Properties

Label 3640.2.a.l.1.2
Level $3640$
Weight $2$
Character 3640.1
Self dual yes
Analytic conductor $29.066$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3640 = 2^{3} \cdot 5 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3640.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(29.0655463357\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Defining polynomial: \( x^{2} - x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.30278\) of defining polynomial
Character \(\chi\) \(=\) 3640.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.30278 q^{3} +1.00000 q^{5} +1.00000 q^{7} -1.30278 q^{9} +O(q^{10})\) \(q+1.30278 q^{3} +1.00000 q^{5} +1.00000 q^{7} -1.30278 q^{9} -4.60555 q^{11} -1.00000 q^{13} +1.30278 q^{15} +6.30278 q^{17} -6.30278 q^{19} +1.30278 q^{21} -8.00000 q^{23} +1.00000 q^{25} -5.60555 q^{27} +1.90833 q^{29} -0.697224 q^{31} -6.00000 q^{33} +1.00000 q^{35} -3.90833 q^{37} -1.30278 q^{39} -4.30278 q^{41} -2.00000 q^{43} -1.30278 q^{45} -4.60555 q^{47} +1.00000 q^{49} +8.21110 q^{51} -2.60555 q^{53} -4.60555 q^{55} -8.21110 q^{57} +11.1194 q^{59} -1.21110 q^{61} -1.30278 q^{63} -1.00000 q^{65} +8.90833 q^{67} -10.4222 q^{69} -2.60555 q^{71} -8.60555 q^{73} +1.30278 q^{75} -4.60555 q^{77} +3.51388 q^{79} -3.39445 q^{81} -11.8167 q^{83} +6.30278 q^{85} +2.48612 q^{87} -7.30278 q^{89} -1.00000 q^{91} -0.908327 q^{93} -6.30278 q^{95} -13.2111 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{3} + 2 q^{5} + 2 q^{7} + q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{3} + 2 q^{5} + 2 q^{7} + q^{9} - 2 q^{11} - 2 q^{13} - q^{15} + 9 q^{17} - 9 q^{19} - q^{21} - 16 q^{23} + 2 q^{25} - 4 q^{27} - 7 q^{29} - 5 q^{31} - 12 q^{33} + 2 q^{35} + 3 q^{37} + q^{39} - 5 q^{41} - 4 q^{43} + q^{45} - 2 q^{47} + 2 q^{49} + 2 q^{51} + 2 q^{53} - 2 q^{55} - 2 q^{57} - 3 q^{59} + 12 q^{61} + q^{63} - 2 q^{65} + 7 q^{67} + 8 q^{69} + 2 q^{71} - 10 q^{73} - q^{75} - 2 q^{77} - 11 q^{79} - 14 q^{81} - 2 q^{83} + 9 q^{85} + 23 q^{87} - 11 q^{89} - 2 q^{91} + 9 q^{93} - 9 q^{95} - 12 q^{97} + 12 q^{99}+O(q^{100}) \) 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
\(3\) 1.30278 0.752158 0.376079 0.926588i \(-0.377272\pi\)
0.376079 + 0.926588i \(0.377272\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −1.30278 −0.434259
\(10\) 0 0
\(11\) −4.60555 −1.38863 −0.694313 0.719673i \(-0.744292\pi\)
−0.694313 + 0.719673i \(0.744292\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) 1.30278 0.336375
\(16\) 0 0
\(17\) 6.30278 1.52865 0.764324 0.644833i \(-0.223073\pi\)
0.764324 + 0.644833i \(0.223073\pi\)
\(18\) 0 0
\(19\) −6.30278 −1.44596 −0.722978 0.690871i \(-0.757227\pi\)
−0.722978 + 0.690871i \(0.757227\pi\)
\(20\) 0 0
\(21\) 1.30278 0.284289
\(22\) 0 0
\(23\) −8.00000 −1.66812 −0.834058 0.551677i \(-0.813988\pi\)
−0.834058 + 0.551677i \(0.813988\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −5.60555 −1.07879
\(28\) 0 0
\(29\) 1.90833 0.354367 0.177184 0.984178i \(-0.443301\pi\)
0.177184 + 0.984178i \(0.443301\pi\)
\(30\) 0 0
\(31\) −0.697224 −0.125225 −0.0626126 0.998038i \(-0.519943\pi\)
−0.0626126 + 0.998038i \(0.519943\pi\)
\(32\) 0 0
\(33\) −6.00000 −1.04447
\(34\) 0 0
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −3.90833 −0.642525 −0.321262 0.946990i \(-0.604107\pi\)
−0.321262 + 0.946990i \(0.604107\pi\)
\(38\) 0 0
\(39\) −1.30278 −0.208611
\(40\) 0 0
\(41\) −4.30278 −0.671981 −0.335990 0.941865i \(-0.609071\pi\)
−0.335990 + 0.941865i \(0.609071\pi\)
\(42\) 0 0
\(43\) −2.00000 −0.304997 −0.152499 0.988304i \(-0.548732\pi\)
−0.152499 + 0.988304i \(0.548732\pi\)
\(44\) 0 0
\(45\) −1.30278 −0.194206
\(46\) 0 0
\(47\) −4.60555 −0.671789 −0.335894 0.941900i \(-0.609039\pi\)
−0.335894 + 0.941900i \(0.609039\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 8.21110 1.14978
\(52\) 0 0
\(53\) −2.60555 −0.357900 −0.178950 0.983858i \(-0.557270\pi\)
−0.178950 + 0.983858i \(0.557270\pi\)
\(54\) 0 0
\(55\) −4.60555 −0.621012
\(56\) 0 0
\(57\) −8.21110 −1.08759
\(58\) 0 0
\(59\) 11.1194 1.44763 0.723813 0.689996i \(-0.242388\pi\)
0.723813 + 0.689996i \(0.242388\pi\)
\(60\) 0 0
\(61\) −1.21110 −0.155066 −0.0775329 0.996990i \(-0.524704\pi\)
−0.0775329 + 0.996990i \(0.524704\pi\)
\(62\) 0 0
\(63\) −1.30278 −0.164134
\(64\) 0 0
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 8.90833 1.08833 0.544163 0.838980i \(-0.316847\pi\)
0.544163 + 0.838980i \(0.316847\pi\)
\(68\) 0 0
\(69\) −10.4222 −1.25469
\(70\) 0 0
\(71\) −2.60555 −0.309222 −0.154611 0.987975i \(-0.549412\pi\)
−0.154611 + 0.987975i \(0.549412\pi\)
\(72\) 0 0
\(73\) −8.60555 −1.00720 −0.503602 0.863936i \(-0.667992\pi\)
−0.503602 + 0.863936i \(0.667992\pi\)
\(74\) 0 0
\(75\) 1.30278 0.150432
\(76\) 0 0
\(77\) −4.60555 −0.524851
\(78\) 0 0
\(79\) 3.51388 0.395342 0.197671 0.980268i \(-0.436662\pi\)
0.197671 + 0.980268i \(0.436662\pi\)
\(80\) 0 0
\(81\) −3.39445 −0.377161
\(82\) 0 0
\(83\) −11.8167 −1.29705 −0.648523 0.761195i \(-0.724613\pi\)
−0.648523 + 0.761195i \(0.724613\pi\)
\(84\) 0 0
\(85\) 6.30278 0.683632
\(86\) 0 0
\(87\) 2.48612 0.266540
\(88\) 0 0
\(89\) −7.30278 −0.774093 −0.387046 0.922060i \(-0.626505\pi\)
−0.387046 + 0.922060i \(0.626505\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) −0.908327 −0.0941891
\(94\) 0 0
\(95\) −6.30278 −0.646651
\(96\) 0 0
\(97\) −13.2111 −1.34138 −0.670692 0.741736i \(-0.734003\pi\)
−0.670692 + 0.741736i \(0.734003\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 6.00000 0.597022 0.298511 0.954406i \(-0.403510\pi\)
0.298511 + 0.954406i \(0.403510\pi\)
\(102\) 0 0
\(103\) −8.90833 −0.877764 −0.438882 0.898545i \(-0.644625\pi\)
−0.438882 + 0.898545i \(0.644625\pi\)
\(104\) 0 0
\(105\) 1.30278 0.127138
\(106\) 0 0
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 0 0
\(109\) −4.00000 −0.383131 −0.191565 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 0 0
\(111\) −5.09167 −0.483280
\(112\) 0 0
\(113\) 7.81665 0.735329 0.367664 0.929959i \(-0.380157\pi\)
0.367664 + 0.929959i \(0.380157\pi\)
\(114\) 0 0
\(115\) −8.00000 −0.746004
\(116\) 0 0
\(117\) 1.30278 0.120442
\(118\) 0 0
\(119\) 6.30278 0.577774
\(120\) 0 0
\(121\) 10.2111 0.928282
\(122\) 0 0
\(123\) −5.60555 −0.505436
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −8.60555 −0.763619 −0.381810 0.924241i \(-0.624699\pi\)
−0.381810 + 0.924241i \(0.624699\pi\)
\(128\) 0 0
\(129\) −2.60555 −0.229406
\(130\) 0 0
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −6.30278 −0.546520
\(134\) 0 0
\(135\) −5.60555 −0.482449
\(136\) 0 0
\(137\) 2.69722 0.230439 0.115220 0.993340i \(-0.463243\pi\)
0.115220 + 0.993340i \(0.463243\pi\)
\(138\) 0 0
\(139\) 16.4222 1.39291 0.696457 0.717599i \(-0.254759\pi\)
0.696457 + 0.717599i \(0.254759\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 4.60555 0.385136
\(144\) 0 0
\(145\) 1.90833 0.158478
\(146\) 0 0
\(147\) 1.30278 0.107451
\(148\) 0 0
\(149\) 8.00000 0.655386 0.327693 0.944784i \(-0.393729\pi\)
0.327693 + 0.944784i \(0.393729\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) 0 0
\(153\) −8.21110 −0.663828
\(154\) 0 0
\(155\) −0.697224 −0.0560024
\(156\) 0 0
\(157\) 10.5139 0.839099 0.419549 0.907732i \(-0.362188\pi\)
0.419549 + 0.907732i \(0.362188\pi\)
\(158\) 0 0
\(159\) −3.39445 −0.269197
\(160\) 0 0
\(161\) −8.00000 −0.630488
\(162\) 0 0
\(163\) 25.1194 1.96751 0.983753 0.179528i \(-0.0574572\pi\)
0.983753 + 0.179528i \(0.0574572\pi\)
\(164\) 0 0
\(165\) −6.00000 −0.467099
\(166\) 0 0
\(167\) −23.2111 −1.79613 −0.898065 0.439864i \(-0.855027\pi\)
−0.898065 + 0.439864i \(0.855027\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 8.21110 0.627919
\(172\) 0 0
\(173\) 18.6972 1.42152 0.710762 0.703433i \(-0.248350\pi\)
0.710762 + 0.703433i \(0.248350\pi\)
\(174\) 0 0
\(175\) 1.00000 0.0755929
\(176\) 0 0
\(177\) 14.4861 1.08884
\(178\) 0 0
\(179\) −9.09167 −0.679544 −0.339772 0.940508i \(-0.610350\pi\)
−0.339772 + 0.940508i \(0.610350\pi\)
\(180\) 0 0
\(181\) 9.81665 0.729666 0.364833 0.931073i \(-0.381126\pi\)
0.364833 + 0.931073i \(0.381126\pi\)
\(182\) 0 0
\(183\) −1.57779 −0.116634
\(184\) 0 0
\(185\) −3.90833 −0.287346
\(186\) 0 0
\(187\) −29.0278 −2.12272
\(188\) 0 0
\(189\) −5.60555 −0.407744
\(190\) 0 0
\(191\) −16.5139 −1.19490 −0.597451 0.801905i \(-0.703820\pi\)
−0.597451 + 0.801905i \(0.703820\pi\)
\(192\) 0 0
\(193\) 10.9083 0.785199 0.392599 0.919710i \(-0.371576\pi\)
0.392599 + 0.919710i \(0.371576\pi\)
\(194\) 0 0
\(195\) −1.30278 −0.0932937
\(196\) 0 0
\(197\) 13.1194 0.934721 0.467360 0.884067i \(-0.345205\pi\)
0.467360 + 0.884067i \(0.345205\pi\)
\(198\) 0 0
\(199\) 1.21110 0.0858528 0.0429264 0.999078i \(-0.486332\pi\)
0.0429264 + 0.999078i \(0.486332\pi\)
\(200\) 0 0
\(201\) 11.6056 0.818592
\(202\) 0 0
\(203\) 1.90833 0.133938
\(204\) 0 0
\(205\) −4.30278 −0.300519
\(206\) 0 0
\(207\) 10.4222 0.724393
\(208\) 0 0
\(209\) 29.0278 2.00789
\(210\) 0 0
\(211\) 11.5139 0.792648 0.396324 0.918111i \(-0.370286\pi\)
0.396324 + 0.918111i \(0.370286\pi\)
\(212\) 0 0
\(213\) −3.39445 −0.232584
\(214\) 0 0
\(215\) −2.00000 −0.136399
\(216\) 0 0
\(217\) −0.697224 −0.0473307
\(218\) 0 0
\(219\) −11.2111 −0.757576
\(220\) 0 0
\(221\) −6.30278 −0.423971
\(222\) 0 0
\(223\) 13.2111 0.884681 0.442340 0.896847i \(-0.354148\pi\)
0.442340 + 0.896847i \(0.354148\pi\)
\(224\) 0 0
\(225\) −1.30278 −0.0868517
\(226\) 0 0
\(227\) −19.8167 −1.31528 −0.657639 0.753333i \(-0.728445\pi\)
−0.657639 + 0.753333i \(0.728445\pi\)
\(228\) 0 0
\(229\) −0.302776 −0.0200080 −0.0100040 0.999950i \(-0.503184\pi\)
−0.0100040 + 0.999950i \(0.503184\pi\)
\(230\) 0 0
\(231\) −6.00000 −0.394771
\(232\) 0 0
\(233\) −1.81665 −0.119013 −0.0595065 0.998228i \(-0.518953\pi\)
−0.0595065 + 0.998228i \(0.518953\pi\)
\(234\) 0 0
\(235\) −4.60555 −0.300433
\(236\) 0 0
\(237\) 4.57779 0.297360
\(238\) 0 0
\(239\) 21.6333 1.39934 0.699671 0.714465i \(-0.253330\pi\)
0.699671 + 0.714465i \(0.253330\pi\)
\(240\) 0 0
\(241\) −16.9083 −1.08916 −0.544581 0.838709i \(-0.683311\pi\)
−0.544581 + 0.838709i \(0.683311\pi\)
\(242\) 0 0
\(243\) 12.3944 0.795104
\(244\) 0 0
\(245\) 1.00000 0.0638877
\(246\) 0 0
\(247\) 6.30278 0.401036
\(248\) 0 0
\(249\) −15.3944 −0.975584
\(250\) 0 0
\(251\) −27.6333 −1.74420 −0.872099 0.489329i \(-0.837242\pi\)
−0.872099 + 0.489329i \(0.837242\pi\)
\(252\) 0 0
\(253\) 36.8444 2.31639
\(254\) 0 0
\(255\) 8.21110 0.514199
\(256\) 0 0
\(257\) 21.6333 1.34945 0.674724 0.738070i \(-0.264263\pi\)
0.674724 + 0.738070i \(0.264263\pi\)
\(258\) 0 0
\(259\) −3.90833 −0.242852
\(260\) 0 0
\(261\) −2.48612 −0.153887
\(262\) 0 0
\(263\) 15.6333 0.963991 0.481996 0.876174i \(-0.339912\pi\)
0.481996 + 0.876174i \(0.339912\pi\)
\(264\) 0 0
\(265\) −2.60555 −0.160058
\(266\) 0 0
\(267\) −9.51388 −0.582240
\(268\) 0 0
\(269\) −17.8167 −1.08630 −0.543150 0.839636i \(-0.682769\pi\)
−0.543150 + 0.839636i \(0.682769\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0 0
\(273\) −1.30278 −0.0788476
\(274\) 0 0
\(275\) −4.60555 −0.277725
\(276\) 0 0
\(277\) 1.21110 0.0727681 0.0363840 0.999338i \(-0.488416\pi\)
0.0363840 + 0.999338i \(0.488416\pi\)
\(278\) 0 0
\(279\) 0.908327 0.0543801
\(280\) 0 0
\(281\) −32.0000 −1.90896 −0.954480 0.298275i \(-0.903589\pi\)
−0.954480 + 0.298275i \(0.903589\pi\)
\(282\) 0 0
\(283\) −15.0917 −0.897107 −0.448553 0.893756i \(-0.648061\pi\)
−0.448553 + 0.893756i \(0.648061\pi\)
\(284\) 0 0
\(285\) −8.21110 −0.486384
\(286\) 0 0
\(287\) −4.30278 −0.253985
\(288\) 0 0
\(289\) 22.7250 1.33676
\(290\) 0 0
\(291\) −17.2111 −1.00893
\(292\) 0 0
\(293\) 2.42221 0.141507 0.0707534 0.997494i \(-0.477460\pi\)
0.0707534 + 0.997494i \(0.477460\pi\)
\(294\) 0 0
\(295\) 11.1194 0.647398
\(296\) 0 0
\(297\) 25.8167 1.49803
\(298\) 0 0
\(299\) 8.00000 0.462652
\(300\) 0 0
\(301\) −2.00000 −0.115278
\(302\) 0 0
\(303\) 7.81665 0.449055
\(304\) 0 0
\(305\) −1.21110 −0.0693475
\(306\) 0 0
\(307\) 7.39445 0.422023 0.211012 0.977484i \(-0.432324\pi\)
0.211012 + 0.977484i \(0.432324\pi\)
\(308\) 0 0
\(309\) −11.6056 −0.660217
\(310\) 0 0
\(311\) −23.0278 −1.30578 −0.652892 0.757451i \(-0.726445\pi\)
−0.652892 + 0.757451i \(0.726445\pi\)
\(312\) 0 0
\(313\) −30.3305 −1.71438 −0.857192 0.514998i \(-0.827793\pi\)
−0.857192 + 0.514998i \(0.827793\pi\)
\(314\) 0 0
\(315\) −1.30278 −0.0734031
\(316\) 0 0
\(317\) −16.4222 −0.922363 −0.461181 0.887306i \(-0.652574\pi\)
−0.461181 + 0.887306i \(0.652574\pi\)
\(318\) 0 0
\(319\) −8.78890 −0.492084
\(320\) 0 0
\(321\) −7.81665 −0.436283
\(322\) 0 0
\(323\) −39.7250 −2.21036
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0 0
\(327\) −5.21110 −0.288175
\(328\) 0 0
\(329\) −4.60555 −0.253912
\(330\) 0 0
\(331\) 18.0000 0.989369 0.494685 0.869072i \(-0.335284\pi\)
0.494685 + 0.869072i \(0.335284\pi\)
\(332\) 0 0
\(333\) 5.09167 0.279022
\(334\) 0 0
\(335\) 8.90833 0.486714
\(336\) 0 0
\(337\) −24.4222 −1.33036 −0.665181 0.746682i \(-0.731646\pi\)
−0.665181 + 0.746682i \(0.731646\pi\)
\(338\) 0 0
\(339\) 10.1833 0.553083
\(340\) 0 0
\(341\) 3.21110 0.173891
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −10.4222 −0.561113
\(346\) 0 0
\(347\) −29.8167 −1.60064 −0.800321 0.599572i \(-0.795338\pi\)
−0.800321 + 0.599572i \(0.795338\pi\)
\(348\) 0 0
\(349\) −22.9361 −1.22774 −0.613870 0.789407i \(-0.710388\pi\)
−0.613870 + 0.789407i \(0.710388\pi\)
\(350\) 0 0
\(351\) 5.60555 0.299202
\(352\) 0 0
\(353\) 17.6333 0.938526 0.469263 0.883058i \(-0.344520\pi\)
0.469263 + 0.883058i \(0.344520\pi\)
\(354\) 0 0
\(355\) −2.60555 −0.138288
\(356\) 0 0
\(357\) 8.21110 0.434578
\(358\) 0 0
\(359\) 25.0278 1.32091 0.660457 0.750864i \(-0.270362\pi\)
0.660457 + 0.750864i \(0.270362\pi\)
\(360\) 0 0
\(361\) 20.7250 1.09079
\(362\) 0 0
\(363\) 13.3028 0.698215
\(364\) 0 0
\(365\) −8.60555 −0.450435
\(366\) 0 0
\(367\) 30.4222 1.58803 0.794013 0.607901i \(-0.207988\pi\)
0.794013 + 0.607901i \(0.207988\pi\)
\(368\) 0 0
\(369\) 5.60555 0.291813
\(370\) 0 0
\(371\) −2.60555 −0.135273
\(372\) 0 0
\(373\) −14.0000 −0.724893 −0.362446 0.932005i \(-0.618058\pi\)
−0.362446 + 0.932005i \(0.618058\pi\)
\(374\) 0 0
\(375\) 1.30278 0.0672750
\(376\) 0 0
\(377\) −1.90833 −0.0982838
\(378\) 0 0
\(379\) −29.6333 −1.52216 −0.761080 0.648658i \(-0.775331\pi\)
−0.761080 + 0.648658i \(0.775331\pi\)
\(380\) 0 0
\(381\) −11.2111 −0.574362
\(382\) 0 0
\(383\) −24.2389 −1.23855 −0.619274 0.785175i \(-0.712573\pi\)
−0.619274 + 0.785175i \(0.712573\pi\)
\(384\) 0 0
\(385\) −4.60555 −0.234721
\(386\) 0 0
\(387\) 2.60555 0.132448
\(388\) 0 0
\(389\) 9.51388 0.482373 0.241186 0.970479i \(-0.422463\pi\)
0.241186 + 0.970479i \(0.422463\pi\)
\(390\) 0 0
\(391\) −50.4222 −2.54996
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 3.51388 0.176802
\(396\) 0 0
\(397\) 29.8167 1.49645 0.748227 0.663442i \(-0.230905\pi\)
0.748227 + 0.663442i \(0.230905\pi\)
\(398\) 0 0
\(399\) −8.21110 −0.411069
\(400\) 0 0
\(401\) −24.0000 −1.19850 −0.599251 0.800561i \(-0.704535\pi\)
−0.599251 + 0.800561i \(0.704535\pi\)
\(402\) 0 0
\(403\) 0.697224 0.0347312
\(404\) 0 0
\(405\) −3.39445 −0.168672
\(406\) 0 0
\(407\) 18.0000 0.892227
\(408\) 0 0
\(409\) −2.00000 −0.0988936 −0.0494468 0.998777i \(-0.515746\pi\)
−0.0494468 + 0.998777i \(0.515746\pi\)
\(410\) 0 0
\(411\) 3.51388 0.173327
\(412\) 0 0
\(413\) 11.1194 0.547151
\(414\) 0 0
\(415\) −11.8167 −0.580057
\(416\) 0 0
\(417\) 21.3944 1.04769
\(418\) 0 0
\(419\) 27.6333 1.34998 0.674988 0.737829i \(-0.264149\pi\)
0.674988 + 0.737829i \(0.264149\pi\)
\(420\) 0 0
\(421\) 16.4222 0.800369 0.400185 0.916435i \(-0.368946\pi\)
0.400185 + 0.916435i \(0.368946\pi\)
\(422\) 0 0
\(423\) 6.00000 0.291730
\(424\) 0 0
\(425\) 6.30278 0.305730
\(426\) 0 0
\(427\) −1.21110 −0.0586094
\(428\) 0 0
\(429\) 6.00000 0.289683
\(430\) 0 0
\(431\) −34.0000 −1.63772 −0.818861 0.573992i \(-0.805394\pi\)
−0.818861 + 0.573992i \(0.805394\pi\)
\(432\) 0 0
\(433\) 21.9361 1.05418 0.527090 0.849809i \(-0.323283\pi\)
0.527090 + 0.849809i \(0.323283\pi\)
\(434\) 0 0
\(435\) 2.48612 0.119200
\(436\) 0 0
\(437\) 50.4222 2.41202
\(438\) 0 0
\(439\) 4.78890 0.228562 0.114281 0.993448i \(-0.463544\pi\)
0.114281 + 0.993448i \(0.463544\pi\)
\(440\) 0 0
\(441\) −1.30278 −0.0620369
\(442\) 0 0
\(443\) 9.39445 0.446344 0.223172 0.974779i \(-0.428359\pi\)
0.223172 + 0.974779i \(0.428359\pi\)
\(444\) 0 0
\(445\) −7.30278 −0.346185
\(446\) 0 0
\(447\) 10.4222 0.492953
\(448\) 0 0
\(449\) 1.02776 0.0485028 0.0242514 0.999706i \(-0.492280\pi\)
0.0242514 + 0.999706i \(0.492280\pi\)
\(450\) 0 0
\(451\) 19.8167 0.933130
\(452\) 0 0
\(453\) −13.0278 −0.612097
\(454\) 0 0
\(455\) −1.00000 −0.0468807
\(456\) 0 0
\(457\) 9.48612 0.443742 0.221871 0.975076i \(-0.428784\pi\)
0.221871 + 0.975076i \(0.428784\pi\)
\(458\) 0 0
\(459\) −35.3305 −1.64909
\(460\) 0 0
\(461\) 14.0917 0.656315 0.328157 0.944623i \(-0.393572\pi\)
0.328157 + 0.944623i \(0.393572\pi\)
\(462\) 0 0
\(463\) −26.7250 −1.24202 −0.621008 0.783805i \(-0.713276\pi\)
−0.621008 + 0.783805i \(0.713276\pi\)
\(464\) 0 0
\(465\) −0.908327 −0.0421227
\(466\) 0 0
\(467\) −37.5139 −1.73594 −0.867968 0.496621i \(-0.834574\pi\)
−0.867968 + 0.496621i \(0.834574\pi\)
\(468\) 0 0
\(469\) 8.90833 0.411348
\(470\) 0 0
\(471\) 13.6972 0.631135
\(472\) 0 0
\(473\) 9.21110 0.423527
\(474\) 0 0
\(475\) −6.30278 −0.289191
\(476\) 0 0
\(477\) 3.39445 0.155421
\(478\) 0 0
\(479\) 30.0917 1.37492 0.687462 0.726221i \(-0.258725\pi\)
0.687462 + 0.726221i \(0.258725\pi\)
\(480\) 0 0
\(481\) 3.90833 0.178204
\(482\) 0 0
\(483\) −10.4222 −0.474227
\(484\) 0 0
\(485\) −13.2111 −0.599885
\(486\) 0 0
\(487\) 26.6972 1.20977 0.604883 0.796314i \(-0.293220\pi\)
0.604883 + 0.796314i \(0.293220\pi\)
\(488\) 0 0
\(489\) 32.7250 1.47987
\(490\) 0 0
\(491\) −1.57779 −0.0712049 −0.0356024 0.999366i \(-0.511335\pi\)
−0.0356024 + 0.999366i \(0.511335\pi\)
\(492\) 0 0
\(493\) 12.0278 0.541703
\(494\) 0 0
\(495\) 6.00000 0.269680
\(496\) 0 0
\(497\) −2.60555 −0.116875
\(498\) 0 0
\(499\) 26.0000 1.16392 0.581960 0.813217i \(-0.302286\pi\)
0.581960 + 0.813217i \(0.302286\pi\)
\(500\) 0 0
\(501\) −30.2389 −1.35097
\(502\) 0 0
\(503\) 15.6333 0.697055 0.348527 0.937299i \(-0.386682\pi\)
0.348527 + 0.937299i \(0.386682\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) 0 0
\(507\) 1.30278 0.0578583
\(508\) 0 0
\(509\) 15.3305 0.679514 0.339757 0.940513i \(-0.389655\pi\)
0.339757 + 0.940513i \(0.389655\pi\)
\(510\) 0 0
\(511\) −8.60555 −0.380687
\(512\) 0 0
\(513\) 35.3305 1.55988
\(514\) 0 0
\(515\) −8.90833 −0.392548
\(516\) 0 0
\(517\) 21.2111 0.932863
\(518\) 0 0
\(519\) 24.3583 1.06921
\(520\) 0 0
\(521\) 28.2389 1.23717 0.618583 0.785719i \(-0.287707\pi\)
0.618583 + 0.785719i \(0.287707\pi\)
\(522\) 0 0
\(523\) 5.57779 0.243900 0.121950 0.992536i \(-0.461085\pi\)
0.121950 + 0.992536i \(0.461085\pi\)
\(524\) 0 0
\(525\) 1.30278 0.0568578
\(526\) 0 0
\(527\) −4.39445 −0.191425
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) −14.4861 −0.628644
\(532\) 0 0
\(533\) 4.30278 0.186374
\(534\) 0 0
\(535\) −6.00000 −0.259403
\(536\) 0 0
\(537\) −11.8444 −0.511124
\(538\) 0 0
\(539\) −4.60555 −0.198375
\(540\) 0 0
\(541\) −34.0555 −1.46416 −0.732080 0.681218i \(-0.761450\pi\)
−0.732080 + 0.681218i \(0.761450\pi\)
\(542\) 0 0
\(543\) 12.7889 0.548824
\(544\) 0 0
\(545\) −4.00000 −0.171341
\(546\) 0 0
\(547\) 5.63331 0.240863 0.120431 0.992722i \(-0.461572\pi\)
0.120431 + 0.992722i \(0.461572\pi\)
\(548\) 0 0
\(549\) 1.57779 0.0673386
\(550\) 0 0
\(551\) −12.0278 −0.512400
\(552\) 0 0
\(553\) 3.51388 0.149425
\(554\) 0 0
\(555\) −5.09167 −0.216129
\(556\) 0 0
\(557\) 14.9083 0.631686 0.315843 0.948811i \(-0.397713\pi\)
0.315843 + 0.948811i \(0.397713\pi\)
\(558\) 0 0
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) −37.8167 −1.59662
\(562\) 0 0
\(563\) −12.5416 −0.528567 −0.264283 0.964445i \(-0.585135\pi\)
−0.264283 + 0.964445i \(0.585135\pi\)
\(564\) 0 0
\(565\) 7.81665 0.328849
\(566\) 0 0
\(567\) −3.39445 −0.142553
\(568\) 0 0
\(569\) −22.7527 −0.953844 −0.476922 0.878946i \(-0.658248\pi\)
−0.476922 + 0.878946i \(0.658248\pi\)
\(570\) 0 0
\(571\) 21.7250 0.909162 0.454581 0.890705i \(-0.349789\pi\)
0.454581 + 0.890705i \(0.349789\pi\)
\(572\) 0 0
\(573\) −21.5139 −0.898755
\(574\) 0 0
\(575\) −8.00000 −0.333623
\(576\) 0 0
\(577\) −7.39445 −0.307835 −0.153917 0.988084i \(-0.549189\pi\)
−0.153917 + 0.988084i \(0.549189\pi\)
\(578\) 0 0
\(579\) 14.2111 0.590593
\(580\) 0 0
\(581\) −11.8167 −0.490237
\(582\) 0 0
\(583\) 12.0000 0.496989
\(584\) 0 0
\(585\) 1.30278 0.0538631
\(586\) 0 0
\(587\) −19.8167 −0.817921 −0.408960 0.912552i \(-0.634109\pi\)
−0.408960 + 0.912552i \(0.634109\pi\)
\(588\) 0 0
\(589\) 4.39445 0.181070
\(590\) 0 0
\(591\) 17.0917 0.703057
\(592\) 0 0
\(593\) −43.8167 −1.79933 −0.899667 0.436576i \(-0.856191\pi\)
−0.899667 + 0.436576i \(0.856191\pi\)
\(594\) 0 0
\(595\) 6.30278 0.258389
\(596\) 0 0
\(597\) 1.57779 0.0645748
\(598\) 0 0
\(599\) −10.4222 −0.425840 −0.212920 0.977070i \(-0.568297\pi\)
−0.212920 + 0.977070i \(0.568297\pi\)
\(600\) 0 0
\(601\) 22.7889 0.929579 0.464789 0.885421i \(-0.346130\pi\)
0.464789 + 0.885421i \(0.346130\pi\)
\(602\) 0 0
\(603\) −11.6056 −0.472615
\(604\) 0 0
\(605\) 10.2111 0.415140
\(606\) 0 0
\(607\) 6.51388 0.264390 0.132195 0.991224i \(-0.457797\pi\)
0.132195 + 0.991224i \(0.457797\pi\)
\(608\) 0 0
\(609\) 2.48612 0.100743
\(610\) 0 0
\(611\) 4.60555 0.186321
\(612\) 0 0
\(613\) 38.8444 1.56891 0.784455 0.620185i \(-0.212943\pi\)
0.784455 + 0.620185i \(0.212943\pi\)
\(614\) 0 0
\(615\) −5.60555 −0.226038
\(616\) 0 0
\(617\) −6.90833 −0.278119 −0.139059 0.990284i \(-0.544408\pi\)
−0.139059 + 0.990284i \(0.544408\pi\)
\(618\) 0 0
\(619\) −21.7250 −0.873201 −0.436600 0.899656i \(-0.643818\pi\)
−0.436600 + 0.899656i \(0.643818\pi\)
\(620\) 0 0
\(621\) 44.8444 1.79954
\(622\) 0 0
\(623\) −7.30278 −0.292580
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 37.8167 1.51025
\(628\) 0 0
\(629\) −24.6333 −0.982194
\(630\) 0 0
\(631\) −15.8167 −0.629651 −0.314826 0.949150i \(-0.601946\pi\)
−0.314826 + 0.949150i \(0.601946\pi\)
\(632\) 0 0
\(633\) 15.0000 0.596196
\(634\) 0 0
\(635\) −8.60555 −0.341501
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 3.39445 0.134282
\(640\) 0 0
\(641\) −6.27502 −0.247848 −0.123924 0.992292i \(-0.539548\pi\)
−0.123924 + 0.992292i \(0.539548\pi\)
\(642\) 0 0
\(643\) −14.8444 −0.585406 −0.292703 0.956203i \(-0.594555\pi\)
−0.292703 + 0.956203i \(0.594555\pi\)
\(644\) 0 0
\(645\) −2.60555 −0.102593
\(646\) 0 0
\(647\) 18.5139 0.727856 0.363928 0.931427i \(-0.381435\pi\)
0.363928 + 0.931427i \(0.381435\pi\)
\(648\) 0 0
\(649\) −51.2111 −2.01021
\(650\) 0 0
\(651\) −0.908327 −0.0356001
\(652\) 0 0
\(653\) −26.4222 −1.03398 −0.516990 0.855991i \(-0.672948\pi\)
−0.516990 + 0.855991i \(0.672948\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 11.2111 0.437387
\(658\) 0 0
\(659\) 31.1472 1.21332 0.606661 0.794961i \(-0.292509\pi\)
0.606661 + 0.794961i \(0.292509\pi\)
\(660\) 0 0
\(661\) 33.5139 1.30354 0.651769 0.758417i \(-0.274027\pi\)
0.651769 + 0.758417i \(0.274027\pi\)
\(662\) 0 0
\(663\) −8.21110 −0.318893
\(664\) 0 0
\(665\) −6.30278 −0.244411
\(666\) 0 0
\(667\) −15.2666 −0.591126
\(668\) 0 0
\(669\) 17.2111 0.665420
\(670\) 0 0
\(671\) 5.57779 0.215328
\(672\) 0 0
\(673\) −13.8167 −0.532593 −0.266296 0.963891i \(-0.585800\pi\)
−0.266296 + 0.963891i \(0.585800\pi\)
\(674\) 0 0
\(675\) −5.60555 −0.215758
\(676\) 0 0
\(677\) 20.4222 0.784889 0.392445 0.919776i \(-0.371629\pi\)
0.392445 + 0.919776i \(0.371629\pi\)
\(678\) 0 0
\(679\) −13.2111 −0.506996
\(680\) 0 0
\(681\) −25.8167 −0.989296
\(682\) 0 0
\(683\) −43.9361 −1.68117 −0.840584 0.541682i \(-0.817788\pi\)
−0.840584 + 0.541682i \(0.817788\pi\)
\(684\) 0 0
\(685\) 2.69722 0.103056
\(686\) 0 0
\(687\) −0.394449 −0.0150492
\(688\) 0 0
\(689\) 2.60555 0.0992636
\(690\) 0 0
\(691\) −13.9083 −0.529098 −0.264549 0.964372i \(-0.585223\pi\)
−0.264549 + 0.964372i \(0.585223\pi\)
\(692\) 0 0
\(693\) 6.00000 0.227921
\(694\) 0 0
\(695\) 16.4222 0.622930
\(696\) 0 0
\(697\) −27.1194 −1.02722
\(698\) 0 0
\(699\) −2.36669 −0.0895165
\(700\) 0 0
\(701\) −9.88057 −0.373184 −0.186592 0.982437i \(-0.559744\pi\)
−0.186592 + 0.982437i \(0.559744\pi\)
\(702\) 0 0
\(703\) 24.6333 0.929063
\(704\) 0 0
\(705\) −6.00000 −0.225973
\(706\) 0 0
\(707\) 6.00000 0.225653
\(708\) 0 0
\(709\) 14.7889 0.555409 0.277704 0.960667i \(-0.410426\pi\)
0.277704 + 0.960667i \(0.410426\pi\)
\(710\) 0 0
\(711\) −4.57779 −0.171681
\(712\) 0 0
\(713\) 5.57779 0.208890
\(714\) 0 0
\(715\) 4.60555 0.172238
\(716\) 0 0
\(717\) 28.1833 1.05253
\(718\) 0 0
\(719\) 26.4222 0.985382 0.492691 0.870204i \(-0.336013\pi\)
0.492691 + 0.870204i \(0.336013\pi\)
\(720\) 0 0
\(721\) −8.90833 −0.331763
\(722\) 0 0
\(723\) −22.0278 −0.819221
\(724\) 0 0
\(725\) 1.90833 0.0708735
\(726\) 0 0
\(727\) −29.3028 −1.08678 −0.543390 0.839480i \(-0.682859\pi\)
−0.543390 + 0.839480i \(0.682859\pi\)
\(728\) 0 0
\(729\) 26.3305 0.975205
\(730\) 0 0
\(731\) −12.6056 −0.466233
\(732\) 0 0
\(733\) 12.0000 0.443230 0.221615 0.975134i \(-0.428867\pi\)
0.221615 + 0.975134i \(0.428867\pi\)
\(734\) 0 0
\(735\) 1.30278 0.0480536
\(736\) 0 0
\(737\) −41.0278 −1.51128
\(738\) 0 0
\(739\) −26.0555 −0.958468 −0.479234 0.877687i \(-0.659085\pi\)
−0.479234 + 0.877687i \(0.659085\pi\)
\(740\) 0 0
\(741\) 8.21110 0.301642
\(742\) 0 0
\(743\) 36.9083 1.35404 0.677018 0.735967i \(-0.263272\pi\)
0.677018 + 0.735967i \(0.263272\pi\)
\(744\) 0 0
\(745\) 8.00000 0.293097
\(746\) 0 0
\(747\) 15.3944 0.563253
\(748\) 0 0
\(749\) −6.00000 −0.219235
\(750\) 0 0
\(751\) 12.5139 0.456638 0.228319 0.973586i \(-0.426677\pi\)
0.228319 + 0.973586i \(0.426677\pi\)
\(752\) 0 0
\(753\) −36.0000 −1.31191
\(754\) 0 0
\(755\) −10.0000 −0.363937
\(756\) 0 0
\(757\) 45.8167 1.66523 0.832617 0.553849i \(-0.186841\pi\)
0.832617 + 0.553849i \(0.186841\pi\)
\(758\) 0 0
\(759\) 48.0000 1.74229
\(760\) 0 0
\(761\) −24.5139 −0.888627 −0.444314 0.895871i \(-0.646552\pi\)
−0.444314 + 0.895871i \(0.646552\pi\)
\(762\) 0 0
\(763\) −4.00000 −0.144810
\(764\) 0 0
\(765\) −8.21110 −0.296873
\(766\) 0 0
\(767\) −11.1194 −0.401499
\(768\) 0 0
\(769\) −15.5778 −0.561750 −0.280875 0.959744i \(-0.590625\pi\)
−0.280875 + 0.959744i \(0.590625\pi\)
\(770\) 0 0
\(771\) 28.1833 1.01500
\(772\) 0 0
\(773\) 16.1833 0.582075 0.291037 0.956712i \(-0.406000\pi\)
0.291037 + 0.956712i \(0.406000\pi\)
\(774\) 0 0
\(775\) −0.697224 −0.0250450
\(776\) 0 0
\(777\) −5.09167 −0.182663
\(778\) 0 0
\(779\) 27.1194 0.971654
\(780\) 0 0
\(781\) 12.0000 0.429394
\(782\) 0 0
\(783\) −10.6972 −0.382288
\(784\) 0 0
\(785\) 10.5139 0.375256
\(786\) 0 0
\(787\) −14.4222 −0.514096 −0.257048 0.966399i \(-0.582750\pi\)
−0.257048 + 0.966399i \(0.582750\pi\)
\(788\) 0 0
\(789\) 20.3667 0.725073
\(790\) 0 0
\(791\) 7.81665 0.277928
\(792\) 0 0
\(793\) 1.21110 0.0430075
\(794\) 0 0
\(795\) −3.39445 −0.120389
\(796\) 0 0
\(797\) −43.5416 −1.54232 −0.771162 0.636639i \(-0.780324\pi\)
−0.771162 + 0.636639i \(0.780324\pi\)
\(798\) 0 0
\(799\) −29.0278 −1.02693
\(800\) 0 0
\(801\) 9.51388 0.336156
\(802\) 0 0
\(803\) 39.6333 1.39863
\(804\) 0 0
\(805\) −8.00000 −0.281963
\(806\) 0 0
\(807\) −23.2111 −0.817070
\(808\) 0 0
\(809\) −21.5139 −0.756388 −0.378194 0.925726i \(-0.623455\pi\)
−0.378194 + 0.925726i \(0.623455\pi\)
\(810\) 0 0
\(811\) −31.6333 −1.11080 −0.555398 0.831585i \(-0.687434\pi\)
−0.555398 + 0.831585i \(0.687434\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 25.1194 0.879895
\(816\) 0 0
\(817\) 12.6056 0.441012
\(818\) 0 0
\(819\) 1.30278 0.0455227
\(820\) 0 0
\(821\) 46.4777 1.62208 0.811042 0.584988i \(-0.198901\pi\)
0.811042 + 0.584988i \(0.198901\pi\)
\(822\) 0 0
\(823\) −3.02776 −0.105541 −0.0527705 0.998607i \(-0.516805\pi\)
−0.0527705 + 0.998607i \(0.516805\pi\)
\(824\) 0 0
\(825\) −6.00000 −0.208893
\(826\) 0 0
\(827\) −3.63331 −0.126342 −0.0631712 0.998003i \(-0.520121\pi\)
−0.0631712 + 0.998003i \(0.520121\pi\)
\(828\) 0 0
\(829\) 9.21110 0.319915 0.159957 0.987124i \(-0.448864\pi\)
0.159957 + 0.987124i \(0.448864\pi\)
\(830\) 0 0
\(831\) 1.57779 0.0547331
\(832\) 0 0
\(833\) 6.30278 0.218378
\(834\) 0 0
\(835\) −23.2111 −0.803253
\(836\) 0 0
\(837\) 3.90833 0.135092
\(838\) 0 0
\(839\) −36.8444 −1.27201 −0.636005 0.771685i \(-0.719414\pi\)
−0.636005 + 0.771685i \(0.719414\pi\)
\(840\) 0 0
\(841\) −25.3583 −0.874424
\(842\) 0 0
\(843\) −41.6888 −1.43584
\(844\) 0 0
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) 10.2111 0.350858
\(848\) 0 0
\(849\) −19.6611 −0.674766
\(850\) 0 0
\(851\) 31.2666 1.07181
\(852\) 0 0
\(853\) 24.1833 0.828022 0.414011 0.910272i \(-0.364128\pi\)
0.414011 + 0.910272i \(0.364128\pi\)
\(854\) 0 0
\(855\) 8.21110 0.280814
\(856\) 0 0
\(857\) 49.3028 1.68415 0.842075 0.539360i \(-0.181334\pi\)
0.842075 + 0.539360i \(0.181334\pi\)
\(858\) 0 0
\(859\) 18.4222 0.628558 0.314279 0.949331i \(-0.398237\pi\)
0.314279 + 0.949331i \(0.398237\pi\)
\(860\) 0 0
\(861\) −5.60555 −0.191037
\(862\) 0 0
\(863\) 50.7250 1.72670 0.863349 0.504607i \(-0.168363\pi\)
0.863349 + 0.504607i \(0.168363\pi\)
\(864\) 0 0
\(865\) 18.6972 0.635725
\(866\) 0 0
\(867\) 29.6056 1.00546
\(868\) 0 0
\(869\) −16.1833 −0.548982
\(870\) 0 0
\(871\) −8.90833 −0.301847
\(872\) 0 0
\(873\) 17.2111 0.582508
\(874\) 0 0
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) 21.0917 0.712215 0.356108 0.934445i \(-0.384104\pi\)
0.356108 + 0.934445i \(0.384104\pi\)
\(878\) 0 0
\(879\) 3.15559 0.106435
\(880\) 0 0
\(881\) 29.4500 0.992194 0.496097 0.868267i \(-0.334766\pi\)
0.496097 + 0.868267i \(0.334766\pi\)
\(882\) 0 0
\(883\) 28.6056 0.962653 0.481327 0.876541i \(-0.340155\pi\)
0.481327 + 0.876541i \(0.340155\pi\)
\(884\) 0 0
\(885\) 14.4861 0.486946
\(886\) 0 0
\(887\) 26.1472 0.877937 0.438968 0.898503i \(-0.355344\pi\)
0.438968 + 0.898503i \(0.355344\pi\)
\(888\) 0 0
\(889\) −8.60555 −0.288621
\(890\) 0 0
\(891\) 15.6333 0.523736
\(892\) 0 0
\(893\) 29.0278 0.971377
\(894\) 0 0
\(895\) −9.09167 −0.303901
\(896\) 0 0
\(897\) 10.4222 0.347987
\(898\) 0 0
\(899\) −1.33053 −0.0443757
\(900\) 0 0
\(901\) −16.4222 −0.547103
\(902\) 0 0
\(903\) −2.60555 −0.0867073
\(904\) 0 0
\(905\) 9.81665 0.326317
\(906\) 0 0
\(907\) 2.60555 0.0865159 0.0432580 0.999064i \(-0.486226\pi\)
0.0432580 + 0.999064i \(0.486226\pi\)
\(908\) 0 0
\(909\) −7.81665 −0.259262
\(910\) 0 0
\(911\) −13.0917 −0.433746 −0.216873 0.976200i \(-0.569586\pi\)
−0.216873 + 0.976200i \(0.569586\pi\)
\(912\) 0 0
\(913\) 54.4222 1.80111
\(914\) 0 0
\(915\) −1.57779 −0.0521603
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 21.5416 0.710593 0.355296 0.934754i \(-0.384380\pi\)
0.355296 + 0.934754i \(0.384380\pi\)
\(920\) 0 0
\(921\) 9.63331 0.317428
\(922\) 0 0
\(923\) 2.60555 0.0857628
\(924\) 0 0
\(925\) −3.90833 −0.128505
\(926\) 0 0
\(927\) 11.6056 0.381176
\(928\) 0 0
\(929\) 34.7527 1.14020 0.570100 0.821575i \(-0.306904\pi\)
0.570100 + 0.821575i \(0.306904\pi\)
\(930\) 0 0
\(931\) −6.30278 −0.206565
\(932\) 0 0
\(933\) −30.0000 −0.982156
\(934\) 0 0
\(935\) −29.0278 −0.949309
\(936\) 0 0
\(937\) −33.6972 −1.10084 −0.550420 0.834888i \(-0.685532\pi\)
−0.550420 + 0.834888i \(0.685532\pi\)
\(938\) 0 0
\(939\) −39.5139 −1.28949
\(940\) 0 0
\(941\) −1.88057 −0.0613048 −0.0306524 0.999530i \(-0.509758\pi\)
−0.0306524 + 0.999530i \(0.509758\pi\)
\(942\) 0 0
\(943\) 34.4222 1.12094
\(944\) 0 0
\(945\) −5.60555 −0.182349
\(946\) 0 0
\(947\) 5.14719 0.167261 0.0836305 0.996497i \(-0.473348\pi\)
0.0836305 + 0.996497i \(0.473348\pi\)
\(948\) 0 0
\(949\) 8.60555 0.279348
\(950\) 0 0
\(951\) −21.3944 −0.693763
\(952\) 0 0
\(953\) −25.0278 −0.810729 −0.405364 0.914155i \(-0.632855\pi\)
−0.405364 + 0.914155i \(0.632855\pi\)
\(954\) 0 0
\(955\) −16.5139 −0.534377
\(956\) 0 0
\(957\) −11.4500 −0.370125
\(958\) 0 0
\(959\) 2.69722 0.0870979
\(960\) 0 0
\(961\) −30.5139 −0.984319
\(962\) 0 0
\(963\) 7.81665 0.251888
\(964\) 0 0
\(965\) 10.9083 0.351151
\(966\) 0 0
\(967\) 30.5139 0.981260 0.490630 0.871368i \(-0.336767\pi\)
0.490630 + 0.871368i \(0.336767\pi\)
\(968\) 0 0
\(969\) −51.7527 −1.66254
\(970\) 0 0
\(971\) 12.9722 0.416299 0.208150 0.978097i \(-0.433256\pi\)
0.208150 + 0.978097i \(0.433256\pi\)
\(972\) 0 0
\(973\) 16.4222 0.526472
\(974\) 0 0
\(975\) −1.30278 −0.0417222
\(976\) 0 0
\(977\) 2.90833 0.0930456 0.0465228 0.998917i \(-0.485186\pi\)
0.0465228 + 0.998917i \(0.485186\pi\)
\(978\) 0 0
\(979\) 33.6333 1.07493
\(980\) 0 0
\(981\) 5.21110 0.166378
\(982\) 0 0
\(983\) 11.4500 0.365197 0.182599 0.983188i \(-0.441549\pi\)
0.182599 + 0.983188i \(0.441549\pi\)
\(984\) 0 0
\(985\) 13.1194 0.418020
\(986\) 0 0
\(987\) −6.00000 −0.190982
\(988\) 0 0
\(989\) 16.0000 0.508770
\(990\) 0 0
\(991\) 27.1472 0.862359 0.431179 0.902266i \(-0.358098\pi\)
0.431179 + 0.902266i \(0.358098\pi\)
\(992\) 0 0
\(993\) 23.4500 0.744162
\(994\) 0 0
\(995\) 1.21110 0.0383945
\(996\) 0 0
\(997\) 55.1472 1.74653 0.873264 0.487247i \(-0.161999\pi\)
0.873264 + 0.487247i \(0.161999\pi\)
\(998\) 0 0
\(999\) 21.9083 0.693149
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 3640.2.a.l.1.2 2
4.3 odd 2 7280.2.a.bh.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3640.2.a.l.1.2 2 1.1 even 1 trivial
7280.2.a.bh.1.1 2 4.3 odd 2