Properties

Label 8020.2.a.c.1.22
Level 8020
Weight 2
Character 8020.1
Self dual yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.22
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.95384 q^{3} -1.00000 q^{5} +2.17117 q^{7} +0.817489 q^{9} +O(q^{10})\) \(q+1.95384 q^{3} -1.00000 q^{5} +2.17117 q^{7} +0.817489 q^{9} +1.00263 q^{11} -0.272452 q^{13} -1.95384 q^{15} -5.86725 q^{17} -8.21631 q^{19} +4.24213 q^{21} +4.96981 q^{23} +1.00000 q^{25} -4.26428 q^{27} -6.90963 q^{29} +8.98865 q^{31} +1.95898 q^{33} -2.17117 q^{35} -5.23167 q^{37} -0.532328 q^{39} +1.37318 q^{41} +2.99770 q^{43} -0.817489 q^{45} -2.43702 q^{47} -2.28600 q^{49} -11.4637 q^{51} +6.76735 q^{53} -1.00263 q^{55} -16.0534 q^{57} +2.44495 q^{59} +4.43871 q^{61} +1.77491 q^{63} +0.272452 q^{65} -12.9828 q^{67} +9.71022 q^{69} -6.91721 q^{71} +3.98738 q^{73} +1.95384 q^{75} +2.17689 q^{77} -9.61707 q^{79} -10.7842 q^{81} -11.8176 q^{83} +5.86725 q^{85} -13.5003 q^{87} -11.9940 q^{89} -0.591541 q^{91} +17.5624 q^{93} +8.21631 q^{95} +10.3855 q^{97} +0.819641 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 3q^{3} - 28q^{5} - 4q^{7} + 17q^{9} + O(q^{10}) \) \( 28q + 3q^{3} - 28q^{5} - 4q^{7} + 17q^{9} + 2q^{11} + 3q^{13} - 3q^{15} - 10q^{17} - 2q^{19} - 12q^{21} - 23q^{23} + 28q^{25} + 9q^{27} - 37q^{29} - 11q^{31} + 2q^{33} + 4q^{35} - 3q^{37} - 19q^{39} - 30q^{41} + 13q^{43} - 17q^{45} - 15q^{47} + 12q^{49} - 8q^{51} - 35q^{53} - 2q^{55} - 22q^{57} - q^{59} - 33q^{61} - 20q^{63} - 3q^{65} + 19q^{67} - 8q^{69} - 31q^{71} + 31q^{73} + 3q^{75} - 42q^{77} - 29q^{79} - 36q^{81} + 14q^{83} + 10q^{85} - 32q^{87} - 32q^{89} - 7q^{91} - 11q^{93} + 2q^{95} + 2q^{97} - 39q^{99} + O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.95384 1.12805 0.564025 0.825758i \(-0.309252\pi\)
0.564025 + 0.825758i \(0.309252\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 2.17117 0.820627 0.410313 0.911945i \(-0.365419\pi\)
0.410313 + 0.911945i \(0.365419\pi\)
\(8\) 0 0
\(9\) 0.817489 0.272496
\(10\) 0 0
\(11\) 1.00263 0.302305 0.151153 0.988510i \(-0.451702\pi\)
0.151153 + 0.988510i \(0.451702\pi\)
\(12\) 0 0
\(13\) −0.272452 −0.0755646 −0.0377823 0.999286i \(-0.512029\pi\)
−0.0377823 + 0.999286i \(0.512029\pi\)
\(14\) 0 0
\(15\) −1.95384 −0.504479
\(16\) 0 0
\(17\) −5.86725 −1.42302 −0.711509 0.702677i \(-0.751988\pi\)
−0.711509 + 0.702677i \(0.751988\pi\)
\(18\) 0 0
\(19\) −8.21631 −1.88495 −0.942476 0.334275i \(-0.891509\pi\)
−0.942476 + 0.334275i \(0.891509\pi\)
\(20\) 0 0
\(21\) 4.24213 0.925708
\(22\) 0 0
\(23\) 4.96981 1.03628 0.518139 0.855297i \(-0.326625\pi\)
0.518139 + 0.855297i \(0.326625\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −4.26428 −0.820660
\(28\) 0 0
\(29\) −6.90963 −1.28309 −0.641543 0.767087i \(-0.721705\pi\)
−0.641543 + 0.767087i \(0.721705\pi\)
\(30\) 0 0
\(31\) 8.98865 1.61441 0.807204 0.590272i \(-0.200980\pi\)
0.807204 + 0.590272i \(0.200980\pi\)
\(32\) 0 0
\(33\) 1.95898 0.341015
\(34\) 0 0
\(35\) −2.17117 −0.366995
\(36\) 0 0
\(37\) −5.23167 −0.860080 −0.430040 0.902810i \(-0.641501\pi\)
−0.430040 + 0.902810i \(0.641501\pi\)
\(38\) 0 0
\(39\) −0.532328 −0.0852406
\(40\) 0 0
\(41\) 1.37318 0.214455 0.107227 0.994235i \(-0.465803\pi\)
0.107227 + 0.994235i \(0.465803\pi\)
\(42\) 0 0
\(43\) 2.99770 0.457146 0.228573 0.973527i \(-0.426594\pi\)
0.228573 + 0.973527i \(0.426594\pi\)
\(44\) 0 0
\(45\) −0.817489 −0.121864
\(46\) 0 0
\(47\) −2.43702 −0.355475 −0.177738 0.984078i \(-0.556878\pi\)
−0.177738 + 0.984078i \(0.556878\pi\)
\(48\) 0 0
\(49\) −2.28600 −0.326572
\(50\) 0 0
\(51\) −11.4637 −1.60523
\(52\) 0 0
\(53\) 6.76735 0.929567 0.464784 0.885424i \(-0.346132\pi\)
0.464784 + 0.885424i \(0.346132\pi\)
\(54\) 0 0
\(55\) −1.00263 −0.135195
\(56\) 0 0
\(57\) −16.0534 −2.12632
\(58\) 0 0
\(59\) 2.44495 0.318306 0.159153 0.987254i \(-0.449124\pi\)
0.159153 + 0.987254i \(0.449124\pi\)
\(60\) 0 0
\(61\) 4.43871 0.568318 0.284159 0.958777i \(-0.408286\pi\)
0.284159 + 0.958777i \(0.408286\pi\)
\(62\) 0 0
\(63\) 1.77491 0.223618
\(64\) 0 0
\(65\) 0.272452 0.0337935
\(66\) 0 0
\(67\) −12.9828 −1.58610 −0.793051 0.609155i \(-0.791509\pi\)
−0.793051 + 0.609155i \(0.791509\pi\)
\(68\) 0 0
\(69\) 9.71022 1.16897
\(70\) 0 0
\(71\) −6.91721 −0.820922 −0.410461 0.911878i \(-0.634632\pi\)
−0.410461 + 0.911878i \(0.634632\pi\)
\(72\) 0 0
\(73\) 3.98738 0.466688 0.233344 0.972394i \(-0.425033\pi\)
0.233344 + 0.972394i \(0.425033\pi\)
\(74\) 0 0
\(75\) 1.95384 0.225610
\(76\) 0 0
\(77\) 2.17689 0.248080
\(78\) 0 0
\(79\) −9.61707 −1.08200 −0.541002 0.841021i \(-0.681955\pi\)
−0.541002 + 0.841021i \(0.681955\pi\)
\(80\) 0 0
\(81\) −10.7842 −1.19824
\(82\) 0 0
\(83\) −11.8176 −1.29715 −0.648573 0.761152i \(-0.724634\pi\)
−0.648573 + 0.761152i \(0.724634\pi\)
\(84\) 0 0
\(85\) 5.86725 0.636393
\(86\) 0 0
\(87\) −13.5003 −1.44739
\(88\) 0 0
\(89\) −11.9940 −1.27137 −0.635683 0.771950i \(-0.719281\pi\)
−0.635683 + 0.771950i \(0.719281\pi\)
\(90\) 0 0
\(91\) −0.591541 −0.0620103
\(92\) 0 0
\(93\) 17.5624 1.82113
\(94\) 0 0
\(95\) 8.21631 0.842976
\(96\) 0 0
\(97\) 10.3855 1.05449 0.527243 0.849715i \(-0.323226\pi\)
0.527243 + 0.849715i \(0.323226\pi\)
\(98\) 0 0
\(99\) 0.819641 0.0823770
\(100\) 0 0
\(101\) −4.61598 −0.459307 −0.229653 0.973272i \(-0.573759\pi\)
−0.229653 + 0.973272i \(0.573759\pi\)
\(102\) 0 0
\(103\) −0.873853 −0.0861033 −0.0430516 0.999073i \(-0.513708\pi\)
−0.0430516 + 0.999073i \(0.513708\pi\)
\(104\) 0 0
\(105\) −4.24213 −0.413989
\(106\) 0 0
\(107\) −9.17487 −0.886968 −0.443484 0.896282i \(-0.646258\pi\)
−0.443484 + 0.896282i \(0.646258\pi\)
\(108\) 0 0
\(109\) −2.64702 −0.253538 −0.126769 0.991932i \(-0.540461\pi\)
−0.126769 + 0.991932i \(0.540461\pi\)
\(110\) 0 0
\(111\) −10.2218 −0.970214
\(112\) 0 0
\(113\) −6.83601 −0.643078 −0.321539 0.946896i \(-0.604200\pi\)
−0.321539 + 0.946896i \(0.604200\pi\)
\(114\) 0 0
\(115\) −4.96981 −0.463437
\(116\) 0 0
\(117\) −0.222727 −0.0205911
\(118\) 0 0
\(119\) −12.7388 −1.16777
\(120\) 0 0
\(121\) −9.99473 −0.908612
\(122\) 0 0
\(123\) 2.68297 0.241916
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 0.696354 0.0617914 0.0308957 0.999523i \(-0.490164\pi\)
0.0308957 + 0.999523i \(0.490164\pi\)
\(128\) 0 0
\(129\) 5.85703 0.515683
\(130\) 0 0
\(131\) 0.720727 0.0629702 0.0314851 0.999504i \(-0.489976\pi\)
0.0314851 + 0.999504i \(0.489976\pi\)
\(132\) 0 0
\(133\) −17.8390 −1.54684
\(134\) 0 0
\(135\) 4.26428 0.367010
\(136\) 0 0
\(137\) −11.8434 −1.01185 −0.505924 0.862578i \(-0.668848\pi\)
−0.505924 + 0.862578i \(0.668848\pi\)
\(138\) 0 0
\(139\) 5.31971 0.451212 0.225606 0.974219i \(-0.427564\pi\)
0.225606 + 0.974219i \(0.427564\pi\)
\(140\) 0 0
\(141\) −4.76154 −0.400994
\(142\) 0 0
\(143\) −0.273169 −0.0228436
\(144\) 0 0
\(145\) 6.90963 0.573814
\(146\) 0 0
\(147\) −4.46649 −0.368390
\(148\) 0 0
\(149\) 9.30295 0.762128 0.381064 0.924549i \(-0.375558\pi\)
0.381064 + 0.924549i \(0.375558\pi\)
\(150\) 0 0
\(151\) 2.32280 0.189027 0.0945135 0.995524i \(-0.469870\pi\)
0.0945135 + 0.995524i \(0.469870\pi\)
\(152\) 0 0
\(153\) −4.79641 −0.387767
\(154\) 0 0
\(155\) −8.98865 −0.721985
\(156\) 0 0
\(157\) −14.5276 −1.15943 −0.579715 0.814819i \(-0.696836\pi\)
−0.579715 + 0.814819i \(0.696836\pi\)
\(158\) 0 0
\(159\) 13.2223 1.04860
\(160\) 0 0
\(161\) 10.7903 0.850397
\(162\) 0 0
\(163\) −0.478693 −0.0374941 −0.0187470 0.999824i \(-0.505968\pi\)
−0.0187470 + 0.999824i \(0.505968\pi\)
\(164\) 0 0
\(165\) −1.95898 −0.152507
\(166\) 0 0
\(167\) −20.9805 −1.62352 −0.811759 0.583993i \(-0.801489\pi\)
−0.811759 + 0.583993i \(0.801489\pi\)
\(168\) 0 0
\(169\) −12.9258 −0.994290
\(170\) 0 0
\(171\) −6.71674 −0.513642
\(172\) 0 0
\(173\) 10.0599 0.764838 0.382419 0.923989i \(-0.375091\pi\)
0.382419 + 0.923989i \(0.375091\pi\)
\(174\) 0 0
\(175\) 2.17117 0.164125
\(176\) 0 0
\(177\) 4.77704 0.359065
\(178\) 0 0
\(179\) 12.0961 0.904103 0.452051 0.891992i \(-0.350692\pi\)
0.452051 + 0.891992i \(0.350692\pi\)
\(180\) 0 0
\(181\) −3.77666 −0.280717 −0.140358 0.990101i \(-0.544825\pi\)
−0.140358 + 0.990101i \(0.544825\pi\)
\(182\) 0 0
\(183\) 8.67252 0.641091
\(184\) 0 0
\(185\) 5.23167 0.384640
\(186\) 0 0
\(187\) −5.88269 −0.430185
\(188\) 0 0
\(189\) −9.25849 −0.673456
\(190\) 0 0
\(191\) 0.0106466 0.000770359 0 0.000385179 1.00000i \(-0.499877\pi\)
0.000385179 1.00000i \(0.499877\pi\)
\(192\) 0 0
\(193\) 7.75149 0.557964 0.278982 0.960296i \(-0.410003\pi\)
0.278982 + 0.960296i \(0.410003\pi\)
\(194\) 0 0
\(195\) 0.532328 0.0381208
\(196\) 0 0
\(197\) 26.0365 1.85502 0.927512 0.373794i \(-0.121943\pi\)
0.927512 + 0.373794i \(0.121943\pi\)
\(198\) 0 0
\(199\) −0.0624479 −0.00442681 −0.00221341 0.999998i \(-0.500705\pi\)
−0.00221341 + 0.999998i \(0.500705\pi\)
\(200\) 0 0
\(201\) −25.3663 −1.78920
\(202\) 0 0
\(203\) −15.0020 −1.05293
\(204\) 0 0
\(205\) −1.37318 −0.0959070
\(206\) 0 0
\(207\) 4.06277 0.282382
\(208\) 0 0
\(209\) −8.23794 −0.569830
\(210\) 0 0
\(211\) 14.9859 1.03167 0.515834 0.856688i \(-0.327482\pi\)
0.515834 + 0.856688i \(0.327482\pi\)
\(212\) 0 0
\(213\) −13.5151 −0.926041
\(214\) 0 0
\(215\) −2.99770 −0.204442
\(216\) 0 0
\(217\) 19.5159 1.32483
\(218\) 0 0
\(219\) 7.79071 0.526447
\(220\) 0 0
\(221\) 1.59854 0.107530
\(222\) 0 0
\(223\) −1.56518 −0.104813 −0.0524063 0.998626i \(-0.516689\pi\)
−0.0524063 + 0.998626i \(0.516689\pi\)
\(224\) 0 0
\(225\) 0.817489 0.0544993
\(226\) 0 0
\(227\) 13.7611 0.913357 0.456678 0.889632i \(-0.349039\pi\)
0.456678 + 0.889632i \(0.349039\pi\)
\(228\) 0 0
\(229\) 23.8675 1.57721 0.788604 0.614901i \(-0.210804\pi\)
0.788604 + 0.614901i \(0.210804\pi\)
\(230\) 0 0
\(231\) 4.25329 0.279846
\(232\) 0 0
\(233\) −4.76607 −0.312235 −0.156118 0.987738i \(-0.549898\pi\)
−0.156118 + 0.987738i \(0.549898\pi\)
\(234\) 0 0
\(235\) 2.43702 0.158973
\(236\) 0 0
\(237\) −18.7902 −1.22056
\(238\) 0 0
\(239\) 7.18157 0.464537 0.232269 0.972652i \(-0.425385\pi\)
0.232269 + 0.972652i \(0.425385\pi\)
\(240\) 0 0
\(241\) −7.59767 −0.489409 −0.244705 0.969598i \(-0.578691\pi\)
−0.244705 + 0.969598i \(0.578691\pi\)
\(242\) 0 0
\(243\) −8.27772 −0.531016
\(244\) 0 0
\(245\) 2.28600 0.146047
\(246\) 0 0
\(247\) 2.23855 0.142436
\(248\) 0 0
\(249\) −23.0896 −1.46325
\(250\) 0 0
\(251\) 27.6754 1.74686 0.873429 0.486952i \(-0.161891\pi\)
0.873429 + 0.486952i \(0.161891\pi\)
\(252\) 0 0
\(253\) 4.98289 0.313272
\(254\) 0 0
\(255\) 11.4637 0.717883
\(256\) 0 0
\(257\) −9.35864 −0.583776 −0.291888 0.956452i \(-0.594283\pi\)
−0.291888 + 0.956452i \(0.594283\pi\)
\(258\) 0 0
\(259\) −11.3589 −0.705805
\(260\) 0 0
\(261\) −5.64855 −0.349636
\(262\) 0 0
\(263\) −28.4491 −1.75425 −0.877124 0.480264i \(-0.840541\pi\)
−0.877124 + 0.480264i \(0.840541\pi\)
\(264\) 0 0
\(265\) −6.76735 −0.415715
\(266\) 0 0
\(267\) −23.4344 −1.43416
\(268\) 0 0
\(269\) 11.5587 0.704746 0.352373 0.935860i \(-0.385375\pi\)
0.352373 + 0.935860i \(0.385375\pi\)
\(270\) 0 0
\(271\) 19.1377 1.16253 0.581266 0.813714i \(-0.302558\pi\)
0.581266 + 0.813714i \(0.302558\pi\)
\(272\) 0 0
\(273\) −1.15578 −0.0699507
\(274\) 0 0
\(275\) 1.00263 0.0604610
\(276\) 0 0
\(277\) 31.0194 1.86377 0.931886 0.362751i \(-0.118162\pi\)
0.931886 + 0.362751i \(0.118162\pi\)
\(278\) 0 0
\(279\) 7.34812 0.439920
\(280\) 0 0
\(281\) −21.1765 −1.26328 −0.631642 0.775261i \(-0.717619\pi\)
−0.631642 + 0.775261i \(0.717619\pi\)
\(282\) 0 0
\(283\) −29.0778 −1.72850 −0.864249 0.503065i \(-0.832206\pi\)
−0.864249 + 0.503065i \(0.832206\pi\)
\(284\) 0 0
\(285\) 16.0534 0.950919
\(286\) 0 0
\(287\) 2.98141 0.175987
\(288\) 0 0
\(289\) 17.4246 1.02498
\(290\) 0 0
\(291\) 20.2916 1.18951
\(292\) 0 0
\(293\) 6.26365 0.365926 0.182963 0.983120i \(-0.441431\pi\)
0.182963 + 0.983120i \(0.441431\pi\)
\(294\) 0 0
\(295\) −2.44495 −0.142351
\(296\) 0 0
\(297\) −4.27550 −0.248090
\(298\) 0 0
\(299\) −1.35404 −0.0783059
\(300\) 0 0
\(301\) 6.50854 0.375146
\(302\) 0 0
\(303\) −9.01888 −0.518121
\(304\) 0 0
\(305\) −4.43871 −0.254160
\(306\) 0 0
\(307\) −0.321321 −0.0183388 −0.00916938 0.999958i \(-0.502919\pi\)
−0.00916938 + 0.999958i \(0.502919\pi\)
\(308\) 0 0
\(309\) −1.70737 −0.0971288
\(310\) 0 0
\(311\) −31.0402 −1.76013 −0.880065 0.474853i \(-0.842501\pi\)
−0.880065 + 0.474853i \(0.842501\pi\)
\(312\) 0 0
\(313\) 9.56373 0.540574 0.270287 0.962780i \(-0.412881\pi\)
0.270287 + 0.962780i \(0.412881\pi\)
\(314\) 0 0
\(315\) −1.77491 −0.100005
\(316\) 0 0
\(317\) 0.417696 0.0234601 0.0117301 0.999931i \(-0.496266\pi\)
0.0117301 + 0.999931i \(0.496266\pi\)
\(318\) 0 0
\(319\) −6.92782 −0.387883
\(320\) 0 0
\(321\) −17.9262 −1.00054
\(322\) 0 0
\(323\) 48.2072 2.68232
\(324\) 0 0
\(325\) −0.272452 −0.0151129
\(326\) 0 0
\(327\) −5.17185 −0.286004
\(328\) 0 0
\(329\) −5.29118 −0.291712
\(330\) 0 0
\(331\) −4.17130 −0.229275 −0.114638 0.993407i \(-0.536571\pi\)
−0.114638 + 0.993407i \(0.536571\pi\)
\(332\) 0 0
\(333\) −4.27683 −0.234369
\(334\) 0 0
\(335\) 12.9828 0.709326
\(336\) 0 0
\(337\) 17.0601 0.929325 0.464662 0.885488i \(-0.346176\pi\)
0.464662 + 0.885488i \(0.346176\pi\)
\(338\) 0 0
\(339\) −13.3565 −0.725424
\(340\) 0 0
\(341\) 9.01231 0.488044
\(342\) 0 0
\(343\) −20.1615 −1.08862
\(344\) 0 0
\(345\) −9.71022 −0.522780
\(346\) 0 0
\(347\) 7.24761 0.389072 0.194536 0.980895i \(-0.437680\pi\)
0.194536 + 0.980895i \(0.437680\pi\)
\(348\) 0 0
\(349\) −2.40862 −0.128930 −0.0644652 0.997920i \(-0.520534\pi\)
−0.0644652 + 0.997920i \(0.520534\pi\)
\(350\) 0 0
\(351\) 1.16181 0.0620129
\(352\) 0 0
\(353\) −8.53463 −0.454253 −0.227126 0.973865i \(-0.572933\pi\)
−0.227126 + 0.973865i \(0.572933\pi\)
\(354\) 0 0
\(355\) 6.91721 0.367128
\(356\) 0 0
\(357\) −24.8896 −1.31730
\(358\) 0 0
\(359\) −25.6473 −1.35361 −0.676805 0.736162i \(-0.736636\pi\)
−0.676805 + 0.736162i \(0.736636\pi\)
\(360\) 0 0
\(361\) 48.5078 2.55304
\(362\) 0 0
\(363\) −19.5281 −1.02496
\(364\) 0 0
\(365\) −3.98738 −0.208709
\(366\) 0 0
\(367\) −3.98511 −0.208021 −0.104011 0.994576i \(-0.533168\pi\)
−0.104011 + 0.994576i \(0.533168\pi\)
\(368\) 0 0
\(369\) 1.12256 0.0584381
\(370\) 0 0
\(371\) 14.6931 0.762828
\(372\) 0 0
\(373\) 6.36807 0.329726 0.164863 0.986316i \(-0.447282\pi\)
0.164863 + 0.986316i \(0.447282\pi\)
\(374\) 0 0
\(375\) −1.95384 −0.100896
\(376\) 0 0
\(377\) 1.88254 0.0969559
\(378\) 0 0
\(379\) −32.6022 −1.67466 −0.837331 0.546696i \(-0.815885\pi\)
−0.837331 + 0.546696i \(0.815885\pi\)
\(380\) 0 0
\(381\) 1.36056 0.0697038
\(382\) 0 0
\(383\) −33.1331 −1.69302 −0.846512 0.532370i \(-0.821302\pi\)
−0.846512 + 0.532370i \(0.821302\pi\)
\(384\) 0 0
\(385\) −2.17689 −0.110945
\(386\) 0 0
\(387\) 2.45059 0.124571
\(388\) 0 0
\(389\) −18.7940 −0.952896 −0.476448 0.879203i \(-0.658076\pi\)
−0.476448 + 0.879203i \(0.658076\pi\)
\(390\) 0 0
\(391\) −29.1591 −1.47464
\(392\) 0 0
\(393\) 1.40818 0.0710335
\(394\) 0 0
\(395\) 9.61707 0.483887
\(396\) 0 0
\(397\) 10.5313 0.528549 0.264274 0.964448i \(-0.414868\pi\)
0.264274 + 0.964448i \(0.414868\pi\)
\(398\) 0 0
\(399\) −34.8546 −1.74491
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) −2.44898 −0.121992
\(404\) 0 0
\(405\) 10.7842 0.535870
\(406\) 0 0
\(407\) −5.24544 −0.260007
\(408\) 0 0
\(409\) −14.3231 −0.708230 −0.354115 0.935202i \(-0.615218\pi\)
−0.354115 + 0.935202i \(0.615218\pi\)
\(410\) 0 0
\(411\) −23.1401 −1.14142
\(412\) 0 0
\(413\) 5.30842 0.261210
\(414\) 0 0
\(415\) 11.8176 0.580101
\(416\) 0 0
\(417\) 10.3939 0.508990
\(418\) 0 0
\(419\) −22.3285 −1.09082 −0.545408 0.838171i \(-0.683625\pi\)
−0.545408 + 0.838171i \(0.683625\pi\)
\(420\) 0 0
\(421\) 31.6709 1.54354 0.771772 0.635900i \(-0.219371\pi\)
0.771772 + 0.635900i \(0.219371\pi\)
\(422\) 0 0
\(423\) −1.99223 −0.0968657
\(424\) 0 0
\(425\) −5.86725 −0.284603
\(426\) 0 0
\(427\) 9.63720 0.466377
\(428\) 0 0
\(429\) −0.533729 −0.0257687
\(430\) 0 0
\(431\) −14.9334 −0.719318 −0.359659 0.933084i \(-0.617107\pi\)
−0.359659 + 0.933084i \(0.617107\pi\)
\(432\) 0 0
\(433\) −35.7623 −1.71863 −0.859314 0.511449i \(-0.829109\pi\)
−0.859314 + 0.511449i \(0.829109\pi\)
\(434\) 0 0
\(435\) 13.5003 0.647290
\(436\) 0 0
\(437\) −40.8335 −1.95333
\(438\) 0 0
\(439\) 6.34741 0.302945 0.151473 0.988461i \(-0.451598\pi\)
0.151473 + 0.988461i \(0.451598\pi\)
\(440\) 0 0
\(441\) −1.86878 −0.0889897
\(442\) 0 0
\(443\) −6.90002 −0.327830 −0.163915 0.986474i \(-0.552412\pi\)
−0.163915 + 0.986474i \(0.552412\pi\)
\(444\) 0 0
\(445\) 11.9940 0.568572
\(446\) 0 0
\(447\) 18.1765 0.859718
\(448\) 0 0
\(449\) −1.51352 −0.0714276 −0.0357138 0.999362i \(-0.511370\pi\)
−0.0357138 + 0.999362i \(0.511370\pi\)
\(450\) 0 0
\(451\) 1.37679 0.0648307
\(452\) 0 0
\(453\) 4.53838 0.213232
\(454\) 0 0
\(455\) 0.591541 0.0277319
\(456\) 0 0
\(457\) 35.2276 1.64788 0.823940 0.566677i \(-0.191771\pi\)
0.823940 + 0.566677i \(0.191771\pi\)
\(458\) 0 0
\(459\) 25.0196 1.16781
\(460\) 0 0
\(461\) −17.4197 −0.811318 −0.405659 0.914025i \(-0.632958\pi\)
−0.405659 + 0.914025i \(0.632958\pi\)
\(462\) 0 0
\(463\) −20.8534 −0.969140 −0.484570 0.874752i \(-0.661024\pi\)
−0.484570 + 0.874752i \(0.661024\pi\)
\(464\) 0 0
\(465\) −17.5624 −0.814436
\(466\) 0 0
\(467\) 29.8140 1.37963 0.689813 0.723988i \(-0.257693\pi\)
0.689813 + 0.723988i \(0.257693\pi\)
\(468\) 0 0
\(469\) −28.1879 −1.30160
\(470\) 0 0
\(471\) −28.3846 −1.30789
\(472\) 0 0
\(473\) 3.00560 0.138197
\(474\) 0 0
\(475\) −8.21631 −0.376990
\(476\) 0 0
\(477\) 5.53224 0.253304
\(478\) 0 0
\(479\) 25.3757 1.15945 0.579724 0.814813i \(-0.303160\pi\)
0.579724 + 0.814813i \(0.303160\pi\)
\(480\) 0 0
\(481\) 1.42538 0.0649916
\(482\) 0 0
\(483\) 21.0826 0.959290
\(484\) 0 0
\(485\) −10.3855 −0.471581
\(486\) 0 0
\(487\) −33.8037 −1.53179 −0.765895 0.642966i \(-0.777704\pi\)
−0.765895 + 0.642966i \(0.777704\pi\)
\(488\) 0 0
\(489\) −0.935288 −0.0422952
\(490\) 0 0
\(491\) −18.9206 −0.853876 −0.426938 0.904281i \(-0.640408\pi\)
−0.426938 + 0.904281i \(0.640408\pi\)
\(492\) 0 0
\(493\) 40.5405 1.82585
\(494\) 0 0
\(495\) −0.819641 −0.0368401
\(496\) 0 0
\(497\) −15.0185 −0.673671
\(498\) 0 0
\(499\) 26.5558 1.18880 0.594401 0.804169i \(-0.297389\pi\)
0.594401 + 0.804169i \(0.297389\pi\)
\(500\) 0 0
\(501\) −40.9925 −1.83141
\(502\) 0 0
\(503\) −10.1522 −0.452663 −0.226331 0.974050i \(-0.572673\pi\)
−0.226331 + 0.974050i \(0.572673\pi\)
\(504\) 0 0
\(505\) 4.61598 0.205408
\(506\) 0 0
\(507\) −25.2549 −1.12161
\(508\) 0 0
\(509\) 19.7875 0.877067 0.438534 0.898715i \(-0.355498\pi\)
0.438534 + 0.898715i \(0.355498\pi\)
\(510\) 0 0
\(511\) 8.65730 0.382977
\(512\) 0 0
\(513\) 35.0366 1.54690
\(514\) 0 0
\(515\) 0.873853 0.0385066
\(516\) 0 0
\(517\) −2.44343 −0.107462
\(518\) 0 0
\(519\) 19.6554 0.862775
\(520\) 0 0
\(521\) −6.91212 −0.302825 −0.151413 0.988471i \(-0.548382\pi\)
−0.151413 + 0.988471i \(0.548382\pi\)
\(522\) 0 0
\(523\) 10.0776 0.440665 0.220332 0.975425i \(-0.429286\pi\)
0.220332 + 0.975425i \(0.429286\pi\)
\(524\) 0 0
\(525\) 4.24213 0.185142
\(526\) 0 0
\(527\) −52.7386 −2.29733
\(528\) 0 0
\(529\) 1.69903 0.0738711
\(530\) 0 0
\(531\) 1.99872 0.0867371
\(532\) 0 0
\(533\) −0.374126 −0.0162052
\(534\) 0 0
\(535\) 9.17487 0.396664
\(536\) 0 0
\(537\) 23.6338 1.01987
\(538\) 0 0
\(539\) −2.29202 −0.0987244
\(540\) 0 0
\(541\) 3.29253 0.141557 0.0707785 0.997492i \(-0.477452\pi\)
0.0707785 + 0.997492i \(0.477452\pi\)
\(542\) 0 0
\(543\) −7.37898 −0.316662
\(544\) 0 0
\(545\) 2.64702 0.113386
\(546\) 0 0
\(547\) −12.2102 −0.522070 −0.261035 0.965329i \(-0.584064\pi\)
−0.261035 + 0.965329i \(0.584064\pi\)
\(548\) 0 0
\(549\) 3.62859 0.154865
\(550\) 0 0
\(551\) 56.7717 2.41855
\(552\) 0 0
\(553\) −20.8803 −0.887922
\(554\) 0 0
\(555\) 10.2218 0.433893
\(556\) 0 0
\(557\) −9.81173 −0.415736 −0.207868 0.978157i \(-0.566652\pi\)
−0.207868 + 0.978157i \(0.566652\pi\)
\(558\) 0 0
\(559\) −0.816731 −0.0345440
\(560\) 0 0
\(561\) −11.4938 −0.485270
\(562\) 0 0
\(563\) −28.1600 −1.18680 −0.593402 0.804906i \(-0.702215\pi\)
−0.593402 + 0.804906i \(0.702215\pi\)
\(564\) 0 0
\(565\) 6.83601 0.287593
\(566\) 0 0
\(567\) −23.4143 −0.983309
\(568\) 0 0
\(569\) 27.0409 1.13361 0.566806 0.823851i \(-0.308179\pi\)
0.566806 + 0.823851i \(0.308179\pi\)
\(570\) 0 0
\(571\) −25.6087 −1.07169 −0.535846 0.844316i \(-0.680007\pi\)
−0.535846 + 0.844316i \(0.680007\pi\)
\(572\) 0 0
\(573\) 0.0208017 0.000869003 0
\(574\) 0 0
\(575\) 4.96981 0.207255
\(576\) 0 0
\(577\) −4.56709 −0.190130 −0.0950652 0.995471i \(-0.530306\pi\)
−0.0950652 + 0.995471i \(0.530306\pi\)
\(578\) 0 0
\(579\) 15.1452 0.629412
\(580\) 0 0
\(581\) −25.6580 −1.06447
\(582\) 0 0
\(583\) 6.78517 0.281013
\(584\) 0 0
\(585\) 0.222727 0.00920861
\(586\) 0 0
\(587\) 30.7643 1.26978 0.634890 0.772603i \(-0.281045\pi\)
0.634890 + 0.772603i \(0.281045\pi\)
\(588\) 0 0
\(589\) −73.8535 −3.04308
\(590\) 0 0
\(591\) 50.8711 2.09256
\(592\) 0 0
\(593\) −34.9191 −1.43395 −0.716977 0.697097i \(-0.754475\pi\)
−0.716977 + 0.697097i \(0.754475\pi\)
\(594\) 0 0
\(595\) 12.7388 0.522241
\(596\) 0 0
\(597\) −0.122013 −0.00499367
\(598\) 0 0
\(599\) 39.9110 1.63072 0.815359 0.578956i \(-0.196540\pi\)
0.815359 + 0.578956i \(0.196540\pi\)
\(600\) 0 0
\(601\) 12.2767 0.500778 0.250389 0.968145i \(-0.419442\pi\)
0.250389 + 0.968145i \(0.419442\pi\)
\(602\) 0 0
\(603\) −10.6133 −0.432207
\(604\) 0 0
\(605\) 9.99473 0.406343
\(606\) 0 0
\(607\) −42.9536 −1.74343 −0.871716 0.490012i \(-0.836992\pi\)
−0.871716 + 0.490012i \(0.836992\pi\)
\(608\) 0 0
\(609\) −29.3115 −1.18776
\(610\) 0 0
\(611\) 0.663970 0.0268614
\(612\) 0 0
\(613\) −29.1808 −1.17860 −0.589300 0.807914i \(-0.700597\pi\)
−0.589300 + 0.807914i \(0.700597\pi\)
\(614\) 0 0
\(615\) −2.68297 −0.108188
\(616\) 0 0
\(617\) −30.1451 −1.21360 −0.606799 0.794855i \(-0.707547\pi\)
−0.606799 + 0.794855i \(0.707547\pi\)
\(618\) 0 0
\(619\) −1.51630 −0.0609452 −0.0304726 0.999536i \(-0.509701\pi\)
−0.0304726 + 0.999536i \(0.509701\pi\)
\(620\) 0 0
\(621\) −21.1927 −0.850432
\(622\) 0 0
\(623\) −26.0412 −1.04332
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −16.0956 −0.642797
\(628\) 0 0
\(629\) 30.6955 1.22391
\(630\) 0 0
\(631\) −8.17323 −0.325371 −0.162686 0.986678i \(-0.552016\pi\)
−0.162686 + 0.986678i \(0.552016\pi\)
\(632\) 0 0
\(633\) 29.2800 1.16377
\(634\) 0 0
\(635\) −0.696354 −0.0276340
\(636\) 0 0
\(637\) 0.622827 0.0246773
\(638\) 0 0
\(639\) −5.65475 −0.223698
\(640\) 0 0
\(641\) 26.4926 1.04640 0.523198 0.852211i \(-0.324739\pi\)
0.523198 + 0.852211i \(0.324739\pi\)
\(642\) 0 0
\(643\) 11.2349 0.443063 0.221531 0.975153i \(-0.428894\pi\)
0.221531 + 0.975153i \(0.428894\pi\)
\(644\) 0 0
\(645\) −5.85703 −0.230620
\(646\) 0 0
\(647\) −36.4248 −1.43201 −0.716004 0.698096i \(-0.754031\pi\)
−0.716004 + 0.698096i \(0.754031\pi\)
\(648\) 0 0
\(649\) 2.45139 0.0962254
\(650\) 0 0
\(651\) 38.1310 1.49447
\(652\) 0 0
\(653\) 11.3383 0.443700 0.221850 0.975081i \(-0.428790\pi\)
0.221850 + 0.975081i \(0.428790\pi\)
\(654\) 0 0
\(655\) −0.720727 −0.0281611
\(656\) 0 0
\(657\) 3.25964 0.127171
\(658\) 0 0
\(659\) 24.0738 0.937784 0.468892 0.883256i \(-0.344653\pi\)
0.468892 + 0.883256i \(0.344653\pi\)
\(660\) 0 0
\(661\) −12.6937 −0.493727 −0.246864 0.969050i \(-0.579400\pi\)
−0.246864 + 0.969050i \(0.579400\pi\)
\(662\) 0 0
\(663\) 3.12330 0.121299
\(664\) 0 0
\(665\) 17.8390 0.691768
\(666\) 0 0
\(667\) −34.3396 −1.32963
\(668\) 0 0
\(669\) −3.05812 −0.118234
\(670\) 0 0
\(671\) 4.45039 0.171805
\(672\) 0 0
\(673\) 27.7973 1.07151 0.535754 0.844374i \(-0.320027\pi\)
0.535754 + 0.844374i \(0.320027\pi\)
\(674\) 0 0
\(675\) −4.26428 −0.164132
\(676\) 0 0
\(677\) 9.33163 0.358644 0.179322 0.983790i \(-0.442610\pi\)
0.179322 + 0.983790i \(0.442610\pi\)
\(678\) 0 0
\(679\) 22.5487 0.865339
\(680\) 0 0
\(681\) 26.8870 1.03031
\(682\) 0 0
\(683\) 27.8946 1.06736 0.533678 0.845688i \(-0.320810\pi\)
0.533678 + 0.845688i \(0.320810\pi\)
\(684\) 0 0
\(685\) 11.8434 0.452512
\(686\) 0 0
\(687\) 46.6333 1.77917
\(688\) 0 0
\(689\) −1.84378 −0.0702424
\(690\) 0 0
\(691\) 33.4529 1.27261 0.636304 0.771438i \(-0.280462\pi\)
0.636304 + 0.771438i \(0.280462\pi\)
\(692\) 0 0
\(693\) 1.77958 0.0676008
\(694\) 0 0
\(695\) −5.31971 −0.201788
\(696\) 0 0
\(697\) −8.05679 −0.305173
\(698\) 0 0
\(699\) −9.31213 −0.352217
\(700\) 0 0
\(701\) −23.6802 −0.894389 −0.447194 0.894437i \(-0.647577\pi\)
−0.447194 + 0.894437i \(0.647577\pi\)
\(702\) 0 0
\(703\) 42.9850 1.62121
\(704\) 0 0
\(705\) 4.76154 0.179330
\(706\) 0 0
\(707\) −10.0221 −0.376919
\(708\) 0 0
\(709\) 39.8489 1.49656 0.748278 0.663385i \(-0.230881\pi\)
0.748278 + 0.663385i \(0.230881\pi\)
\(710\) 0 0
\(711\) −7.86185 −0.294842
\(712\) 0 0
\(713\) 44.6719 1.67298
\(714\) 0 0
\(715\) 0.273169 0.0102160
\(716\) 0 0
\(717\) 14.0316 0.524021
\(718\) 0 0
\(719\) 25.2914 0.943209 0.471605 0.881810i \(-0.343675\pi\)
0.471605 + 0.881810i \(0.343675\pi\)
\(720\) 0 0
\(721\) −1.89729 −0.0706586
\(722\) 0 0
\(723\) −14.8446 −0.552078
\(724\) 0 0
\(725\) −6.90963 −0.256617
\(726\) 0 0
\(727\) 48.2882 1.79091 0.895454 0.445154i \(-0.146851\pi\)
0.895454 + 0.445154i \(0.146851\pi\)
\(728\) 0 0
\(729\) 16.1792 0.599229
\(730\) 0 0
\(731\) −17.5883 −0.650526
\(732\) 0 0
\(733\) 42.3662 1.56483 0.782416 0.622757i \(-0.213987\pi\)
0.782416 + 0.622757i \(0.213987\pi\)
\(734\) 0 0
\(735\) 4.46649 0.164749
\(736\) 0 0
\(737\) −13.0170 −0.479487
\(738\) 0 0
\(739\) −22.6921 −0.834743 −0.417371 0.908736i \(-0.637049\pi\)
−0.417371 + 0.908736i \(0.637049\pi\)
\(740\) 0 0
\(741\) 4.37377 0.160674
\(742\) 0 0
\(743\) 31.9848 1.17341 0.586703 0.809802i \(-0.300425\pi\)
0.586703 + 0.809802i \(0.300425\pi\)
\(744\) 0 0
\(745\) −9.30295 −0.340834
\(746\) 0 0
\(747\) −9.66073 −0.353467
\(748\) 0 0
\(749\) −19.9202 −0.727870
\(750\) 0 0
\(751\) −6.31847 −0.230564 −0.115282 0.993333i \(-0.536777\pi\)
−0.115282 + 0.993333i \(0.536777\pi\)
\(752\) 0 0
\(753\) 54.0733 1.97054
\(754\) 0 0
\(755\) −2.32280 −0.0845354
\(756\) 0 0
\(757\) 14.0729 0.511488 0.255744 0.966745i \(-0.417680\pi\)
0.255744 + 0.966745i \(0.417680\pi\)
\(758\) 0 0
\(759\) 9.73578 0.353386
\(760\) 0 0
\(761\) 10.1389 0.367535 0.183768 0.982970i \(-0.441171\pi\)
0.183768 + 0.982970i \(0.441171\pi\)
\(762\) 0 0
\(763\) −5.74714 −0.208060
\(764\) 0 0
\(765\) 4.79641 0.173415
\(766\) 0 0
\(767\) −0.666132 −0.0240526
\(768\) 0 0
\(769\) 6.73480 0.242863 0.121432 0.992600i \(-0.461251\pi\)
0.121432 + 0.992600i \(0.461251\pi\)
\(770\) 0 0
\(771\) −18.2853 −0.658528
\(772\) 0 0
\(773\) 28.6933 1.03203 0.516013 0.856581i \(-0.327416\pi\)
0.516013 + 0.856581i \(0.327416\pi\)
\(774\) 0 0
\(775\) 8.98865 0.322882
\(776\) 0 0
\(777\) −22.1934 −0.796183
\(778\) 0 0
\(779\) −11.2825 −0.404237
\(780\) 0 0
\(781\) −6.93542 −0.248169
\(782\) 0 0
\(783\) 29.4646 1.05298
\(784\) 0 0
\(785\) 14.5276 0.518513
\(786\) 0 0
\(787\) 0.345425 0.0123131 0.00615654 0.999981i \(-0.498040\pi\)
0.00615654 + 0.999981i \(0.498040\pi\)
\(788\) 0 0
\(789\) −55.5850 −1.97888
\(790\) 0 0
\(791\) −14.8422 −0.527727
\(792\) 0 0
\(793\) −1.20933 −0.0429447
\(794\) 0 0
\(795\) −13.2223 −0.468947
\(796\) 0 0
\(797\) −40.4292 −1.43208 −0.716038 0.698061i \(-0.754046\pi\)
−0.716038 + 0.698061i \(0.754046\pi\)
\(798\) 0 0
\(799\) 14.2986 0.505847
\(800\) 0 0
\(801\) −9.80500 −0.346443
\(802\) 0 0
\(803\) 3.99788 0.141082
\(804\) 0 0
\(805\) −10.7903 −0.380309
\(806\) 0 0
\(807\) 22.5838 0.794988
\(808\) 0 0
\(809\) −16.7938 −0.590438 −0.295219 0.955430i \(-0.595393\pi\)
−0.295219 + 0.955430i \(0.595393\pi\)
\(810\) 0 0
\(811\) 28.9934 1.01809 0.509047 0.860739i \(-0.329998\pi\)
0.509047 + 0.860739i \(0.329998\pi\)
\(812\) 0 0
\(813\) 37.3920 1.31139
\(814\) 0 0
\(815\) 0.478693 0.0167679
\(816\) 0 0
\(817\) −24.6301 −0.861697
\(818\) 0 0
\(819\) −0.483578 −0.0168976
\(820\) 0 0
\(821\) −15.2016 −0.530539 −0.265269 0.964174i \(-0.585461\pi\)
−0.265269 + 0.964174i \(0.585461\pi\)
\(822\) 0 0
\(823\) 8.28104 0.288659 0.144329 0.989530i \(-0.453898\pi\)
0.144329 + 0.989530i \(0.453898\pi\)
\(824\) 0 0
\(825\) 1.95898 0.0682030
\(826\) 0 0
\(827\) 34.3396 1.19410 0.597052 0.802202i \(-0.296338\pi\)
0.597052 + 0.802202i \(0.296338\pi\)
\(828\) 0 0
\(829\) 10.5395 0.366050 0.183025 0.983108i \(-0.441411\pi\)
0.183025 + 0.983108i \(0.441411\pi\)
\(830\) 0 0
\(831\) 60.6068 2.10243
\(832\) 0 0
\(833\) 13.4126 0.464718
\(834\) 0 0
\(835\) 20.9805 0.726059
\(836\) 0 0
\(837\) −38.3301 −1.32488
\(838\) 0 0
\(839\) −32.6721 −1.12797 −0.563983 0.825786i \(-0.690732\pi\)
−0.563983 + 0.825786i \(0.690732\pi\)
\(840\) 0 0
\(841\) 18.7430 0.646310
\(842\) 0 0
\(843\) −41.3755 −1.42505
\(844\) 0 0
\(845\) 12.9258 0.444660
\(846\) 0 0
\(847\) −21.7003 −0.745631
\(848\) 0 0
\(849\) −56.8134 −1.94983
\(850\) 0 0
\(851\) −26.0004 −0.891282
\(852\) 0 0
\(853\) −24.8395 −0.850487 −0.425243 0.905079i \(-0.639812\pi\)
−0.425243 + 0.905079i \(0.639812\pi\)
\(854\) 0 0
\(855\) 6.71674 0.229708
\(856\) 0 0
\(857\) −31.1677 −1.06467 −0.532335 0.846534i \(-0.678685\pi\)
−0.532335 + 0.846534i \(0.678685\pi\)
\(858\) 0 0
\(859\) 29.8739 1.01928 0.509642 0.860386i \(-0.329778\pi\)
0.509642 + 0.860386i \(0.329778\pi\)
\(860\) 0 0
\(861\) 5.82520 0.198522
\(862\) 0 0
\(863\) 42.7868 1.45648 0.728239 0.685323i \(-0.240339\pi\)
0.728239 + 0.685323i \(0.240339\pi\)
\(864\) 0 0
\(865\) −10.0599 −0.342046
\(866\) 0 0
\(867\) 34.0449 1.15623
\(868\) 0 0
\(869\) −9.64238 −0.327096
\(870\) 0 0
\(871\) 3.53719 0.119853
\(872\) 0 0
\(873\) 8.49002 0.287344
\(874\) 0 0
\(875\) −2.17117 −0.0733991
\(876\) 0 0
\(877\) −22.0240 −0.743698 −0.371849 0.928293i \(-0.621276\pi\)
−0.371849 + 0.928293i \(0.621276\pi\)
\(878\) 0 0
\(879\) 12.2382 0.412783
\(880\) 0 0
\(881\) −9.14501 −0.308103 −0.154052 0.988063i \(-0.549232\pi\)
−0.154052 + 0.988063i \(0.549232\pi\)
\(882\) 0 0
\(883\) 41.1298 1.38413 0.692064 0.721836i \(-0.256701\pi\)
0.692064 + 0.721836i \(0.256701\pi\)
\(884\) 0 0
\(885\) −4.77704 −0.160579
\(886\) 0 0
\(887\) 44.1121 1.48114 0.740569 0.671980i \(-0.234556\pi\)
0.740569 + 0.671980i \(0.234556\pi\)
\(888\) 0 0
\(889\) 1.51190 0.0507077
\(890\) 0 0
\(891\) −10.8126 −0.362235
\(892\) 0 0
\(893\) 20.0233 0.670054
\(894\) 0 0
\(895\) −12.0961 −0.404327
\(896\) 0 0
\(897\) −2.64557 −0.0883330
\(898\) 0 0
\(899\) −62.1082 −2.07143
\(900\) 0 0
\(901\) −39.7058 −1.32279
\(902\) 0 0
\(903\) 12.7166 0.423183
\(904\) 0 0
\(905\) 3.77666 0.125540
\(906\) 0 0
\(907\) 31.0518 1.03106 0.515528 0.856872i \(-0.327596\pi\)
0.515528 + 0.856872i \(0.327596\pi\)
\(908\) 0 0
\(909\) −3.77351 −0.125159
\(910\) 0 0
\(911\) −52.9618 −1.75470 −0.877351 0.479849i \(-0.840691\pi\)
−0.877351 + 0.479849i \(0.840691\pi\)
\(912\) 0 0
\(913\) −11.8487 −0.392134
\(914\) 0 0
\(915\) −8.67252 −0.286705
\(916\) 0 0
\(917\) 1.56482 0.0516750
\(918\) 0 0
\(919\) −5.80731 −0.191565 −0.0957827 0.995402i \(-0.530535\pi\)
−0.0957827 + 0.995402i \(0.530535\pi\)
\(920\) 0 0
\(921\) −0.627810 −0.0206870
\(922\) 0 0
\(923\) 1.88461 0.0620327
\(924\) 0 0
\(925\) −5.23167 −0.172016
\(926\) 0 0
\(927\) −0.714365 −0.0234628
\(928\) 0 0
\(929\) 23.2136 0.761615 0.380807 0.924654i \(-0.375646\pi\)
0.380807 + 0.924654i \(0.375646\pi\)
\(930\) 0 0
\(931\) 18.7825 0.615572
\(932\) 0 0
\(933\) −60.6476 −1.98551
\(934\) 0 0
\(935\) 5.88269 0.192385
\(936\) 0 0
\(937\) −22.9324 −0.749169 −0.374584 0.927193i \(-0.622215\pi\)
−0.374584 + 0.927193i \(0.622215\pi\)
\(938\) 0 0
\(939\) 18.6860 0.609794
\(940\) 0 0
\(941\) −41.3910 −1.34931 −0.674654 0.738134i \(-0.735707\pi\)
−0.674654 + 0.738134i \(0.735707\pi\)
\(942\) 0 0
\(943\) 6.82445 0.222235
\(944\) 0 0
\(945\) 9.25849 0.301179
\(946\) 0 0
\(947\) 1.94821 0.0633083 0.0316542 0.999499i \(-0.489922\pi\)
0.0316542 + 0.999499i \(0.489922\pi\)
\(948\) 0 0
\(949\) −1.08637 −0.0352651
\(950\) 0 0
\(951\) 0.816110 0.0264642
\(952\) 0 0
\(953\) −19.2668 −0.624114 −0.312057 0.950063i \(-0.601018\pi\)
−0.312057 + 0.950063i \(0.601018\pi\)
\(954\) 0 0
\(955\) −0.0106466 −0.000344515 0
\(956\) 0 0
\(957\) −13.5358 −0.437552
\(958\) 0 0
\(959\) −25.7140 −0.830350
\(960\) 0 0
\(961\) 49.7958 1.60632
\(962\) 0 0
\(963\) −7.50036 −0.241696
\(964\) 0 0
\(965\) −7.75149 −0.249529
\(966\) 0 0
\(967\) −52.3285 −1.68277 −0.841385 0.540436i \(-0.818259\pi\)
−0.841385 + 0.540436i \(0.818259\pi\)
\(968\) 0 0
\(969\) 94.1890 3.02579
\(970\) 0 0
\(971\) 16.4905 0.529206 0.264603 0.964357i \(-0.414759\pi\)
0.264603 + 0.964357i \(0.414759\pi\)
\(972\) 0 0
\(973\) 11.5500 0.370277
\(974\) 0 0
\(975\) −0.532328 −0.0170481
\(976\) 0 0
\(977\) 19.5252 0.624666 0.312333 0.949973i \(-0.398890\pi\)
0.312333 + 0.949973i \(0.398890\pi\)
\(978\) 0 0
\(979\) −12.0256 −0.384340
\(980\) 0 0
\(981\) −2.16391 −0.0690882
\(982\) 0 0
\(983\) −16.9262 −0.539863 −0.269932 0.962879i \(-0.587001\pi\)
−0.269932 + 0.962879i \(0.587001\pi\)
\(984\) 0 0
\(985\) −26.0365 −0.829592
\(986\) 0 0
\(987\) −10.3381 −0.329066
\(988\) 0 0
\(989\) 14.8980 0.473730
\(990\) 0 0
\(991\) 39.6379 1.25914 0.629569 0.776945i \(-0.283232\pi\)
0.629569 + 0.776945i \(0.283232\pi\)
\(992\) 0 0
\(993\) −8.15004 −0.258634
\(994\) 0 0
\(995\) 0.0624479 0.00197973
\(996\) 0 0
\(997\) 55.0315 1.74287 0.871433 0.490515i \(-0.163191\pi\)
0.871433 + 0.490515i \(0.163191\pi\)
\(998\) 0 0
\(999\) 22.3093 0.705834
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 8020.2.a.c.1.22 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8020.2.a.c.1.22 28 1.1 even 1 trivial