277 0.805735i \(-0.701771\pi\)
−0.592277 + 0.805735i \(0.701771\pi\)
\(822\) 0 0
\(823\) 3.93326 0.137105 0.0685524 0.997648i \(-0.478162\pi\)
0.0685524 + 0.997648i \(0.478162\pi\)
\(824\) 26.0922 0.908964
\(825\) 0 0
\(826\) −4.25834 −0.148167
\(827\) −52.5969 −1.82897 −0.914486 0.404617i \(-0.867405\pi\)
−0.914486 + 0.404617i \(0.867405\pi\)
\(828\) 0 0
\(829\) 27.2250 0.945562 0.472781 0.881180i \(-0.343250\pi\)
0.472781 + 0.881180i \(0.343250\pi\)
\(830\) −21.8495 −0.758408
\(831\) 0 0
\(832\) 13.9333 0.483049
\(833\) −0.182676 −0.00632934
\(834\) 0 0
\(835\) −36.9333 −1.27813
\(836\) 0 0
\(837\) 0 0
\(838\) −25.6749 −0.886925
\(839\) −6.20488 −0.214216 −0.107108 0.994247i \(-0.534159\pi\)
−0.107108 + 0.994247i \(0.534159\pi\)
\(840\) 0 0
\(841\) 15.9666 0.550573
\(842\) 31.7962 1.09577
\(843\) 0 0
\(844\) 0 0
\(845\) 26.3692 0.907129
\(846\) 0 0
\(847\) 0 0
\(848\) 31.0183 1.06517
\(849\) 0 0
\(850\) 0.516685 0.0177222
\(851\) −77.0038 −2.63966
\(852\) 0 0
\(853\) 9.03337 0.309297 0.154648 0.987970i \(-0.450576\pi\)
0.154648 + 0.987970i \(0.450576\pi\)
\(854\) 8.11993 0.277858
\(855\) 0 0
\(856\) −2.96663 −0.101397
\(857\) −24.1771 −0.825874 −0.412937 0.910759i \(-0.635497\pi\)
−0.412937 + 0.910759i \(0.635497\pi\)
\(858\) 0 0
\(859\) 14.4499 0.493026 0.246513 0.969140i \(-0.420715\pi\)
0.246513 + 0.969140i \(0.420715\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 22.4499 0.764648
\(863\) −13.0461 −0.444094 −0.222047 0.975036i \(-0.571274\pi\)
−0.222047 + 0.975036i \(0.571274\pi\)
\(864\) 0 0
\(865\) −28.4833 −0.968462
\(866\) −8.11993 −0.275926
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 14.7750 0.500633
\(872\) 4.28983 0.145272
\(873\) 0 0
\(874\) 16.5167 0.558685
\(875\) 7.93725 0.268328
\(876\) 0 0
\(877\) −40.8999 −1.38109 −0.690546 0.723289i \(-0.742629\pi\)
−0.690546 + 0.723289i \(0.742629\pi\)
\(878\) 6.38756 0.215570
\(879\) 0 0
\(880\) 0 0
\(881\) 22.2621 0.750028 0.375014 0.927019i \(-0.377638\pi\)
0.375014 + 0.927019i \(0.377638\pi\)
\(882\) 0 0
\(883\) −22.4166 −0.754378 −0.377189 0.926136i \(-0.623109\pi\)
−0.377189 + 0.926136i \(0.623109\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 53.4833 1.79681
\(887\) −18.1549 −0.609582 −0.304791 0.952419i \(-0.598587\pi\)
−0.304791 + 0.952419i \(0.598587\pi\)
\(888\) 0 0
\(889\) −1.51669 −0.0508680
\(890\) 41.6485 1.39606
\(891\) 0 0
\(892\) 0 0
\(893\) 0.318159 0.0106468
\(894\) 0 0
\(895\) −37.4166 −1.25070
\(896\) −11.3137 −0.377964
\(897\) 0 0
\(898\) 30.4499 1.01613
\(899\) −63.5924 −2.12093
\(900\) 0 0
\(901\) 1.41657 0.0471929
\(902\) 0 0
\(903\) 0 0
\(904\) −14.9666 −0.497783
\(905\) 0 0
\(906\) 0 0
\(907\) 13.4833 0.447706 0.223853 0.974623i \(-0.428136\pi\)
0.223853 + 0.974623i \(0.428136\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 6.51669 0.216026
\(911\) −17.7013 −0.586469 −0.293235 0.956041i \(-0.594732\pi\)
−0.293235 + 0.956041i \(0.594732\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 32.5269 1.07589
\(915\) 0 0
\(916\) 0 0
\(917\) −13.9595 −0.460982
\(918\) 0 0
\(919\) −56.9666 −1.87916 −0.939578 0.342335i \(-0.888782\pi\)
−0.939578 + 0.342335i \(0.888782\pi\)
\(920\) −50.1810 −1.65442
\(921\) 0 0
\(922\) −42.1916 −1.38951
\(923\) −2.46308 −0.0810731
\(924\) 0 0
\(925\) −22.9666 −0.755138
\(926\) 3.55913 0.116960
\(927\) 0 0
\(928\) 0 0
\(929\) −0.548027 −0.0179802 −0.00899010 0.999960i \(-0.502862\pi\)
−0.00899010 + 0.999960i \(0.502862\pi\)
\(930\) 0 0
\(931\) −1.74166 −0.0570805
\(932\) 0 0
\(933\) 0 0
\(934\) 45.4166 1.48608
\(935\) 0 0
\(936\) 0 0
\(937\) 28.2583 0.923160 0.461580 0.887099i \(-0.347283\pi\)
0.461580 + 0.887099i \(0.347283\pi\)
\(938\) −11.9972 −0.391723
\(939\) 0 0
\(940\) 0 0
\(941\) 17.2415 0.562058 0.281029 0.959699i \(-0.409324\pi\)
0.281029 + 0.959699i \(0.409324\pi\)
\(942\) 0 0
\(943\) 37.9333 1.23528
\(944\) −12.0444 −0.392012
\(945\) 0 0
\(946\) 0 0
\(947\) −12.7751 −0.415135 −0.207568 0.978221i \(-0.566555\pi\)
−0.207568 + 0.978221i \(0.566555\pi\)
\(948\) 0 0
\(949\) −14.3832 −0.466899
\(950\) 4.92615 0.159825
\(951\) 0 0
\(952\) −0.516685 −0.0167459
\(953\) 39.9633 1.29454 0.647270 0.762261i \(-0.275911\pi\)
0.647270 + 0.762261i \(0.275911\pi\)
\(954\) 0 0
\(955\) 3.74166 0.121077
\(956\) 0 0
\(957\) 0 0
\(958\) 55.2250 1.78424
\(959\) −22.9456 −0.740951
\(960\) 0 0
\(961\) 58.9333 1.90107
\(962\) 28.2843 0.911922
\(963\) 0 0
\(964\) 0 0
\(965\) 4.01277 0.129176
\(966\) 0 0
\(967\) −28.9333 −0.930431 −0.465215 0.885197i \(-0.654023\pi\)
−0.465215 + 0.885197i \(0.654023\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 56.9666 1.82909
\(971\) 32.2970 1.03646 0.518231 0.855241i \(-0.326591\pi\)
0.518231 + 0.855241i \(0.326591\pi\)
\(972\) 0 0
\(973\) −3.74166 −0.119952
\(974\) −28.9678 −0.928188
\(975\) 0 0
\(976\) 22.9666 0.735144
\(977\) −22.5802 −0.722405 −0.361203 0.932487i \(-0.617634\pi\)
−0.361203 + 0.932487i \(0.617634\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) −42.0000 −1.34027
\(983\) 2.82843 0.0902128 0.0451064 0.998982i \(-0.485637\pi\)
0.0451064 + 0.998982i \(0.485637\pi\)
\(984\) 0 0
\(985\) 30.8999 0.984552
\(986\) 1.73237 0.0551700
\(987\) 0 0
\(988\) 0 0
\(989\) −6.70572 −0.213229
\(990\) 0 0
\(991\) −44.4499 −1.41200 −0.706000 0.708212i \(-0.749502\pi\)
−0.706000 + 0.708212i \(0.749502\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 2.00000 0.0634361
\(995\) −25.7740 −0.817091
\(996\) 0 0
\(997\) −18.9666 −0.600679 −0.300340 0.953832i \(-0.597100\pi\)
−0.300340 + 0.953832i \(0.597100\pi\)
\(998\) −16.9234 −0.535700
\(999\) 0 0
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 7623.2.a.ck.1.1 yes 4
3.2 odd 2 inner 7623.2.a.ck.1.4 yes 4
11.10 odd 2 7623.2.a.cj.1.3 yes 4
33.32 even 2 7623.2.a.cj.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
7623.2.a.cj.1.2 4 33.32 even 2
7623.2.a.cj.1.3 yes 4 11.10 odd 2
7623.2.a.ck.1.1 yes 4 1.1 even 1 trivial
7623.2.a.ck.1.4 yes 4 3.2 odd 2 inner