Properties

Label 5265.2.a.ba.1.6
Level $5265$
Weight $2$
Character 5265.1
Self dual yes
Analytic conductor $42.041$
Analytic rank $1$
Dimension $8$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 5265 = 3^{4} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5265.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(42.0412366642\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \( x^{8} - 3x^{7} - 8x^{6} + 31x^{5} - x^{4} - 70x^{3} + 66x^{2} - 19x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 585)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(0.0672022\) of defining polynomial
Character \(\chi\) \(=\) 5265.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.0672022 q^{2} -1.99548 q^{4} +1.00000 q^{5} +2.46357 q^{7} +0.268505 q^{8} +O(q^{10})\) \(q-0.0672022 q^{2} -1.99548 q^{4} +1.00000 q^{5} +2.46357 q^{7} +0.268505 q^{8} -0.0672022 q^{10} -3.21214 q^{11} -1.00000 q^{13} -0.165558 q^{14} +3.97292 q^{16} +4.77678 q^{17} -3.94903 q^{19} -1.99548 q^{20} +0.215863 q^{22} -4.26977 q^{23} +1.00000 q^{25} +0.0672022 q^{26} -4.91602 q^{28} +2.30629 q^{29} -7.63305 q^{31} -0.804000 q^{32} -0.321010 q^{34} +2.46357 q^{35} +4.87293 q^{37} +0.265384 q^{38} +0.268505 q^{40} +2.53036 q^{41} -4.56607 q^{43} +6.40978 q^{44} +0.286938 q^{46} +6.26567 q^{47} -0.930808 q^{49} -0.0672022 q^{50} +1.99548 q^{52} -12.4968 q^{53} -3.21214 q^{55} +0.661482 q^{56} -0.154987 q^{58} -2.85019 q^{59} +12.7000 q^{61} +0.512957 q^{62} -7.89182 q^{64} -1.00000 q^{65} -13.5072 q^{67} -9.53198 q^{68} -0.165558 q^{70} -7.79224 q^{71} +2.26796 q^{73} -0.327472 q^{74} +7.88023 q^{76} -7.91335 q^{77} +9.13335 q^{79} +3.97292 q^{80} -0.170046 q^{82} -10.5119 q^{83} +4.77678 q^{85} +0.306850 q^{86} -0.862477 q^{88} -0.966612 q^{89} -2.46357 q^{91} +8.52026 q^{92} -0.421067 q^{94} -3.94903 q^{95} -18.7804 q^{97} +0.0625523 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 3 q^{2} + 9 q^{4} + 8 q^{5} - 11 q^{7} + 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 3 q^{2} + 9 q^{4} + 8 q^{5} - 11 q^{7} + 6 q^{8} - 3 q^{10} - 6 q^{11} - 8 q^{13} - 10 q^{14} + 11 q^{16} + 2 q^{17} - 10 q^{19} + 9 q^{20} + 3 q^{22} - 6 q^{23} + 8 q^{25} + 3 q^{26} - 34 q^{28} - 14 q^{29} - 31 q^{31} - q^{32} - 7 q^{34} - 11 q^{35} + q^{37} - 9 q^{38} + 6 q^{40} + 12 q^{41} + 15 q^{43} - 16 q^{44} - 32 q^{46} + 18 q^{47} + 17 q^{49} - 3 q^{50} - 9 q^{52} - 2 q^{53} - 6 q^{55} - 16 q^{56} - 42 q^{58} - 24 q^{59} - 9 q^{61} + 20 q^{62} - 30 q^{64} - 8 q^{65} - 18 q^{67} + 14 q^{68} - 10 q^{70} - 10 q^{71} + 6 q^{73} + 37 q^{74} - 53 q^{76} + 34 q^{77} - 3 q^{79} + 11 q^{80} - 34 q^{82} + 10 q^{83} + 2 q^{85} - 60 q^{86} - 14 q^{88} + 13 q^{89} + 11 q^{91} - 5 q^{92} + 17 q^{94} - 10 q^{95} - 34 q^{97} + 30 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.0672022 −0.0475191 −0.0237596 0.999718i \(-0.507564\pi\)
−0.0237596 + 0.999718i \(0.507564\pi\)
\(3\) 0 0
\(4\) −1.99548 −0.997742
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 2.46357 0.931143 0.465572 0.885010i \(-0.345849\pi\)
0.465572 + 0.885010i \(0.345849\pi\)
\(8\) 0.268505 0.0949309
\(9\) 0 0
\(10\) −0.0672022 −0.0212512
\(11\) −3.21214 −0.968498 −0.484249 0.874930i \(-0.660907\pi\)
−0.484249 + 0.874930i \(0.660907\pi\)
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) −0.165558 −0.0442471
\(15\) 0 0
\(16\) 3.97292 0.993231
\(17\) 4.77678 1.15854 0.579269 0.815136i \(-0.303338\pi\)
0.579269 + 0.815136i \(0.303338\pi\)
\(18\) 0 0
\(19\) −3.94903 −0.905970 −0.452985 0.891518i \(-0.649641\pi\)
−0.452985 + 0.891518i \(0.649641\pi\)
\(20\) −1.99548 −0.446204
\(21\) 0 0
\(22\) 0.215863 0.0460222
\(23\) −4.26977 −0.890309 −0.445154 0.895454i \(-0.646851\pi\)
−0.445154 + 0.895454i \(0.646851\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0.0672022 0.0131794
\(27\) 0 0
\(28\) −4.91602 −0.929040
\(29\) 2.30629 0.428267 0.214133 0.976804i \(-0.431307\pi\)
0.214133 + 0.976804i \(0.431307\pi\)
\(30\) 0 0
\(31\) −7.63305 −1.37094 −0.685468 0.728103i \(-0.740402\pi\)
−0.685468 + 0.728103i \(0.740402\pi\)
\(32\) −0.804000 −0.142128
\(33\) 0 0
\(34\) −0.321010 −0.0550527
\(35\) 2.46357 0.416420
\(36\) 0 0
\(37\) 4.87293 0.801105 0.400553 0.916274i \(-0.368818\pi\)
0.400553 + 0.916274i \(0.368818\pi\)
\(38\) 0.265384 0.0430509
\(39\) 0 0
\(40\) 0.268505 0.0424544
\(41\) 2.53036 0.395176 0.197588 0.980285i \(-0.436689\pi\)
0.197588 + 0.980285i \(0.436689\pi\)
\(42\) 0 0
\(43\) −4.56607 −0.696319 −0.348160 0.937435i \(-0.613193\pi\)
−0.348160 + 0.937435i \(0.613193\pi\)
\(44\) 6.40978 0.966311
\(45\) 0 0
\(46\) 0.286938 0.0423067
\(47\) 6.26567 0.913942 0.456971 0.889482i \(-0.348934\pi\)
0.456971 + 0.889482i \(0.348934\pi\)
\(48\) 0 0
\(49\) −0.930808 −0.132973
\(50\) −0.0672022 −0.00950382
\(51\) 0 0
\(52\) 1.99548 0.276724
\(53\) −12.4968 −1.71657 −0.858286 0.513172i \(-0.828470\pi\)
−0.858286 + 0.513172i \(0.828470\pi\)
\(54\) 0 0
\(55\) −3.21214 −0.433125
\(56\) 0.661482 0.0883943
\(57\) 0 0
\(58\) −0.154987 −0.0203509
\(59\) −2.85019 −0.371063 −0.185531 0.982638i \(-0.559401\pi\)
−0.185531 + 0.982638i \(0.559401\pi\)
\(60\) 0 0
\(61\) 12.7000 1.62607 0.813034 0.582216i \(-0.197814\pi\)
0.813034 + 0.582216i \(0.197814\pi\)
\(62\) 0.512957 0.0651457
\(63\) 0 0
\(64\) −7.89182 −0.986477
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) −13.5072 −1.65016 −0.825082 0.565013i \(-0.808871\pi\)
−0.825082 + 0.565013i \(0.808871\pi\)
\(68\) −9.53198 −1.15592
\(69\) 0 0
\(70\) −0.165558 −0.0197879
\(71\) −7.79224 −0.924769 −0.462384 0.886680i \(-0.653006\pi\)
−0.462384 + 0.886680i \(0.653006\pi\)
\(72\) 0 0
\(73\) 2.26796 0.265444 0.132722 0.991153i \(-0.457628\pi\)
0.132722 + 0.991153i \(0.457628\pi\)
\(74\) −0.327472 −0.0380678
\(75\) 0 0
\(76\) 7.88023 0.903924
\(77\) −7.91335 −0.901810
\(78\) 0 0
\(79\) 9.13335 1.02758 0.513791 0.857915i \(-0.328241\pi\)
0.513791 + 0.857915i \(0.328241\pi\)
\(80\) 3.97292 0.444186
\(81\) 0 0
\(82\) −0.170046 −0.0187784
\(83\) −10.5119 −1.15383 −0.576915 0.816804i \(-0.695744\pi\)
−0.576915 + 0.816804i \(0.695744\pi\)
\(84\) 0 0
\(85\) 4.77678 0.518114
\(86\) 0.306850 0.0330885
\(87\) 0 0
\(88\) −0.862477 −0.0919404
\(89\) −0.966612 −0.102461 −0.0512303 0.998687i \(-0.516314\pi\)
−0.0512303 + 0.998687i \(0.516314\pi\)
\(90\) 0 0
\(91\) −2.46357 −0.258253
\(92\) 8.52026 0.888299
\(93\) 0 0
\(94\) −0.421067 −0.0434297
\(95\) −3.94903 −0.405162
\(96\) 0 0
\(97\) −18.7804 −1.90686 −0.953431 0.301612i \(-0.902475\pi\)
−0.953431 + 0.301612i \(0.902475\pi\)
\(98\) 0.0625523 0.00631874
\(99\) 0 0
\(100\) −1.99548 −0.199548
\(101\) 18.5575 1.84654 0.923268 0.384157i \(-0.125508\pi\)
0.923268 + 0.384157i \(0.125508\pi\)
\(102\) 0 0
\(103\) 10.2563 1.01058 0.505292 0.862949i \(-0.331385\pi\)
0.505292 + 0.862949i \(0.331385\pi\)
\(104\) −0.268505 −0.0263291
\(105\) 0 0
\(106\) 0.839814 0.0815700
\(107\) 13.3729 1.29281 0.646403 0.762996i \(-0.276273\pi\)
0.646403 + 0.762996i \(0.276273\pi\)
\(108\) 0 0
\(109\) −1.35788 −0.130061 −0.0650306 0.997883i \(-0.520715\pi\)
−0.0650306 + 0.997883i \(0.520715\pi\)
\(110\) 0.215863 0.0205817
\(111\) 0 0
\(112\) 9.78759 0.924840
\(113\) 7.35696 0.692085 0.346042 0.938219i \(-0.387525\pi\)
0.346042 + 0.938219i \(0.387525\pi\)
\(114\) 0 0
\(115\) −4.26977 −0.398158
\(116\) −4.60216 −0.427300
\(117\) 0 0
\(118\) 0.191539 0.0176326
\(119\) 11.7679 1.07877
\(120\) 0 0
\(121\) −0.682134 −0.0620121
\(122\) −0.853468 −0.0772693
\(123\) 0 0
\(124\) 15.2316 1.36784
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −5.97693 −0.530367 −0.265183 0.964198i \(-0.585433\pi\)
−0.265183 + 0.964198i \(0.585433\pi\)
\(128\) 2.13835 0.189005
\(129\) 0 0
\(130\) 0.0672022 0.00589402
\(131\) −17.8734 −1.56161 −0.780803 0.624778i \(-0.785190\pi\)
−0.780803 + 0.624778i \(0.785190\pi\)
\(132\) 0 0
\(133\) −9.72873 −0.843588
\(134\) 0.907712 0.0784144
\(135\) 0 0
\(136\) 1.28259 0.109981
\(137\) −10.4931 −0.896483 −0.448241 0.893913i \(-0.647949\pi\)
−0.448241 + 0.893913i \(0.647949\pi\)
\(138\) 0 0
\(139\) −10.7069 −0.908143 −0.454072 0.890965i \(-0.650029\pi\)
−0.454072 + 0.890965i \(0.650029\pi\)
\(140\) −4.91602 −0.415480
\(141\) 0 0
\(142\) 0.523655 0.0439442
\(143\) 3.21214 0.268613
\(144\) 0 0
\(145\) 2.30629 0.191527
\(146\) −0.152412 −0.0126137
\(147\) 0 0
\(148\) −9.72386 −0.799296
\(149\) 20.3190 1.66460 0.832300 0.554325i \(-0.187023\pi\)
0.832300 + 0.554325i \(0.187023\pi\)
\(150\) 0 0
\(151\) −17.0220 −1.38523 −0.692615 0.721308i \(-0.743541\pi\)
−0.692615 + 0.721308i \(0.743541\pi\)
\(152\) −1.06034 −0.0860046
\(153\) 0 0
\(154\) 0.531794 0.0428532
\(155\) −7.63305 −0.613101
\(156\) 0 0
\(157\) −1.30787 −0.104379 −0.0521897 0.998637i \(-0.516620\pi\)
−0.0521897 + 0.998637i \(0.516620\pi\)
\(158\) −0.613781 −0.0488298
\(159\) 0 0
\(160\) −0.804000 −0.0635618
\(161\) −10.5189 −0.829005
\(162\) 0 0
\(163\) −9.81120 −0.768473 −0.384236 0.923235i \(-0.625535\pi\)
−0.384236 + 0.923235i \(0.625535\pi\)
\(164\) −5.04930 −0.394284
\(165\) 0 0
\(166\) 0.706422 0.0548290
\(167\) −8.17491 −0.632593 −0.316297 0.948660i \(-0.602440\pi\)
−0.316297 + 0.948660i \(0.602440\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) −0.321010 −0.0246203
\(171\) 0 0
\(172\) 9.11152 0.694747
\(173\) 6.39771 0.486409 0.243204 0.969975i \(-0.421801\pi\)
0.243204 + 0.969975i \(0.421801\pi\)
\(174\) 0 0
\(175\) 2.46357 0.186229
\(176\) −12.7616 −0.961942
\(177\) 0 0
\(178\) 0.0649584 0.00486884
\(179\) 15.6316 1.16836 0.584180 0.811624i \(-0.301416\pi\)
0.584180 + 0.811624i \(0.301416\pi\)
\(180\) 0 0
\(181\) 11.1033 0.825299 0.412650 0.910890i \(-0.364603\pi\)
0.412650 + 0.910890i \(0.364603\pi\)
\(182\) 0.165558 0.0122719
\(183\) 0 0
\(184\) −1.14646 −0.0845179
\(185\) 4.87293 0.358265
\(186\) 0 0
\(187\) −15.3437 −1.12204
\(188\) −12.5030 −0.911878
\(189\) 0 0
\(190\) 0.265384 0.0192530
\(191\) −15.5825 −1.12751 −0.563753 0.825943i \(-0.690643\pi\)
−0.563753 + 0.825943i \(0.690643\pi\)
\(192\) 0 0
\(193\) −18.6960 −1.34577 −0.672884 0.739748i \(-0.734945\pi\)
−0.672884 + 0.739748i \(0.734945\pi\)
\(194\) 1.26208 0.0906124
\(195\) 0 0
\(196\) 1.85741 0.132672
\(197\) 10.2024 0.726893 0.363447 0.931615i \(-0.381600\pi\)
0.363447 + 0.931615i \(0.381600\pi\)
\(198\) 0 0
\(199\) −16.4798 −1.16822 −0.584112 0.811673i \(-0.698557\pi\)
−0.584112 + 0.811673i \(0.698557\pi\)
\(200\) 0.268505 0.0189862
\(201\) 0 0
\(202\) −1.24710 −0.0877457
\(203\) 5.68170 0.398777
\(204\) 0 0
\(205\) 2.53036 0.176728
\(206\) −0.689246 −0.0480220
\(207\) 0 0
\(208\) −3.97292 −0.275473
\(209\) 12.6849 0.877430
\(210\) 0 0
\(211\) −25.1982 −1.73472 −0.867359 0.497684i \(-0.834184\pi\)
−0.867359 + 0.497684i \(0.834184\pi\)
\(212\) 24.9372 1.71270
\(213\) 0 0
\(214\) −0.898687 −0.0614330
\(215\) −4.56607 −0.311403
\(216\) 0 0
\(217\) −18.8046 −1.27654
\(218\) 0.0912525 0.00618040
\(219\) 0 0
\(220\) 6.40978 0.432147
\(221\) −4.77678 −0.321321
\(222\) 0 0
\(223\) 7.58438 0.507888 0.253944 0.967219i \(-0.418272\pi\)
0.253944 + 0.967219i \(0.418272\pi\)
\(224\) −1.98071 −0.132342
\(225\) 0 0
\(226\) −0.494404 −0.0328873
\(227\) −0.301037 −0.0199806 −0.00999028 0.999950i \(-0.503180\pi\)
−0.00999028 + 0.999950i \(0.503180\pi\)
\(228\) 0 0
\(229\) −4.63317 −0.306168 −0.153084 0.988213i \(-0.548921\pi\)
−0.153084 + 0.988213i \(0.548921\pi\)
\(230\) 0.286938 0.0189201
\(231\) 0 0
\(232\) 0.619250 0.0406558
\(233\) −5.62440 −0.368466 −0.184233 0.982883i \(-0.558980\pi\)
−0.184233 + 0.982883i \(0.558980\pi\)
\(234\) 0 0
\(235\) 6.26567 0.408727
\(236\) 5.68750 0.370225
\(237\) 0 0
\(238\) −0.790831 −0.0512620
\(239\) −2.56185 −0.165712 −0.0828562 0.996562i \(-0.526404\pi\)
−0.0828562 + 0.996562i \(0.526404\pi\)
\(240\) 0 0
\(241\) −14.9830 −0.965139 −0.482569 0.875858i \(-0.660296\pi\)
−0.482569 + 0.875858i \(0.660296\pi\)
\(242\) 0.0458409 0.00294676
\(243\) 0 0
\(244\) −25.3426 −1.62240
\(245\) −0.930808 −0.0594671
\(246\) 0 0
\(247\) 3.94903 0.251271
\(248\) −2.04951 −0.130144
\(249\) 0 0
\(250\) −0.0672022 −0.00425024
\(251\) 7.27387 0.459123 0.229561 0.973294i \(-0.426271\pi\)
0.229561 + 0.973294i \(0.426271\pi\)
\(252\) 0 0
\(253\) 13.7151 0.862262
\(254\) 0.401663 0.0252026
\(255\) 0 0
\(256\) 15.6399 0.977496
\(257\) 9.06613 0.565530 0.282765 0.959189i \(-0.408748\pi\)
0.282765 + 0.959189i \(0.408748\pi\)
\(258\) 0 0
\(259\) 12.0048 0.745944
\(260\) 1.99548 0.123755
\(261\) 0 0
\(262\) 1.20113 0.0742061
\(263\) −27.5384 −1.69809 −0.849045 0.528320i \(-0.822822\pi\)
−0.849045 + 0.528320i \(0.822822\pi\)
\(264\) 0 0
\(265\) −12.4968 −0.767674
\(266\) 0.653792 0.0400866
\(267\) 0 0
\(268\) 26.9534 1.64644
\(269\) 6.82403 0.416069 0.208034 0.978122i \(-0.433293\pi\)
0.208034 + 0.978122i \(0.433293\pi\)
\(270\) 0 0
\(271\) 1.91734 0.116470 0.0582352 0.998303i \(-0.481453\pi\)
0.0582352 + 0.998303i \(0.481453\pi\)
\(272\) 18.9778 1.15070
\(273\) 0 0
\(274\) 0.705157 0.0426001
\(275\) −3.21214 −0.193700
\(276\) 0 0
\(277\) −27.2990 −1.64024 −0.820119 0.572193i \(-0.806093\pi\)
−0.820119 + 0.572193i \(0.806093\pi\)
\(278\) 0.719524 0.0431542
\(279\) 0 0
\(280\) 0.661482 0.0395311
\(281\) 0.656824 0.0391828 0.0195914 0.999808i \(-0.493763\pi\)
0.0195914 + 0.999808i \(0.493763\pi\)
\(282\) 0 0
\(283\) −5.01978 −0.298395 −0.149198 0.988807i \(-0.547669\pi\)
−0.149198 + 0.988807i \(0.547669\pi\)
\(284\) 15.5493 0.922680
\(285\) 0 0
\(286\) −0.215863 −0.0127643
\(287\) 6.23373 0.367966
\(288\) 0 0
\(289\) 5.81760 0.342212
\(290\) −0.154987 −0.00910118
\(291\) 0 0
\(292\) −4.52567 −0.264845
\(293\) 12.2237 0.714114 0.357057 0.934083i \(-0.383780\pi\)
0.357057 + 0.934083i \(0.383780\pi\)
\(294\) 0 0
\(295\) −2.85019 −0.165944
\(296\) 1.30841 0.0760497
\(297\) 0 0
\(298\) −1.36548 −0.0791004
\(299\) 4.26977 0.246927
\(300\) 0 0
\(301\) −11.2489 −0.648373
\(302\) 1.14391 0.0658249
\(303\) 0 0
\(304\) −15.6892 −0.899838
\(305\) 12.7000 0.727200
\(306\) 0 0
\(307\) −1.01733 −0.0580619 −0.0290309 0.999579i \(-0.509242\pi\)
−0.0290309 + 0.999579i \(0.509242\pi\)
\(308\) 15.7910 0.899774
\(309\) 0 0
\(310\) 0.512957 0.0291340
\(311\) 22.2892 1.26390 0.631952 0.775008i \(-0.282254\pi\)
0.631952 + 0.775008i \(0.282254\pi\)
\(312\) 0 0
\(313\) −23.7748 −1.34383 −0.671915 0.740628i \(-0.734528\pi\)
−0.671915 + 0.740628i \(0.734528\pi\)
\(314\) 0.0878917 0.00496001
\(315\) 0 0
\(316\) −18.2255 −1.02526
\(317\) −28.0373 −1.57473 −0.787366 0.616485i \(-0.788556\pi\)
−0.787366 + 0.616485i \(0.788556\pi\)
\(318\) 0 0
\(319\) −7.40812 −0.414775
\(320\) −7.89182 −0.441166
\(321\) 0 0
\(322\) 0.706893 0.0393936
\(323\) −18.8636 −1.04960
\(324\) 0 0
\(325\) −1.00000 −0.0554700
\(326\) 0.659334 0.0365172
\(327\) 0 0
\(328\) 0.679416 0.0375145
\(329\) 15.4359 0.851011
\(330\) 0 0
\(331\) −17.8604 −0.981694 −0.490847 0.871246i \(-0.663313\pi\)
−0.490847 + 0.871246i \(0.663313\pi\)
\(332\) 20.9763 1.15122
\(333\) 0 0
\(334\) 0.549372 0.0300603
\(335\) −13.5072 −0.737976
\(336\) 0 0
\(337\) 9.77161 0.532294 0.266147 0.963932i \(-0.414249\pi\)
0.266147 + 0.963932i \(0.414249\pi\)
\(338\) −0.0672022 −0.00365532
\(339\) 0 0
\(340\) −9.53198 −0.516944
\(341\) 24.5184 1.32775
\(342\) 0 0
\(343\) −19.5381 −1.05496
\(344\) −1.22601 −0.0661023
\(345\) 0 0
\(346\) −0.429940 −0.0231137
\(347\) −21.0145 −1.12812 −0.564059 0.825735i \(-0.690761\pi\)
−0.564059 + 0.825735i \(0.690761\pi\)
\(348\) 0 0
\(349\) −9.23952 −0.494580 −0.247290 0.968941i \(-0.579540\pi\)
−0.247290 + 0.968941i \(0.579540\pi\)
\(350\) −0.165558 −0.00884942
\(351\) 0 0
\(352\) 2.58256 0.137651
\(353\) −4.50725 −0.239896 −0.119948 0.992780i \(-0.538273\pi\)
−0.119948 + 0.992780i \(0.538273\pi\)
\(354\) 0 0
\(355\) −7.79224 −0.413569
\(356\) 1.92886 0.102229
\(357\) 0 0
\(358\) −1.05048 −0.0555195
\(359\) −25.2752 −1.33397 −0.666986 0.745070i \(-0.732416\pi\)
−0.666986 + 0.745070i \(0.732416\pi\)
\(360\) 0 0
\(361\) −3.40514 −0.179218
\(362\) −0.746164 −0.0392175
\(363\) 0 0
\(364\) 4.91602 0.257669
\(365\) 2.26796 0.118710
\(366\) 0 0
\(367\) −11.1067 −0.579766 −0.289883 0.957062i \(-0.593616\pi\)
−0.289883 + 0.957062i \(0.593616\pi\)
\(368\) −16.9635 −0.884282
\(369\) 0 0
\(370\) −0.327472 −0.0170244
\(371\) −30.7868 −1.59837
\(372\) 0 0
\(373\) −7.73645 −0.400578 −0.200289 0.979737i \(-0.564188\pi\)
−0.200289 + 0.979737i \(0.564188\pi\)
\(374\) 1.03113 0.0533185
\(375\) 0 0
\(376\) 1.68237 0.0867614
\(377\) −2.30629 −0.118780
\(378\) 0 0
\(379\) 26.0870 1.34000 0.669999 0.742362i \(-0.266295\pi\)
0.669999 + 0.742362i \(0.266295\pi\)
\(380\) 7.88023 0.404247
\(381\) 0 0
\(382\) 1.04718 0.0535781
\(383\) 0.842569 0.0430533 0.0215266 0.999768i \(-0.493147\pi\)
0.0215266 + 0.999768i \(0.493147\pi\)
\(384\) 0 0
\(385\) −7.91335 −0.403302
\(386\) 1.25641 0.0639497
\(387\) 0 0
\(388\) 37.4760 1.90256
\(389\) 8.75451 0.443871 0.221936 0.975061i \(-0.428762\pi\)
0.221936 + 0.975061i \(0.428762\pi\)
\(390\) 0 0
\(391\) −20.3958 −1.03146
\(392\) −0.249927 −0.0126232
\(393\) 0 0
\(394\) −0.685626 −0.0345413
\(395\) 9.13335 0.459549
\(396\) 0 0
\(397\) −6.72904 −0.337721 −0.168860 0.985640i \(-0.554009\pi\)
−0.168860 + 0.985640i \(0.554009\pi\)
\(398\) 1.10748 0.0555130
\(399\) 0 0
\(400\) 3.97292 0.198646
\(401\) 28.8942 1.44291 0.721453 0.692463i \(-0.243474\pi\)
0.721453 + 0.692463i \(0.243474\pi\)
\(402\) 0 0
\(403\) 7.63305 0.380229
\(404\) −37.0311 −1.84237
\(405\) 0 0
\(406\) −0.381823 −0.0189496
\(407\) −15.6526 −0.775869
\(408\) 0 0
\(409\) −18.3885 −0.909254 −0.454627 0.890682i \(-0.650227\pi\)
−0.454627 + 0.890682i \(0.650227\pi\)
\(410\) −0.170046 −0.00839797
\(411\) 0 0
\(412\) −20.4663 −1.00830
\(413\) −7.02164 −0.345513
\(414\) 0 0
\(415\) −10.5119 −0.516008
\(416\) 0.804000 0.0394193
\(417\) 0 0
\(418\) −0.852450 −0.0416947
\(419\) 25.2007 1.23113 0.615567 0.788085i \(-0.288927\pi\)
0.615567 + 0.788085i \(0.288927\pi\)
\(420\) 0 0
\(421\) −17.8645 −0.870664 −0.435332 0.900270i \(-0.643369\pi\)
−0.435332 + 0.900270i \(0.643369\pi\)
\(422\) 1.69338 0.0824322
\(423\) 0 0
\(424\) −3.35546 −0.162956
\(425\) 4.77678 0.231708
\(426\) 0 0
\(427\) 31.2874 1.51410
\(428\) −26.6854 −1.28989
\(429\) 0 0
\(430\) 0.306850 0.0147976
\(431\) −28.4290 −1.36937 −0.684687 0.728837i \(-0.740061\pi\)
−0.684687 + 0.728837i \(0.740061\pi\)
\(432\) 0 0
\(433\) −20.4163 −0.981146 −0.490573 0.871400i \(-0.663212\pi\)
−0.490573 + 0.871400i \(0.663212\pi\)
\(434\) 1.26371 0.0606599
\(435\) 0 0
\(436\) 2.70963 0.129768
\(437\) 16.8615 0.806593
\(438\) 0 0
\(439\) 9.82504 0.468924 0.234462 0.972125i \(-0.424667\pi\)
0.234462 + 0.972125i \(0.424667\pi\)
\(440\) −0.862477 −0.0411170
\(441\) 0 0
\(442\) 0.321010 0.0152689
\(443\) 19.6477 0.933489 0.466745 0.884392i \(-0.345427\pi\)
0.466745 + 0.884392i \(0.345427\pi\)
\(444\) 0 0
\(445\) −0.966612 −0.0458218
\(446\) −0.509687 −0.0241344
\(447\) 0 0
\(448\) −19.4421 −0.918551
\(449\) −27.3713 −1.29173 −0.645866 0.763451i \(-0.723504\pi\)
−0.645866 + 0.763451i \(0.723504\pi\)
\(450\) 0 0
\(451\) −8.12789 −0.382727
\(452\) −14.6807 −0.690522
\(453\) 0 0
\(454\) 0.0202304 0.000949459 0
\(455\) −2.46357 −0.115494
\(456\) 0 0
\(457\) −24.4583 −1.14411 −0.572056 0.820215i \(-0.693854\pi\)
−0.572056 + 0.820215i \(0.693854\pi\)
\(458\) 0.311359 0.0145488
\(459\) 0 0
\(460\) 8.52026 0.397259
\(461\) −8.76073 −0.408028 −0.204014 0.978968i \(-0.565399\pi\)
−0.204014 + 0.978968i \(0.565399\pi\)
\(462\) 0 0
\(463\) 15.1032 0.701905 0.350952 0.936393i \(-0.385858\pi\)
0.350952 + 0.936393i \(0.385858\pi\)
\(464\) 9.16270 0.425368
\(465\) 0 0
\(466\) 0.377972 0.0175092
\(467\) 19.5484 0.904591 0.452296 0.891868i \(-0.350605\pi\)
0.452296 + 0.891868i \(0.350605\pi\)
\(468\) 0 0
\(469\) −33.2759 −1.53654
\(470\) −0.421067 −0.0194224
\(471\) 0 0
\(472\) −0.765290 −0.0352253
\(473\) 14.6669 0.674384
\(474\) 0 0
\(475\) −3.94903 −0.181194
\(476\) −23.4827 −1.07633
\(477\) 0 0
\(478\) 0.172162 0.00787451
\(479\) −1.30713 −0.0597242 −0.0298621 0.999554i \(-0.509507\pi\)
−0.0298621 + 0.999554i \(0.509507\pi\)
\(480\) 0 0
\(481\) −4.87293 −0.222187
\(482\) 1.00689 0.0458626
\(483\) 0 0
\(484\) 1.36119 0.0618721
\(485\) −18.7804 −0.852774
\(486\) 0 0
\(487\) 30.3533 1.37544 0.687719 0.725977i \(-0.258612\pi\)
0.687719 + 0.725977i \(0.258612\pi\)
\(488\) 3.41002 0.154364
\(489\) 0 0
\(490\) 0.0625523 0.00282583
\(491\) −8.37717 −0.378056 −0.189028 0.981972i \(-0.560534\pi\)
−0.189028 + 0.981972i \(0.560534\pi\)
\(492\) 0 0
\(493\) 11.0166 0.496163
\(494\) −0.265384 −0.0119402
\(495\) 0 0
\(496\) −30.3255 −1.36166
\(497\) −19.1967 −0.861092
\(498\) 0 0
\(499\) 12.8603 0.575704 0.287852 0.957675i \(-0.407059\pi\)
0.287852 + 0.957675i \(0.407059\pi\)
\(500\) −1.99548 −0.0892408
\(501\) 0 0
\(502\) −0.488820 −0.0218171
\(503\) −5.22447 −0.232947 −0.116474 0.993194i \(-0.537159\pi\)
−0.116474 + 0.993194i \(0.537159\pi\)
\(504\) 0 0
\(505\) 18.5575 0.825796
\(506\) −0.921686 −0.0409739
\(507\) 0 0
\(508\) 11.9269 0.529169
\(509\) −10.0224 −0.444234 −0.222117 0.975020i \(-0.571297\pi\)
−0.222117 + 0.975020i \(0.571297\pi\)
\(510\) 0 0
\(511\) 5.58728 0.247167
\(512\) −5.32773 −0.235455
\(513\) 0 0
\(514\) −0.609264 −0.0268735
\(515\) 10.2563 0.451947
\(516\) 0 0
\(517\) −20.1262 −0.885151
\(518\) −0.806751 −0.0354466
\(519\) 0 0
\(520\) −0.268505 −0.0117747
\(521\) −20.3192 −0.890202 −0.445101 0.895480i \(-0.646832\pi\)
−0.445101 + 0.895480i \(0.646832\pi\)
\(522\) 0 0
\(523\) −0.572523 −0.0250347 −0.0125173 0.999922i \(-0.503984\pi\)
−0.0125173 + 0.999922i \(0.503984\pi\)
\(524\) 35.6661 1.55808
\(525\) 0 0
\(526\) 1.85064 0.0806918
\(527\) −36.4614 −1.58828
\(528\) 0 0
\(529\) −4.76905 −0.207350
\(530\) 0.839814 0.0364792
\(531\) 0 0
\(532\) 19.4135 0.841683
\(533\) −2.53036 −0.109602
\(534\) 0 0
\(535\) 13.3729 0.578160
\(536\) −3.62675 −0.156652
\(537\) 0 0
\(538\) −0.458590 −0.0197712
\(539\) 2.98989 0.128784
\(540\) 0 0
\(541\) −23.5766 −1.01364 −0.506819 0.862052i \(-0.669179\pi\)
−0.506819 + 0.862052i \(0.669179\pi\)
\(542\) −0.128850 −0.00553457
\(543\) 0 0
\(544\) −3.84053 −0.164661
\(545\) −1.35788 −0.0581652
\(546\) 0 0
\(547\) −3.75708 −0.160641 −0.0803205 0.996769i \(-0.525594\pi\)
−0.0803205 + 0.996769i \(0.525594\pi\)
\(548\) 20.9387 0.894458
\(549\) 0 0
\(550\) 0.215863 0.00920443
\(551\) −9.10760 −0.387997
\(552\) 0 0
\(553\) 22.5007 0.956826
\(554\) 1.83455 0.0779427
\(555\) 0 0
\(556\) 21.3654 0.906093
\(557\) 39.9225 1.69157 0.845785 0.533523i \(-0.179132\pi\)
0.845785 + 0.533523i \(0.179132\pi\)
\(558\) 0 0
\(559\) 4.56607 0.193124
\(560\) 9.78759 0.413601
\(561\) 0 0
\(562\) −0.0441400 −0.00186193
\(563\) −33.5570 −1.41426 −0.707130 0.707084i \(-0.750010\pi\)
−0.707130 + 0.707084i \(0.750010\pi\)
\(564\) 0 0
\(565\) 7.35696 0.309510
\(566\) 0.337340 0.0141795
\(567\) 0 0
\(568\) −2.09226 −0.0877892
\(569\) −15.4337 −0.647016 −0.323508 0.946225i \(-0.604862\pi\)
−0.323508 + 0.946225i \(0.604862\pi\)
\(570\) 0 0
\(571\) 39.9382 1.67136 0.835681 0.549215i \(-0.185073\pi\)
0.835681 + 0.549215i \(0.185073\pi\)
\(572\) −6.40978 −0.268006
\(573\) 0 0
\(574\) −0.418921 −0.0174854
\(575\) −4.26977 −0.178062
\(576\) 0 0
\(577\) 25.4359 1.05891 0.529455 0.848338i \(-0.322396\pi\)
0.529455 + 0.848338i \(0.322396\pi\)
\(578\) −0.390956 −0.0162616
\(579\) 0 0
\(580\) −4.60216 −0.191094
\(581\) −25.8968 −1.07438
\(582\) 0 0
\(583\) 40.1416 1.66250
\(584\) 0.608958 0.0251989
\(585\) 0 0
\(586\) −0.821457 −0.0339341
\(587\) 40.9279 1.68927 0.844637 0.535339i \(-0.179816\pi\)
0.844637 + 0.535339i \(0.179816\pi\)
\(588\) 0 0
\(589\) 30.1431 1.24203
\(590\) 0.191539 0.00788553
\(591\) 0 0
\(592\) 19.3598 0.795683
\(593\) 1.00808 0.0413971 0.0206985 0.999786i \(-0.493411\pi\)
0.0206985 + 0.999786i \(0.493411\pi\)
\(594\) 0 0
\(595\) 11.7679 0.482439
\(596\) −40.5463 −1.66084
\(597\) 0 0
\(598\) −0.286938 −0.0117338
\(599\) −1.87952 −0.0767949 −0.0383975 0.999263i \(-0.512225\pi\)
−0.0383975 + 0.999263i \(0.512225\pi\)
\(600\) 0 0
\(601\) −2.94528 −0.120140 −0.0600702 0.998194i \(-0.519132\pi\)
−0.0600702 + 0.998194i \(0.519132\pi\)
\(602\) 0.755947 0.0308101
\(603\) 0 0
\(604\) 33.9671 1.38210
\(605\) −0.682134 −0.0277327
\(606\) 0 0
\(607\) 1.34069 0.0544171 0.0272085 0.999630i \(-0.491338\pi\)
0.0272085 + 0.999630i \(0.491338\pi\)
\(608\) 3.17502 0.128764
\(609\) 0 0
\(610\) −0.853468 −0.0345559
\(611\) −6.26567 −0.253482
\(612\) 0 0
\(613\) −20.1796 −0.815046 −0.407523 0.913195i \(-0.633607\pi\)
−0.407523 + 0.913195i \(0.633607\pi\)
\(614\) 0.0683665 0.00275905
\(615\) 0 0
\(616\) −2.12478 −0.0856097
\(617\) 7.13478 0.287235 0.143618 0.989633i \(-0.454126\pi\)
0.143618 + 0.989633i \(0.454126\pi\)
\(618\) 0 0
\(619\) −30.8954 −1.24179 −0.620895 0.783894i \(-0.713231\pi\)
−0.620895 + 0.783894i \(0.713231\pi\)
\(620\) 15.2316 0.611717
\(621\) 0 0
\(622\) −1.49788 −0.0600596
\(623\) −2.38132 −0.0954055
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 1.59772 0.0638576
\(627\) 0 0
\(628\) 2.60983 0.104144
\(629\) 23.2769 0.928112
\(630\) 0 0
\(631\) 11.8799 0.472932 0.236466 0.971640i \(-0.424011\pi\)
0.236466 + 0.971640i \(0.424011\pi\)
\(632\) 2.45235 0.0975494
\(633\) 0 0
\(634\) 1.88417 0.0748299
\(635\) −5.97693 −0.237187
\(636\) 0 0
\(637\) 0.930808 0.0368800
\(638\) 0.497842 0.0197098
\(639\) 0 0
\(640\) 2.13835 0.0845256
\(641\) −25.1307 −0.992605 −0.496302 0.868150i \(-0.665309\pi\)
−0.496302 + 0.868150i \(0.665309\pi\)
\(642\) 0 0
\(643\) −37.8971 −1.49452 −0.747258 0.664534i \(-0.768630\pi\)
−0.747258 + 0.664534i \(0.768630\pi\)
\(644\) 20.9903 0.827133
\(645\) 0 0
\(646\) 1.26768 0.0498761
\(647\) 5.59065 0.219791 0.109896 0.993943i \(-0.464948\pi\)
0.109896 + 0.993943i \(0.464948\pi\)
\(648\) 0 0
\(649\) 9.15521 0.359373
\(650\) 0.0672022 0.00263589
\(651\) 0 0
\(652\) 19.5781 0.766737
\(653\) 8.58496 0.335955 0.167978 0.985791i \(-0.446276\pi\)
0.167978 + 0.985791i \(0.446276\pi\)
\(654\) 0 0
\(655\) −17.8734 −0.698371
\(656\) 10.0529 0.392501
\(657\) 0 0
\(658\) −1.03733 −0.0404393
\(659\) 19.7197 0.768172 0.384086 0.923297i \(-0.374517\pi\)
0.384086 + 0.923297i \(0.374517\pi\)
\(660\) 0 0
\(661\) 35.3485 1.37490 0.687448 0.726234i \(-0.258731\pi\)
0.687448 + 0.726234i \(0.258731\pi\)
\(662\) 1.20025 0.0466492
\(663\) 0 0
\(664\) −2.82250 −0.109534
\(665\) −9.72873 −0.377264
\(666\) 0 0
\(667\) −9.84732 −0.381290
\(668\) 16.3129 0.631165
\(669\) 0 0
\(670\) 0.907712 0.0350680
\(671\) −40.7942 −1.57484
\(672\) 0 0
\(673\) 17.0655 0.657826 0.328913 0.944360i \(-0.393318\pi\)
0.328913 + 0.944360i \(0.393318\pi\)
\(674\) −0.656674 −0.0252941
\(675\) 0 0
\(676\) −1.99548 −0.0767494
\(677\) 11.0885 0.426164 0.213082 0.977034i \(-0.431650\pi\)
0.213082 + 0.977034i \(0.431650\pi\)
\(678\) 0 0
\(679\) −46.2669 −1.77556
\(680\) 1.28259 0.0491851
\(681\) 0 0
\(682\) −1.64769 −0.0630934
\(683\) 42.5037 1.62636 0.813179 0.582014i \(-0.197735\pi\)
0.813179 + 0.582014i \(0.197735\pi\)
\(684\) 0 0
\(685\) −10.4931 −0.400919
\(686\) 1.31300 0.0501308
\(687\) 0 0
\(688\) −18.1407 −0.691606
\(689\) 12.4968 0.476091
\(690\) 0 0
\(691\) 1.31266 0.0499361 0.0249681 0.999688i \(-0.492052\pi\)
0.0249681 + 0.999688i \(0.492052\pi\)
\(692\) −12.7665 −0.485310
\(693\) 0 0
\(694\) 1.41222 0.0536072
\(695\) −10.7069 −0.406134
\(696\) 0 0
\(697\) 12.0870 0.457827
\(698\) 0.620916 0.0235020
\(699\) 0 0
\(700\) −4.91602 −0.185808
\(701\) −21.2054 −0.800916 −0.400458 0.916315i \(-0.631149\pi\)
−0.400458 + 0.916315i \(0.631149\pi\)
\(702\) 0 0
\(703\) −19.2434 −0.725778
\(704\) 25.3496 0.955401
\(705\) 0 0
\(706\) 0.302897 0.0113997
\(707\) 45.7176 1.71939
\(708\) 0 0
\(709\) 49.2060 1.84797 0.923985 0.382429i \(-0.124912\pi\)
0.923985 + 0.382429i \(0.124912\pi\)
\(710\) 0.523655 0.0196524
\(711\) 0 0
\(712\) −0.259540 −0.00972669
\(713\) 32.5914 1.22056
\(714\) 0 0
\(715\) 3.21214 0.120127
\(716\) −31.1926 −1.16572
\(717\) 0 0
\(718\) 1.69855 0.0633892
\(719\) 31.1080 1.16013 0.580067 0.814569i \(-0.303026\pi\)
0.580067 + 0.814569i \(0.303026\pi\)
\(720\) 0 0
\(721\) 25.2671 0.940998
\(722\) 0.228833 0.00851629
\(723\) 0 0
\(724\) −22.1564 −0.823436
\(725\) 2.30629 0.0856533
\(726\) 0 0
\(727\) 30.0940 1.11612 0.558062 0.829799i \(-0.311545\pi\)
0.558062 + 0.829799i \(0.311545\pi\)
\(728\) −0.661482 −0.0245162
\(729\) 0 0
\(730\) −0.152412 −0.00564101
\(731\) −21.8111 −0.806713
\(732\) 0 0
\(733\) −12.9997 −0.480156 −0.240078 0.970754i \(-0.577173\pi\)
−0.240078 + 0.970754i \(0.577173\pi\)
\(734\) 0.746396 0.0275500
\(735\) 0 0
\(736\) 3.43290 0.126538
\(737\) 43.3870 1.59818
\(738\) 0 0
\(739\) 43.9402 1.61637 0.808183 0.588932i \(-0.200451\pi\)
0.808183 + 0.588932i \(0.200451\pi\)
\(740\) −9.72386 −0.357456
\(741\) 0 0
\(742\) 2.06894 0.0759533
\(743\) 48.8508 1.79216 0.896081 0.443890i \(-0.146402\pi\)
0.896081 + 0.443890i \(0.146402\pi\)
\(744\) 0 0
\(745\) 20.3190 0.744432
\(746\) 0.519907 0.0190351
\(747\) 0 0
\(748\) 30.6181 1.11951
\(749\) 32.9451 1.20379
\(750\) 0 0
\(751\) −33.4142 −1.21930 −0.609651 0.792670i \(-0.708690\pi\)
−0.609651 + 0.792670i \(0.708690\pi\)
\(752\) 24.8930 0.907756
\(753\) 0 0
\(754\) 0.154987 0.00564431
\(755\) −17.0220 −0.619493
\(756\) 0 0
\(757\) 45.6922 1.66071 0.830356 0.557233i \(-0.188137\pi\)
0.830356 + 0.557233i \(0.188137\pi\)
\(758\) −1.75310 −0.0636755
\(759\) 0 0
\(760\) −1.06034 −0.0384624
\(761\) 4.87858 0.176848 0.0884242 0.996083i \(-0.471817\pi\)
0.0884242 + 0.996083i \(0.471817\pi\)
\(762\) 0 0
\(763\) −3.34524 −0.121106
\(764\) 31.0945 1.12496
\(765\) 0 0
\(766\) −0.0566225 −0.00204585
\(767\) 2.85019 0.102914
\(768\) 0 0
\(769\) 11.2596 0.406030 0.203015 0.979176i \(-0.434926\pi\)
0.203015 + 0.979176i \(0.434926\pi\)
\(770\) 0.531794 0.0191645
\(771\) 0 0
\(772\) 37.3076 1.34273
\(773\) −17.8461 −0.641880 −0.320940 0.947100i \(-0.603999\pi\)
−0.320940 + 0.947100i \(0.603999\pi\)
\(774\) 0 0
\(775\) −7.63305 −0.274187
\(776\) −5.04264 −0.181020
\(777\) 0 0
\(778\) −0.588323 −0.0210924
\(779\) −9.99248 −0.358018
\(780\) 0 0
\(781\) 25.0298 0.895636
\(782\) 1.37064 0.0490140
\(783\) 0 0
\(784\) −3.69803 −0.132072
\(785\) −1.30787 −0.0466799
\(786\) 0 0
\(787\) 24.7113 0.880863 0.440432 0.897786i \(-0.354825\pi\)
0.440432 + 0.897786i \(0.354825\pi\)
\(788\) −20.3588 −0.725252
\(789\) 0 0
\(790\) −0.613781 −0.0218374
\(791\) 18.1244 0.644430
\(792\) 0 0
\(793\) −12.7000 −0.450990
\(794\) 0.452206 0.0160482
\(795\) 0 0
\(796\) 32.8852 1.16559
\(797\) −39.7377 −1.40758 −0.703791 0.710407i \(-0.748511\pi\)
−0.703791 + 0.710407i \(0.748511\pi\)
\(798\) 0 0
\(799\) 29.9297 1.05884
\(800\) −0.804000 −0.0284257
\(801\) 0 0
\(802\) −1.94175 −0.0685657
\(803\) −7.28500 −0.257082
\(804\) 0 0
\(805\) −10.5189 −0.370742
\(806\) −0.512957 −0.0180682
\(807\) 0 0
\(808\) 4.98277 0.175293
\(809\) −40.0717 −1.40885 −0.704423 0.709780i \(-0.748794\pi\)
−0.704423 + 0.709780i \(0.748794\pi\)
\(810\) 0 0
\(811\) 49.6910 1.74489 0.872444 0.488714i \(-0.162534\pi\)
0.872444 + 0.488714i \(0.162534\pi\)
\(812\) −11.3377 −0.397877
\(813\) 0 0
\(814\) 1.05189 0.0368686
\(815\) −9.81120 −0.343671
\(816\) 0 0
\(817\) 18.0316 0.630845
\(818\) 1.23575 0.0432070
\(819\) 0 0
\(820\) −5.04930 −0.176329
\(821\) −18.8802 −0.658924 −0.329462 0.944169i \(-0.606867\pi\)
−0.329462 + 0.944169i \(0.606867\pi\)
\(822\) 0 0
\(823\) −28.4726 −0.992494 −0.496247 0.868182i \(-0.665289\pi\)
−0.496247 + 0.868182i \(0.665289\pi\)
\(824\) 2.75387 0.0959356
\(825\) 0 0
\(826\) 0.471870 0.0164185
\(827\) 15.9961 0.556239 0.278120 0.960546i \(-0.410289\pi\)
0.278120 + 0.960546i \(0.410289\pi\)
\(828\) 0 0
\(829\) 20.7729 0.721474 0.360737 0.932668i \(-0.382525\pi\)
0.360737 + 0.932668i \(0.382525\pi\)
\(830\) 0.706422 0.0245203
\(831\) 0 0
\(832\) 7.89182 0.273600
\(833\) −4.44626 −0.154054
\(834\) 0 0
\(835\) −8.17491 −0.282904
\(836\) −25.3124 −0.875449
\(837\) 0 0
\(838\) −1.69354 −0.0585024
\(839\) 17.1840 0.593259 0.296630 0.954993i \(-0.404137\pi\)
0.296630 + 0.954993i \(0.404137\pi\)
\(840\) 0 0
\(841\) −23.6810 −0.816588
\(842\) 1.20054 0.0413732
\(843\) 0 0
\(844\) 50.2826 1.73080
\(845\) 1.00000 0.0344010
\(846\) 0 0
\(847\) −1.68049 −0.0577422
\(848\) −49.6489 −1.70495
\(849\) 0 0
\(850\) −0.321010 −0.0110105
\(851\) −20.8063 −0.713231
\(852\) 0 0
\(853\) 33.0733 1.13241 0.566203 0.824266i \(-0.308412\pi\)
0.566203 + 0.824266i \(0.308412\pi\)
\(854\) −2.10258 −0.0719488
\(855\) 0 0
\(856\) 3.59069 0.122727
\(857\) 39.6295 1.35372 0.676859 0.736113i \(-0.263341\pi\)
0.676859 + 0.736113i \(0.263341\pi\)
\(858\) 0 0
\(859\) −1.17288 −0.0400183 −0.0200091 0.999800i \(-0.506370\pi\)
−0.0200091 + 0.999800i \(0.506370\pi\)
\(860\) 9.11152 0.310700
\(861\) 0 0
\(862\) 1.91049 0.0650715
\(863\) 54.3303 1.84943 0.924713 0.380665i \(-0.124305\pi\)
0.924713 + 0.380665i \(0.124305\pi\)
\(864\) 0 0
\(865\) 6.39771 0.217529
\(866\) 1.37202 0.0466232
\(867\) 0 0
\(868\) 37.5242 1.27365
\(869\) −29.3376 −0.995211
\(870\) 0 0
\(871\) 13.5072 0.457673
\(872\) −0.364598 −0.0123468
\(873\) 0 0
\(874\) −1.13313 −0.0383286
\(875\) 2.46357 0.0832840
\(876\) 0 0
\(877\) 47.7735 1.61319 0.806597 0.591101i \(-0.201307\pi\)
0.806597 + 0.591101i \(0.201307\pi\)
\(878\) −0.660265 −0.0222828
\(879\) 0 0
\(880\) −12.7616 −0.430193
\(881\) −28.0225 −0.944101 −0.472050 0.881572i \(-0.656486\pi\)
−0.472050 + 0.881572i \(0.656486\pi\)
\(882\) 0 0
\(883\) −2.71952 −0.0915191 −0.0457595 0.998952i \(-0.514571\pi\)
−0.0457595 + 0.998952i \(0.514571\pi\)
\(884\) 9.53198 0.320595
\(885\) 0 0
\(886\) −1.32037 −0.0443586
\(887\) 4.76247 0.159908 0.0799541 0.996799i \(-0.474523\pi\)
0.0799541 + 0.996799i \(0.474523\pi\)
\(888\) 0 0
\(889\) −14.7246 −0.493848
\(890\) 0.0649584 0.00217741
\(891\) 0 0
\(892\) −15.1345 −0.506741
\(893\) −24.7433 −0.828004
\(894\) 0 0
\(895\) 15.6316 0.522507
\(896\) 5.26797 0.175991
\(897\) 0 0
\(898\) 1.83941 0.0613820
\(899\) −17.6040 −0.587126
\(900\) 0 0
\(901\) −59.6946 −1.98871
\(902\) 0.546212 0.0181869
\(903\) 0 0
\(904\) 1.97538 0.0657003
\(905\) 11.1033 0.369085
\(906\) 0 0
\(907\) −23.1462 −0.768556 −0.384278 0.923217i \(-0.625550\pi\)
−0.384278 + 0.923217i \(0.625550\pi\)
\(908\) 0.600715 0.0199354
\(909\) 0 0
\(910\) 0.165558 0.00548818
\(911\) 11.5589 0.382963 0.191481 0.981496i \(-0.438671\pi\)
0.191481 + 0.981496i \(0.438671\pi\)
\(912\) 0 0
\(913\) 33.7657 1.11748
\(914\) 1.64365 0.0543672
\(915\) 0 0
\(916\) 9.24541 0.305477
\(917\) −44.0324 −1.45408
\(918\) 0 0
\(919\) −45.9902 −1.51708 −0.758538 0.651629i \(-0.774086\pi\)
−0.758538 + 0.651629i \(0.774086\pi\)
\(920\) −1.14646 −0.0377975
\(921\) 0 0
\(922\) 0.588740 0.0193891
\(923\) 7.79224 0.256485
\(924\) 0 0
\(925\) 4.87293 0.160221
\(926\) −1.01497 −0.0333539
\(927\) 0 0
\(928\) −1.85425 −0.0608689
\(929\) −42.6792 −1.40026 −0.700130 0.714016i \(-0.746875\pi\)
−0.700130 + 0.714016i \(0.746875\pi\)
\(930\) 0 0
\(931\) 3.67579 0.120469
\(932\) 11.2234 0.367634
\(933\) 0 0
\(934\) −1.31369 −0.0429854
\(935\) −15.3437 −0.501792
\(936\) 0 0
\(937\) −47.1687 −1.54093 −0.770467 0.637480i \(-0.779977\pi\)
−0.770467 + 0.637480i \(0.779977\pi\)
\(938\) 2.23621 0.0730150
\(939\) 0 0
\(940\) −12.5030 −0.407804
\(941\) −40.1783 −1.30977 −0.654887 0.755727i \(-0.727284\pi\)
−0.654887 + 0.755727i \(0.727284\pi\)
\(942\) 0 0
\(943\) −10.8041 −0.351829
\(944\) −11.3236 −0.368551
\(945\) 0 0
\(946\) −0.985646 −0.0320461
\(947\) 0.805932 0.0261893 0.0130946 0.999914i \(-0.495832\pi\)
0.0130946 + 0.999914i \(0.495832\pi\)
\(948\) 0 0
\(949\) −2.26796 −0.0736210
\(950\) 0.265384 0.00861018
\(951\) 0 0
\(952\) 3.15975 0.102408
\(953\) 8.33532 0.270007 0.135004 0.990845i \(-0.456895\pi\)
0.135004 + 0.990845i \(0.456895\pi\)
\(954\) 0 0
\(955\) −15.5825 −0.504236
\(956\) 5.11214 0.165338
\(957\) 0 0
\(958\) 0.0878419 0.00283804
\(959\) −25.8504 −0.834754
\(960\) 0 0
\(961\) 27.2634 0.879464
\(962\) 0.327472 0.0105581
\(963\) 0 0
\(964\) 29.8983 0.962960
\(965\) −18.6960 −0.601846
\(966\) 0 0
\(967\) −42.1925 −1.35682 −0.678410 0.734683i \(-0.737331\pi\)
−0.678410 + 0.734683i \(0.737331\pi\)
\(968\) −0.183156 −0.00588687
\(969\) 0 0
\(970\) 1.26208 0.0405231
\(971\) −25.3293 −0.812856 −0.406428 0.913683i \(-0.633226\pi\)
−0.406428 + 0.913683i \(0.633226\pi\)
\(972\) 0 0
\(973\) −26.3771 −0.845611
\(974\) −2.03981 −0.0653596
\(975\) 0 0
\(976\) 50.4561 1.61506
\(977\) −36.0931 −1.15472 −0.577360 0.816489i \(-0.695917\pi\)
−0.577360 + 0.816489i \(0.695917\pi\)
\(978\) 0 0
\(979\) 3.10490 0.0992329
\(980\) 1.85741 0.0593329
\(981\) 0 0
\(982\) 0.562964 0.0179649
\(983\) 60.9563 1.94420 0.972102 0.234560i \(-0.0753650\pi\)
0.972102 + 0.234560i \(0.0753650\pi\)
\(984\) 0 0
\(985\) 10.2024 0.325077
\(986\) −0.740341 −0.0235773
\(987\) 0 0
\(988\) −7.88023 −0.250704
\(989\) 19.4961 0.619939
\(990\) 0 0
\(991\) 56.5677 1.79693 0.898466 0.439042i \(-0.144682\pi\)
0.898466 + 0.439042i \(0.144682\pi\)
\(992\) 6.13697 0.194849
\(993\) 0 0
\(994\) 1.29006 0.0409183
\(995\) −16.4798 −0.522446
\(996\) 0 0
\(997\) −2.37781 −0.0753060 −0.0376530 0.999291i \(-0.511988\pi\)
−0.0376530 + 0.999291i \(0.511988\pi\)
\(998\) −0.864237 −0.0273569
\(999\) 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 5265.2.a.ba.1.6 8
3.2 odd 2 5265.2.a.bf.1.3 8
9.2 odd 6 585.2.i.e.391.6 yes 16
9.4 even 3 1755.2.i.f.586.3 16
9.5 odd 6 585.2.i.e.196.6 16
9.7 even 3 1755.2.i.f.1171.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
585.2.i.e.196.6 16 9.5 odd 6
585.2.i.e.391.6 yes 16 9.2 odd 6
1755.2.i.f.586.3 16 9.4 even 3
1755.2.i.f.1171.3 16 9.7 even 3
5265.2.a.ba.1.6 8 1.1 even 1 trivial
5265.2.a.bf.1.3 8 3.2 odd 2