Properties

Label 3380.2.a.r.1.2
Level $3380$
Weight $2$
Character 3380.1
Self dual yes
Analytic conductor $26.989$
Analytic rank $0$
Dimension $9$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 3380 = 2^{2} \cdot 5 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3380.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(26.9894358832\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
Defining polynomial: \(x^{9} - x^{8} - 19 x^{7} + 16 x^{6} + 106 x^{5} - 87 x^{4} - 153 x^{3} + 149 x^{2} - 26 x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(2.52382\) of defining polynomial
Character \(\chi\) \(=\) 3380.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.52382 q^{3} -1.00000 q^{5} +4.54727 q^{7} +3.36968 q^{9} +O(q^{10})\) \(q-2.52382 q^{3} -1.00000 q^{5} +4.54727 q^{7} +3.36968 q^{9} +2.52395 q^{11} +2.52382 q^{15} +5.14630 q^{17} +7.52781 q^{19} -11.4765 q^{21} +2.63662 q^{23} +1.00000 q^{25} -0.933014 q^{27} -8.61995 q^{29} +8.44094 q^{31} -6.37000 q^{33} -4.54727 q^{35} +6.98381 q^{37} +2.66091 q^{41} -9.74401 q^{43} -3.36968 q^{45} -8.15221 q^{47} +13.6776 q^{49} -12.9884 q^{51} -1.43808 q^{53} -2.52395 q^{55} -18.9989 q^{57} +0.0833281 q^{59} -0.818691 q^{61} +15.3229 q^{63} +5.08761 q^{67} -6.65437 q^{69} -7.78118 q^{71} +0.148454 q^{73} -2.52382 q^{75} +11.4771 q^{77} +7.18836 q^{79} -7.75429 q^{81} -16.9198 q^{83} -5.14630 q^{85} +21.7552 q^{87} +3.05664 q^{89} -21.3034 q^{93} -7.52781 q^{95} +8.27717 q^{97} +8.50490 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q - q^{3} - 9 q^{5} - q^{7} + 12 q^{9} + O(q^{10}) \) \( 9 q - q^{3} - 9 q^{5} - q^{7} + 12 q^{9} + 7 q^{11} + q^{15} + 13 q^{17} + 4 q^{19} + 3 q^{21} + 12 q^{23} + 9 q^{25} - 4 q^{27} + 16 q^{29} - 13 q^{31} - 34 q^{33} + q^{35} - q^{37} + 6 q^{41} + q^{43} - 12 q^{45} + 2 q^{47} + 20 q^{49} + 11 q^{51} + 30 q^{53} - 7 q^{55} - 38 q^{57} - 15 q^{59} + 21 q^{61} + 17 q^{63} + 7 q^{67} + 15 q^{69} + 7 q^{71} + 28 q^{73} - q^{75} + 46 q^{77} + 31 q^{79} + 41 q^{81} - 45 q^{83} - 13 q^{85} + 28 q^{87} + 41 q^{89} + 11 q^{93} - 4 q^{95} - 8 q^{97} + 81 q^{99} + O(q^{100}) \)

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
\(3\) −2.52382 −1.45713 −0.728565 0.684977i \(-0.759812\pi\)
−0.728565 + 0.684977i \(0.759812\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 4.54727 1.71871 0.859353 0.511383i \(-0.170867\pi\)
0.859353 + 0.511383i \(0.170867\pi\)
\(8\) 0 0
\(9\) 3.36968 1.12323
\(10\) 0 0
\(11\) 2.52395 0.760999 0.380499 0.924781i \(-0.375752\pi\)
0.380499 + 0.924781i \(0.375752\pi\)
\(12\) 0 0
\(13\) 0 0
\(14\) 0 0
\(15\) 2.52382 0.651648
\(16\) 0 0
\(17\) 5.14630 1.24816 0.624081 0.781360i \(-0.285474\pi\)
0.624081 + 0.781360i \(0.285474\pi\)
\(18\) 0 0
\(19\) 7.52781 1.72700 0.863499 0.504350i \(-0.168268\pi\)
0.863499 + 0.504350i \(0.168268\pi\)
\(20\) 0 0
\(21\) −11.4765 −2.50438
\(22\) 0 0
\(23\) 2.63662 0.549774 0.274887 0.961477i \(-0.411360\pi\)
0.274887 + 0.961477i \(0.411360\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) −0.933014 −0.179559
\(28\) 0 0
\(29\) −8.61995 −1.60068 −0.800342 0.599544i \(-0.795349\pi\)
−0.800342 + 0.599544i \(0.795349\pi\)
\(30\) 0 0
\(31\) 8.44094 1.51604 0.758018 0.652233i \(-0.226168\pi\)
0.758018 + 0.652233i \(0.226168\pi\)
\(32\) 0 0
\(33\) −6.37000 −1.10887
\(34\) 0 0
\(35\) −4.54727 −0.768629
\(36\) 0 0
\(37\) 6.98381 1.14813 0.574065 0.818810i \(-0.305366\pi\)
0.574065 + 0.818810i \(0.305366\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.66091 0.415564 0.207782 0.978175i \(-0.433376\pi\)
0.207782 + 0.978175i \(0.433376\pi\)
\(42\) 0 0
\(43\) −9.74401 −1.48595 −0.742974 0.669320i \(-0.766585\pi\)
−0.742974 + 0.669320i \(0.766585\pi\)
\(44\) 0 0
\(45\) −3.36968 −0.502323
\(46\) 0 0
\(47\) −8.15221 −1.18912 −0.594561 0.804051i \(-0.702674\pi\)
−0.594561 + 0.804051i \(0.702674\pi\)
\(48\) 0 0
\(49\) 13.6776 1.95395
\(50\) 0 0
\(51\) −12.9884 −1.81873
\(52\) 0 0
\(53\) −1.43808 −0.197535 −0.0987677 0.995111i \(-0.531490\pi\)
−0.0987677 + 0.995111i \(0.531490\pi\)
\(54\) 0 0
\(55\) −2.52395 −0.340329
\(56\) 0 0
\(57\) −18.9989 −2.51646
\(58\) 0 0
\(59\) 0.0833281 0.0108484 0.00542420 0.999985i \(-0.498273\pi\)
0.00542420 + 0.999985i \(0.498273\pi\)
\(60\) 0 0
\(61\) −0.818691 −0.104823 −0.0524113 0.998626i \(-0.516691\pi\)
−0.0524113 + 0.998626i \(0.516691\pi\)
\(62\) 0 0
\(63\) 15.3229 1.93050
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 5.08761 0.621550 0.310775 0.950483i \(-0.399411\pi\)
0.310775 + 0.950483i \(0.399411\pi\)
\(68\) 0 0
\(69\) −6.65437 −0.801092
\(70\) 0 0
\(71\) −7.78118 −0.923456 −0.461728 0.887021i \(-0.652770\pi\)
−0.461728 + 0.887021i \(0.652770\pi\)
\(72\) 0 0
\(73\) 0.148454 0.0173753 0.00868764 0.999962i \(-0.497235\pi\)
0.00868764 + 0.999962i \(0.497235\pi\)
\(74\) 0 0
\(75\) −2.52382 −0.291426
\(76\) 0 0
\(77\) 11.4771 1.30793
\(78\) 0 0
\(79\) 7.18836 0.808754 0.404377 0.914592i \(-0.367488\pi\)
0.404377 + 0.914592i \(0.367488\pi\)
\(80\) 0 0
\(81\) −7.75429 −0.861587
\(82\) 0 0
\(83\) −16.9198 −1.85719 −0.928597 0.371089i \(-0.878984\pi\)
−0.928597 + 0.371089i \(0.878984\pi\)
\(84\) 0 0
\(85\) −5.14630 −0.558195
\(86\) 0 0
\(87\) 21.7552 2.33240
\(88\) 0 0
\(89\) 3.05664 0.324003 0.162002 0.986790i \(-0.448205\pi\)
0.162002 + 0.986790i \(0.448205\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −21.3034 −2.20906
\(94\) 0 0
\(95\) −7.52781 −0.772337
\(96\) 0 0
\(97\) 8.27717 0.840419 0.420209 0.907427i \(-0.361957\pi\)
0.420209 + 0.907427i \(0.361957\pi\)
\(98\) 0 0
\(99\) 8.50490 0.854775
\(100\) 0 0
\(101\) 2.46123 0.244902 0.122451 0.992475i \(-0.460925\pi\)
0.122451 + 0.992475i \(0.460925\pi\)
\(102\) 0 0
\(103\) −10.6923 −1.05355 −0.526773 0.850006i \(-0.676598\pi\)
−0.526773 + 0.850006i \(0.676598\pi\)
\(104\) 0 0
\(105\) 11.4765 1.11999
\(106\) 0 0
\(107\) −0.880036 −0.0850763 −0.0425381 0.999095i \(-0.513544\pi\)
−0.0425381 + 0.999095i \(0.513544\pi\)
\(108\) 0 0
\(109\) −1.54141 −0.147640 −0.0738201 0.997272i \(-0.523519\pi\)
−0.0738201 + 0.997272i \(0.523519\pi\)
\(110\) 0 0
\(111\) −17.6259 −1.67298
\(112\) 0 0
\(113\) 10.7763 1.01375 0.506874 0.862020i \(-0.330801\pi\)
0.506874 + 0.862020i \(0.330801\pi\)
\(114\) 0 0
\(115\) −2.63662 −0.245866
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 23.4016 2.14522
\(120\) 0 0
\(121\) −4.62969 −0.420881
\(122\) 0 0
\(123\) −6.71566 −0.605531
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 6.09528 0.540868 0.270434 0.962738i \(-0.412833\pi\)
0.270434 + 0.962738i \(0.412833\pi\)
\(128\) 0 0
\(129\) 24.5922 2.16522
\(130\) 0 0
\(131\) 10.4044 0.909039 0.454520 0.890737i \(-0.349811\pi\)
0.454520 + 0.890737i \(0.349811\pi\)
\(132\) 0 0
\(133\) 34.2310 2.96820
\(134\) 0 0
\(135\) 0.933014 0.0803011
\(136\) 0 0
\(137\) 4.89180 0.417934 0.208967 0.977923i \(-0.432990\pi\)
0.208967 + 0.977923i \(0.432990\pi\)
\(138\) 0 0
\(139\) −22.4823 −1.90692 −0.953460 0.301519i \(-0.902506\pi\)
−0.953460 + 0.301519i \(0.902506\pi\)
\(140\) 0 0
\(141\) 20.5747 1.73270
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 8.61995 0.715848
\(146\) 0 0
\(147\) −34.5200 −2.84716
\(148\) 0 0
\(149\) 20.4563 1.67584 0.837922 0.545790i \(-0.183770\pi\)
0.837922 + 0.545790i \(0.183770\pi\)
\(150\) 0 0
\(151\) −0.0637311 −0.00518637 −0.00259318 0.999997i \(-0.500825\pi\)
−0.00259318 + 0.999997i \(0.500825\pi\)
\(152\) 0 0
\(153\) 17.3414 1.40197
\(154\) 0 0
\(155\) −8.44094 −0.677992
\(156\) 0 0
\(157\) −0.0591648 −0.00472187 −0.00236093 0.999997i \(-0.500752\pi\)
−0.00236093 + 0.999997i \(0.500752\pi\)
\(158\) 0 0
\(159\) 3.62946 0.287835
\(160\) 0 0
\(161\) 11.9894 0.944900
\(162\) 0 0
\(163\) −15.9234 −1.24721 −0.623607 0.781738i \(-0.714334\pi\)
−0.623607 + 0.781738i \(0.714334\pi\)
\(164\) 0 0
\(165\) 6.37000 0.495904
\(166\) 0 0
\(167\) −22.1436 −1.71352 −0.856762 0.515711i \(-0.827528\pi\)
−0.856762 + 0.515711i \(0.827528\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 25.3663 1.93981
\(172\) 0 0
\(173\) 18.7289 1.42393 0.711966 0.702214i \(-0.247805\pi\)
0.711966 + 0.702214i \(0.247805\pi\)
\(174\) 0 0
\(175\) 4.54727 0.343741
\(176\) 0 0
\(177\) −0.210305 −0.0158075
\(178\) 0 0
\(179\) 8.89212 0.664628 0.332314 0.943169i \(-0.392171\pi\)
0.332314 + 0.943169i \(0.392171\pi\)
\(180\) 0 0
\(181\) −3.90674 −0.290386 −0.145193 0.989403i \(-0.546380\pi\)
−0.145193 + 0.989403i \(0.546380\pi\)
\(182\) 0 0
\(183\) 2.06623 0.152740
\(184\) 0 0
\(185\) −6.98381 −0.513460
\(186\) 0 0
\(187\) 12.9890 0.949850
\(188\) 0 0
\(189\) −4.24267 −0.308609
\(190\) 0 0
\(191\) 22.0068 1.59236 0.796179 0.605061i \(-0.206851\pi\)
0.796179 + 0.605061i \(0.206851\pi\)
\(192\) 0 0
\(193\) −6.46062 −0.465046 −0.232523 0.972591i \(-0.574698\pi\)
−0.232523 + 0.972591i \(0.574698\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −19.2295 −1.37004 −0.685021 0.728523i \(-0.740207\pi\)
−0.685021 + 0.728523i \(0.740207\pi\)
\(198\) 0 0
\(199\) 16.3145 1.15651 0.578253 0.815858i \(-0.303735\pi\)
0.578253 + 0.815858i \(0.303735\pi\)
\(200\) 0 0
\(201\) −12.8402 −0.905679
\(202\) 0 0
\(203\) −39.1972 −2.75111
\(204\) 0 0
\(205\) −2.66091 −0.185846
\(206\) 0 0
\(207\) 8.88458 0.617521
\(208\) 0 0
\(209\) 18.9998 1.31424
\(210\) 0 0
\(211\) 21.2686 1.46419 0.732094 0.681204i \(-0.238543\pi\)
0.732094 + 0.681204i \(0.238543\pi\)
\(212\) 0 0
\(213\) 19.6383 1.34560
\(214\) 0 0
\(215\) 9.74401 0.664536
\(216\) 0 0
\(217\) 38.3832 2.60562
\(218\) 0 0
\(219\) −0.374673 −0.0253180
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 9.75386 0.653167 0.326583 0.945168i \(-0.394103\pi\)
0.326583 + 0.945168i \(0.394103\pi\)
\(224\) 0 0
\(225\) 3.36968 0.224646
\(226\) 0 0
\(227\) −26.0411 −1.72841 −0.864205 0.503140i \(-0.832178\pi\)
−0.864205 + 0.503140i \(0.832178\pi\)
\(228\) 0 0
\(229\) 15.9818 1.05610 0.528052 0.849212i \(-0.322923\pi\)
0.528052 + 0.849212i \(0.322923\pi\)
\(230\) 0 0
\(231\) −28.9661 −1.90583
\(232\) 0 0
\(233\) −7.67734 −0.502960 −0.251480 0.967863i \(-0.580917\pi\)
−0.251480 + 0.967863i \(0.580917\pi\)
\(234\) 0 0
\(235\) 8.15221 0.531791
\(236\) 0 0
\(237\) −18.1422 −1.17846
\(238\) 0 0
\(239\) 18.1981 1.17714 0.588570 0.808446i \(-0.299691\pi\)
0.588570 + 0.808446i \(0.299691\pi\)
\(240\) 0 0
\(241\) −13.7693 −0.886958 −0.443479 0.896285i \(-0.646256\pi\)
−0.443479 + 0.896285i \(0.646256\pi\)
\(242\) 0 0
\(243\) 22.3695 1.43500
\(244\) 0 0
\(245\) −13.6776 −0.873833
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 42.7027 2.70617
\(250\) 0 0
\(251\) 9.54318 0.602360 0.301180 0.953567i \(-0.402619\pi\)
0.301180 + 0.953567i \(0.402619\pi\)
\(252\) 0 0
\(253\) 6.65470 0.418377
\(254\) 0 0
\(255\) 12.9884 0.813363
\(256\) 0 0
\(257\) −9.56768 −0.596816 −0.298408 0.954438i \(-0.596456\pi\)
−0.298408 + 0.954438i \(0.596456\pi\)
\(258\) 0 0
\(259\) 31.7572 1.97330
\(260\) 0 0
\(261\) −29.0465 −1.79793
\(262\) 0 0
\(263\) 21.2418 1.30982 0.654912 0.755705i \(-0.272705\pi\)
0.654912 + 0.755705i \(0.272705\pi\)
\(264\) 0 0
\(265\) 1.43808 0.0883405
\(266\) 0 0
\(267\) −7.71442 −0.472115
\(268\) 0 0
\(269\) 24.1110 1.47008 0.735038 0.678026i \(-0.237164\pi\)
0.735038 + 0.678026i \(0.237164\pi\)
\(270\) 0 0
\(271\) 2.12699 0.129205 0.0646026 0.997911i \(-0.479422\pi\)
0.0646026 + 0.997911i \(0.479422\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 2.52395 0.152200
\(276\) 0 0
\(277\) 24.5197 1.47325 0.736623 0.676303i \(-0.236419\pi\)
0.736623 + 0.676303i \(0.236419\pi\)
\(278\) 0 0
\(279\) 28.4433 1.70285
\(280\) 0 0
\(281\) 9.63729 0.574913 0.287456 0.957794i \(-0.407190\pi\)
0.287456 + 0.957794i \(0.407190\pi\)
\(282\) 0 0
\(283\) −23.5987 −1.40280 −0.701400 0.712768i \(-0.747441\pi\)
−0.701400 + 0.712768i \(0.747441\pi\)
\(284\) 0 0
\(285\) 18.9989 1.12540
\(286\) 0 0
\(287\) 12.0999 0.714232
\(288\) 0 0
\(289\) 9.48444 0.557908
\(290\) 0 0
\(291\) −20.8901 −1.22460
\(292\) 0 0
\(293\) 5.38348 0.314506 0.157253 0.987558i \(-0.449736\pi\)
0.157253 + 0.987558i \(0.449736\pi\)
\(294\) 0 0
\(295\) −0.0833281 −0.00485155
\(296\) 0 0
\(297\) −2.35488 −0.136644
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −44.3086 −2.55391
\(302\) 0 0
\(303\) −6.21171 −0.356854
\(304\) 0 0
\(305\) 0.818691 0.0468781
\(306\) 0 0
\(307\) −12.1743 −0.694825 −0.347413 0.937712i \(-0.612940\pi\)
−0.347413 + 0.937712i \(0.612940\pi\)
\(308\) 0 0
\(309\) 26.9855 1.53515
\(310\) 0 0
\(311\) −13.2103 −0.749085 −0.374543 0.927210i \(-0.622200\pi\)
−0.374543 + 0.927210i \(0.622200\pi\)
\(312\) 0 0
\(313\) −24.1485 −1.36495 −0.682476 0.730908i \(-0.739097\pi\)
−0.682476 + 0.730908i \(0.739097\pi\)
\(314\) 0 0
\(315\) −15.3229 −0.863345
\(316\) 0 0
\(317\) −6.42443 −0.360832 −0.180416 0.983590i \(-0.557744\pi\)
−0.180416 + 0.983590i \(0.557744\pi\)
\(318\) 0 0
\(319\) −21.7563 −1.21812
\(320\) 0 0
\(321\) 2.22105 0.123967
\(322\) 0 0
\(323\) 38.7404 2.15557
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 3.89024 0.215131
\(328\) 0 0
\(329\) −37.0703 −2.04375
\(330\) 0 0
\(331\) 21.8105 1.19881 0.599407 0.800444i \(-0.295403\pi\)
0.599407 + 0.800444i \(0.295403\pi\)
\(332\) 0 0
\(333\) 23.5332 1.28961
\(334\) 0 0
\(335\) −5.08761 −0.277966
\(336\) 0 0
\(337\) 5.94670 0.323937 0.161969 0.986796i \(-0.448216\pi\)
0.161969 + 0.986796i \(0.448216\pi\)
\(338\) 0 0
\(339\) −27.1975 −1.47716
\(340\) 0 0
\(341\) 21.3045 1.15370
\(342\) 0 0
\(343\) 30.3651 1.63956
\(344\) 0 0
\(345\) 6.65437 0.358259
\(346\) 0 0
\(347\) −20.7097 −1.11175 −0.555877 0.831264i \(-0.687618\pi\)
−0.555877 + 0.831264i \(0.687618\pi\)
\(348\) 0 0
\(349\) −8.05214 −0.431021 −0.215511 0.976502i \(-0.569142\pi\)
−0.215511 + 0.976502i \(0.569142\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7.11032 −0.378444 −0.189222 0.981934i \(-0.560597\pi\)
−0.189222 + 0.981934i \(0.560597\pi\)
\(354\) 0 0
\(355\) 7.78118 0.412982
\(356\) 0 0
\(357\) −59.0616 −3.12587
\(358\) 0 0
\(359\) −6.26310 −0.330554 −0.165277 0.986247i \(-0.552852\pi\)
−0.165277 + 0.986247i \(0.552852\pi\)
\(360\) 0 0
\(361\) 37.6679 1.98252
\(362\) 0 0
\(363\) 11.6845 0.613278
\(364\) 0 0
\(365\) −0.148454 −0.00777046
\(366\) 0 0
\(367\) 15.9522 0.832697 0.416349 0.909205i \(-0.363310\pi\)
0.416349 + 0.909205i \(0.363310\pi\)
\(368\) 0 0
\(369\) 8.96642 0.466773
\(370\) 0 0
\(371\) −6.53934 −0.339505
\(372\) 0 0
\(373\) −1.42611 −0.0738410 −0.0369205 0.999318i \(-0.511755\pi\)
−0.0369205 + 0.999318i \(0.511755\pi\)
\(374\) 0 0
\(375\) 2.52382 0.130330
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 3.57360 0.183564 0.0917818 0.995779i \(-0.470744\pi\)
0.0917818 + 0.995779i \(0.470744\pi\)
\(380\) 0 0
\(381\) −15.3834 −0.788115
\(382\) 0 0
\(383\) 4.84620 0.247629 0.123815 0.992305i \(-0.460487\pi\)
0.123815 + 0.992305i \(0.460487\pi\)
\(384\) 0 0
\(385\) −11.4771 −0.584925
\(386\) 0 0
\(387\) −32.8342 −1.66906
\(388\) 0 0
\(389\) −33.7772 −1.71257 −0.856285 0.516503i \(-0.827233\pi\)
−0.856285 + 0.516503i \(0.827233\pi\)
\(390\) 0 0
\(391\) 13.5689 0.686207
\(392\) 0 0
\(393\) −26.2589 −1.32459
\(394\) 0 0
\(395\) −7.18836 −0.361686
\(396\) 0 0
\(397\) 0.483569 0.0242696 0.0121348 0.999926i \(-0.496137\pi\)
0.0121348 + 0.999926i \(0.496137\pi\)
\(398\) 0 0
\(399\) −86.3929 −4.32506
\(400\) 0 0
\(401\) −18.0902 −0.903380 −0.451690 0.892175i \(-0.649179\pi\)
−0.451690 + 0.892175i \(0.649179\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 7.75429 0.385314
\(406\) 0 0
\(407\) 17.6268 0.873726
\(408\) 0 0
\(409\) 34.5327 1.70753 0.853766 0.520657i \(-0.174313\pi\)
0.853766 + 0.520657i \(0.174313\pi\)
\(410\) 0 0
\(411\) −12.3460 −0.608985
\(412\) 0 0
\(413\) 0.378915 0.0186452
\(414\) 0 0
\(415\) 16.9198 0.830563
\(416\) 0 0
\(417\) 56.7412 2.77863
\(418\) 0 0
\(419\) −23.0215 −1.12467 −0.562337 0.826908i \(-0.690098\pi\)
−0.562337 + 0.826908i \(0.690098\pi\)
\(420\) 0 0
\(421\) −7.63811 −0.372259 −0.186129 0.982525i \(-0.559594\pi\)
−0.186129 + 0.982525i \(0.559594\pi\)
\(422\) 0 0
\(423\) −27.4704 −1.33565
\(424\) 0 0
\(425\) 5.14630 0.249632
\(426\) 0 0
\(427\) −3.72281 −0.180159
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −22.3076 −1.07452 −0.537260 0.843417i \(-0.680541\pi\)
−0.537260 + 0.843417i \(0.680541\pi\)
\(432\) 0 0
\(433\) 1.01305 0.0486838 0.0243419 0.999704i \(-0.492251\pi\)
0.0243419 + 0.999704i \(0.492251\pi\)
\(434\) 0 0
\(435\) −21.7552 −1.04308
\(436\) 0 0
\(437\) 19.8480 0.949459
\(438\) 0 0
\(439\) −40.1466 −1.91609 −0.958046 0.286613i \(-0.907471\pi\)
−0.958046 + 0.286613i \(0.907471\pi\)
\(440\) 0 0
\(441\) 46.0893 2.19473
\(442\) 0 0
\(443\) −37.0607 −1.76080 −0.880402 0.474228i \(-0.842727\pi\)
−0.880402 + 0.474228i \(0.842727\pi\)
\(444\) 0 0
\(445\) −3.05664 −0.144899
\(446\) 0 0
\(447\) −51.6281 −2.44192
\(448\) 0 0
\(449\) −11.4726 −0.541424 −0.270712 0.962660i \(-0.587259\pi\)
−0.270712 + 0.962660i \(0.587259\pi\)
\(450\) 0 0
\(451\) 6.71599 0.316244
\(452\) 0 0
\(453\) 0.160846 0.00755721
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9.21789 0.431195 0.215597 0.976482i \(-0.430830\pi\)
0.215597 + 0.976482i \(0.430830\pi\)
\(458\) 0 0
\(459\) −4.80157 −0.224118
\(460\) 0 0
\(461\) 3.78265 0.176176 0.0880878 0.996113i \(-0.471924\pi\)
0.0880878 + 0.996113i \(0.471924\pi\)
\(462\) 0 0
\(463\) −2.59710 −0.120698 −0.0603488 0.998177i \(-0.519221\pi\)
−0.0603488 + 0.998177i \(0.519221\pi\)
\(464\) 0 0
\(465\) 21.3034 0.987923
\(466\) 0 0
\(467\) −39.2664 −1.81703 −0.908516 0.417849i \(-0.862784\pi\)
−0.908516 + 0.417849i \(0.862784\pi\)
\(468\) 0 0
\(469\) 23.1347 1.06826
\(470\) 0 0
\(471\) 0.149321 0.00688037
\(472\) 0 0
\(473\) −24.5934 −1.13080
\(474\) 0 0
\(475\) 7.52781 0.345400
\(476\) 0 0
\(477\) −4.84587 −0.221877
\(478\) 0 0
\(479\) −35.8940 −1.64004 −0.820019 0.572337i \(-0.806037\pi\)
−0.820019 + 0.572337i \(0.806037\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −30.2592 −1.37684
\(484\) 0 0
\(485\) −8.27717 −0.375847
\(486\) 0 0
\(487\) −30.6683 −1.38971 −0.694856 0.719149i \(-0.744532\pi\)
−0.694856 + 0.719149i \(0.744532\pi\)
\(488\) 0 0
\(489\) 40.1878 1.81735
\(490\) 0 0
\(491\) 30.2621 1.36571 0.682856 0.730553i \(-0.260738\pi\)
0.682856 + 0.730553i \(0.260738\pi\)
\(492\) 0 0
\(493\) −44.3609 −1.99791
\(494\) 0 0
\(495\) −8.50490 −0.382267
\(496\) 0 0
\(497\) −35.3831 −1.58715
\(498\) 0 0
\(499\) 11.5036 0.514973 0.257486 0.966282i \(-0.417106\pi\)
0.257486 + 0.966282i \(0.417106\pi\)
\(500\) 0 0
\(501\) 55.8866 2.49683
\(502\) 0 0
\(503\) −14.0889 −0.628195 −0.314097 0.949391i \(-0.601702\pi\)
−0.314097 + 0.949391i \(0.601702\pi\)
\(504\) 0 0
\(505\) −2.46123 −0.109523
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.07854 −0.358075 −0.179037 0.983842i \(-0.557298\pi\)
−0.179037 + 0.983842i \(0.557298\pi\)
\(510\) 0 0
\(511\) 0.675062 0.0298630
\(512\) 0 0
\(513\) −7.02355 −0.310097
\(514\) 0 0
\(515\) 10.6923 0.471160
\(516\) 0 0
\(517\) −20.5757 −0.904920
\(518\) 0 0
\(519\) −47.2684 −2.07485
\(520\) 0 0
\(521\) 31.6830 1.38806 0.694028 0.719948i \(-0.255834\pi\)
0.694028 + 0.719948i \(0.255834\pi\)
\(522\) 0 0
\(523\) 5.56717 0.243435 0.121718 0.992565i \(-0.461160\pi\)
0.121718 + 0.992565i \(0.461160\pi\)
\(524\) 0 0
\(525\) −11.4765 −0.500876
\(526\) 0 0
\(527\) 43.4396 1.89226
\(528\) 0 0
\(529\) −16.0482 −0.697749
\(530\) 0 0
\(531\) 0.280789 0.0121852
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0.880036 0.0380473
\(536\) 0 0
\(537\) −22.4421 −0.968449
\(538\) 0 0
\(539\) 34.5217 1.48695
\(540\) 0 0
\(541\) 3.01207 0.129499 0.0647496 0.997902i \(-0.479375\pi\)
0.0647496 + 0.997902i \(0.479375\pi\)
\(542\) 0 0
\(543\) 9.85992 0.423130
\(544\) 0 0
\(545\) 1.54141 0.0660267
\(546\) 0 0
\(547\) 23.1320 0.989053 0.494527 0.869163i \(-0.335341\pi\)
0.494527 + 0.869163i \(0.335341\pi\)
\(548\) 0 0
\(549\) −2.75873 −0.117740
\(550\) 0 0
\(551\) −64.8893 −2.76438
\(552\) 0 0
\(553\) 32.6874 1.39001
\(554\) 0 0
\(555\) 17.6259 0.748177
\(556\) 0 0
\(557\) 7.18919 0.304616 0.152308 0.988333i \(-0.451329\pi\)
0.152308 + 0.988333i \(0.451329\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −32.7819 −1.38405
\(562\) 0 0
\(563\) 5.32860 0.224574 0.112287 0.993676i \(-0.464182\pi\)
0.112287 + 0.993676i \(0.464182\pi\)
\(564\) 0 0
\(565\) −10.7763 −0.453362
\(566\) 0 0
\(567\) −35.2608 −1.48082
\(568\) 0 0
\(569\) 39.8437 1.67034 0.835168 0.549995i \(-0.185370\pi\)
0.835168 + 0.549995i \(0.185370\pi\)
\(570\) 0 0
\(571\) 3.28735 0.137571 0.0687857 0.997631i \(-0.478088\pi\)
0.0687857 + 0.997631i \(0.478088\pi\)
\(572\) 0 0
\(573\) −55.5414 −2.32027
\(574\) 0 0
\(575\) 2.63662 0.109955
\(576\) 0 0
\(577\) 16.3187 0.679358 0.339679 0.940541i \(-0.389682\pi\)
0.339679 + 0.940541i \(0.389682\pi\)
\(578\) 0 0
\(579\) 16.3055 0.677632
\(580\) 0 0
\(581\) −76.9391 −3.19197
\(582\) 0 0
\(583\) −3.62964 −0.150324
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 21.3533 0.881344 0.440672 0.897668i \(-0.354740\pi\)
0.440672 + 0.897668i \(0.354740\pi\)
\(588\) 0 0
\(589\) 63.5418 2.61819
\(590\) 0 0
\(591\) 48.5317 1.99633
\(592\) 0 0
\(593\) −26.2461 −1.07780 −0.538898 0.842371i \(-0.681159\pi\)
−0.538898 + 0.842371i \(0.681159\pi\)
\(594\) 0 0
\(595\) −23.4016 −0.959373
\(596\) 0 0
\(597\) −41.1750 −1.68518
\(598\) 0 0
\(599\) −25.6381 −1.04754 −0.523772 0.851858i \(-0.675476\pi\)
−0.523772 + 0.851858i \(0.675476\pi\)
\(600\) 0 0
\(601\) 14.6633 0.598128 0.299064 0.954233i \(-0.403326\pi\)
0.299064 + 0.954233i \(0.403326\pi\)
\(602\) 0 0
\(603\) 17.1436 0.698142
\(604\) 0 0
\(605\) 4.62969 0.188224
\(606\) 0 0
\(607\) 14.8341 0.602100 0.301050 0.953608i \(-0.402663\pi\)
0.301050 + 0.953608i \(0.402663\pi\)
\(608\) 0 0
\(609\) 98.9268 4.00872
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0.253642 0.0102445 0.00512225 0.999987i \(-0.498370\pi\)
0.00512225 + 0.999987i \(0.498370\pi\)
\(614\) 0 0
\(615\) 6.71566 0.270802
\(616\) 0 0
\(617\) 9.99816 0.402511 0.201255 0.979539i \(-0.435498\pi\)
0.201255 + 0.979539i \(0.435498\pi\)
\(618\) 0 0
\(619\) −6.07953 −0.244357 −0.122178 0.992508i \(-0.538988\pi\)
−0.122178 + 0.992508i \(0.538988\pi\)
\(620\) 0 0
\(621\) −2.46001 −0.0987167
\(622\) 0 0
\(623\) 13.8994 0.556866
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −47.9521 −1.91502
\(628\) 0 0
\(629\) 35.9408 1.43305
\(630\) 0 0
\(631\) 40.4143 1.60887 0.804434 0.594041i \(-0.202468\pi\)
0.804434 + 0.594041i \(0.202468\pi\)
\(632\) 0 0
\(633\) −53.6781 −2.13351
\(634\) 0 0
\(635\) −6.09528 −0.241884
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) −26.2201 −1.03725
\(640\) 0 0
\(641\) 10.7514 0.424653 0.212327 0.977199i \(-0.431896\pi\)
0.212327 + 0.977199i \(0.431896\pi\)
\(642\) 0 0
\(643\) 15.7425 0.620823 0.310412 0.950602i \(-0.399533\pi\)
0.310412 + 0.950602i \(0.399533\pi\)
\(644\) 0 0
\(645\) −24.5922 −0.968315
\(646\) 0 0
\(647\) −13.4404 −0.528399 −0.264199 0.964468i \(-0.585108\pi\)
−0.264199 + 0.964468i \(0.585108\pi\)
\(648\) 0 0
\(649\) 0.210316 0.00825562
\(650\) 0 0
\(651\) −96.8724 −3.79673
\(652\) 0 0
\(653\) 1.21367 0.0474948 0.0237474 0.999718i \(-0.492440\pi\)
0.0237474 + 0.999718i \(0.492440\pi\)
\(654\) 0 0
\(655\) −10.4044 −0.406535
\(656\) 0 0
\(657\) 0.500245 0.0195164
\(658\) 0 0
\(659\) −11.8299 −0.460827 −0.230413 0.973093i \(-0.574008\pi\)
−0.230413 + 0.973093i \(0.574008\pi\)
\(660\) 0 0
\(661\) −44.4477 −1.72882 −0.864409 0.502790i \(-0.832307\pi\)
−0.864409 + 0.502790i \(0.832307\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −34.2310 −1.32742
\(666\) 0 0
\(667\) −22.7276 −0.880015
\(668\) 0 0
\(669\) −24.6170 −0.951749
\(670\) 0 0
\(671\) −2.06633 −0.0797699
\(672\) 0 0
\(673\) 12.2950 0.473936 0.236968 0.971517i \(-0.423846\pi\)
0.236968 + 0.971517i \(0.423846\pi\)
\(674\) 0 0
\(675\) −0.933014 −0.0359117
\(676\) 0 0
\(677\) −7.57026 −0.290949 −0.145474 0.989362i \(-0.546471\pi\)
−0.145474 + 0.989362i \(0.546471\pi\)
\(678\) 0 0
\(679\) 37.6385 1.44443
\(680\) 0 0
\(681\) 65.7232 2.51852
\(682\) 0 0
\(683\) 16.7077 0.639303 0.319651 0.947535i \(-0.396434\pi\)
0.319651 + 0.947535i \(0.396434\pi\)
\(684\) 0 0
\(685\) −4.89180 −0.186906
\(686\) 0 0
\(687\) −40.3351 −1.53888
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 18.5620 0.706131 0.353065 0.935599i \(-0.385139\pi\)
0.353065 + 0.935599i \(0.385139\pi\)
\(692\) 0 0
\(693\) 38.6741 1.46911
\(694\) 0 0
\(695\) 22.4823 0.852801
\(696\) 0 0
\(697\) 13.6938 0.518691
\(698\) 0 0
\(699\) 19.3763 0.732877
\(700\) 0 0
\(701\) 25.7585 0.972886 0.486443 0.873712i \(-0.338294\pi\)
0.486443 + 0.873712i \(0.338294\pi\)
\(702\) 0 0
\(703\) 52.5728 1.98282
\(704\) 0 0
\(705\) −20.5747 −0.774889
\(706\) 0 0
\(707\) 11.1919 0.420914
\(708\) 0 0
\(709\) 5.33378 0.200314 0.100157 0.994972i \(-0.468065\pi\)
0.100157 + 0.994972i \(0.468065\pi\)
\(710\) 0 0
\(711\) 24.2225 0.908415
\(712\) 0 0
\(713\) 22.2556 0.833478
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −45.9289 −1.71525
\(718\) 0 0
\(719\) −18.5517 −0.691861 −0.345930 0.938260i \(-0.612437\pi\)
−0.345930 + 0.938260i \(0.612437\pi\)
\(720\) 0 0
\(721\) −48.6208 −1.81073
\(722\) 0 0
\(723\) 34.7513 1.29241
\(724\) 0 0
\(725\) −8.61995 −0.320137
\(726\) 0 0
\(727\) 14.5977 0.541400 0.270700 0.962664i \(-0.412745\pi\)
0.270700 + 0.962664i \(0.412745\pi\)
\(728\) 0 0
\(729\) −33.1938 −1.22940
\(730\) 0 0
\(731\) −50.1456 −1.85470
\(732\) 0 0
\(733\) 28.2807 1.04457 0.522286 0.852770i \(-0.325079\pi\)
0.522286 + 0.852770i \(0.325079\pi\)
\(734\) 0 0
\(735\) 34.5200 1.27329
\(736\) 0 0
\(737\) 12.8409 0.472999
\(738\) 0 0
\(739\) 2.37192 0.0872523 0.0436262 0.999048i \(-0.486109\pi\)
0.0436262 + 0.999048i \(0.486109\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 26.4361 0.969845 0.484923 0.874557i \(-0.338848\pi\)
0.484923 + 0.874557i \(0.338848\pi\)
\(744\) 0 0
\(745\) −20.4563 −0.749460
\(746\) 0 0
\(747\) −57.0145 −2.08605
\(748\) 0 0
\(749\) −4.00176 −0.146221
\(750\) 0 0
\(751\) −13.0414 −0.475889 −0.237944 0.971279i \(-0.576474\pi\)
−0.237944 + 0.971279i \(0.576474\pi\)
\(752\) 0 0
\(753\) −24.0853 −0.877717
\(754\) 0 0
\(755\) 0.0637311 0.00231941
\(756\) 0 0
\(757\) −43.6023 −1.58475 −0.792377 0.610032i \(-0.791157\pi\)
−0.792377 + 0.610032i \(0.791157\pi\)
\(758\) 0 0
\(759\) −16.7953 −0.609630
\(760\) 0 0
\(761\) −17.2976 −0.627038 −0.313519 0.949582i \(-0.601508\pi\)
−0.313519 + 0.949582i \(0.601508\pi\)
\(762\) 0 0
\(763\) −7.00920 −0.253750
\(764\) 0 0
\(765\) −17.3414 −0.626980
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 27.3193 0.985158 0.492579 0.870268i \(-0.336054\pi\)
0.492579 + 0.870268i \(0.336054\pi\)
\(770\) 0 0
\(771\) 24.1471 0.869638
\(772\) 0 0
\(773\) −21.4675 −0.772131 −0.386066 0.922471i \(-0.626166\pi\)
−0.386066 + 0.922471i \(0.626166\pi\)
\(774\) 0 0
\(775\) 8.44094 0.303207
\(776\) 0 0
\(777\) −80.1497 −2.87535
\(778\) 0 0
\(779\) 20.0308 0.717678
\(780\) 0 0
\(781\) −19.6393 −0.702749
\(782\) 0 0
\(783\) 8.04253 0.287417
\(784\) 0 0
\(785\) 0.0591648 0.00211168
\(786\) 0 0
\(787\) 21.4097 0.763174 0.381587 0.924333i \(-0.375378\pi\)
0.381587 + 0.924333i \(0.375378\pi\)
\(788\) 0 0
\(789\) −53.6105 −1.90859
\(790\) 0 0
\(791\) 49.0027 1.74234
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) −3.62946 −0.128724
\(796\) 0 0
\(797\) 15.0647 0.533617 0.266809 0.963750i \(-0.414031\pi\)
0.266809 + 0.963750i \(0.414031\pi\)
\(798\) 0 0
\(799\) −41.9537 −1.48422
\(800\) 0 0
\(801\) 10.2999 0.363930
\(802\) 0 0
\(803\) 0.374691 0.0132226
\(804\) 0 0
\(805\) −11.9894 −0.422572
\(806\) 0 0
\(807\) −60.8520 −2.14209
\(808\) 0 0
\(809\) 26.7046 0.938885 0.469442 0.882963i \(-0.344455\pi\)
0.469442 + 0.882963i \(0.344455\pi\)
\(810\) 0 0
\(811\) −21.8145 −0.766011 −0.383005 0.923746i \(-0.625111\pi\)
−0.383005 + 0.923746i \(0.625111\pi\)
\(812\) 0 0
\(813\) −5.36814 −0.188269
\(814\) 0 0
\(815\) 15.9234 0.557771
\(816\) 0 0
\(817\) −73.3511 −2.56623
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 29.0913 1.01529 0.507646 0.861565i \(-0.330516\pi\)
0.507646 + 0.861565i \(0.330516\pi\)
\(822\) 0 0
\(823\) −20.4597 −0.713182 −0.356591 0.934261i \(-0.616061\pi\)
−0.356591 + 0.934261i \(0.616061\pi\)
\(824\) 0 0
\(825\) −6.37000 −0.221775
\(826\) 0 0
\(827\) −24.2164 −0.842086 −0.421043 0.907041i \(-0.638336\pi\)
−0.421043 + 0.907041i \(0.638336\pi\)
\(828\) 0 0
\(829\) −3.77286 −0.131037 −0.0655185 0.997851i \(-0.520870\pi\)
−0.0655185 + 0.997851i \(0.520870\pi\)
\(830\) 0 0
\(831\) −61.8834 −2.14671
\(832\) 0 0
\(833\) 70.3893 2.43885
\(834\) 0 0
\(835\) 22.1436 0.766312
\(836\) 0 0
\(837\) −7.87551 −0.272218
\(838\) 0 0
\(839\) 12.0985 0.417685 0.208843 0.977949i \(-0.433030\pi\)
0.208843 + 0.977949i \(0.433030\pi\)
\(840\) 0 0
\(841\) 45.3035 1.56219
\(842\) 0 0
\(843\) −24.3228 −0.837723
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −21.0524 −0.723370
\(848\) 0 0
\(849\) 59.5591 2.04406
\(850\) 0 0
\(851\) 18.4137 0.631212
\(852\) 0 0
\(853\) 45.2655 1.54986 0.774930 0.632047i \(-0.217785\pi\)
0.774930 + 0.632047i \(0.217785\pi\)
\(854\) 0 0
\(855\) −25.3663 −0.867510
\(856\) 0 0
\(857\) −11.4321 −0.390514 −0.195257 0.980752i \(-0.562554\pi\)
−0.195257 + 0.980752i \(0.562554\pi\)
\(858\) 0 0
\(859\) −48.9331 −1.66957 −0.834787 0.550573i \(-0.814409\pi\)
−0.834787 + 0.550573i \(0.814409\pi\)
\(860\) 0 0
\(861\) −30.5379 −1.04073
\(862\) 0 0
\(863\) −7.25636 −0.247009 −0.123505 0.992344i \(-0.539413\pi\)
−0.123505 + 0.992344i \(0.539413\pi\)
\(864\) 0 0
\(865\) −18.7289 −0.636802
\(866\) 0 0
\(867\) −23.9371 −0.812945
\(868\) 0 0
\(869\) 18.1430 0.615461
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 27.8914 0.943982
\(874\) 0 0
\(875\) −4.54727 −0.153726
\(876\) 0 0
\(877\) −12.2767 −0.414555 −0.207277 0.978282i \(-0.566460\pi\)
−0.207277 + 0.978282i \(0.566460\pi\)
\(878\) 0 0
\(879\) −13.5869 −0.458276
\(880\) 0 0
\(881\) −22.2767 −0.750520 −0.375260 0.926920i \(-0.622447\pi\)
−0.375260 + 0.926920i \(0.622447\pi\)
\(882\) 0 0
\(883\) 42.4148 1.42737 0.713686 0.700465i \(-0.247024\pi\)
0.713686 + 0.700465i \(0.247024\pi\)
\(884\) 0 0
\(885\) 0.210305 0.00706934
\(886\) 0 0
\(887\) −3.44309 −0.115608 −0.0578038 0.998328i \(-0.518410\pi\)
−0.0578038 + 0.998328i \(0.518410\pi\)
\(888\) 0 0
\(889\) 27.7169 0.929594
\(890\) 0 0
\(891\) −19.5714 −0.655667
\(892\) 0 0
\(893\) −61.3683 −2.05361
\(894\) 0 0
\(895\) −8.89212 −0.297231
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −72.7604 −2.42670
\(900\) 0 0
\(901\) −7.40080 −0.246556
\(902\) 0 0
\(903\) 111.827 3.72138
\(904\) 0 0
\(905\) 3.90674 0.129864
\(906\) 0 0
\(907\) −24.8493 −0.825108 −0.412554 0.910933i \(-0.635363\pi\)
−0.412554 + 0.910933i \(0.635363\pi\)
\(908\) 0 0
\(909\) 8.29357 0.275080
\(910\) 0 0
\(911\) 12.5928 0.417218 0.208609 0.977999i \(-0.433106\pi\)
0.208609 + 0.977999i \(0.433106\pi\)
\(912\) 0 0
\(913\) −42.7048 −1.41332
\(914\) 0 0
\(915\) −2.06623 −0.0683075
\(916\) 0 0
\(917\) 47.3117 1.56237
\(918\) 0 0
\(919\) 39.6595 1.30825 0.654124 0.756388i \(-0.273038\pi\)
0.654124 + 0.756388i \(0.273038\pi\)
\(920\) 0 0
\(921\) 30.7258 1.01245
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 6.98381 0.229626
\(926\) 0 0
\(927\) −36.0297 −1.18337
\(928\) 0 0
\(929\) 41.5553 1.36338 0.681692 0.731639i \(-0.261244\pi\)
0.681692 + 0.731639i \(0.261244\pi\)
\(930\) 0 0
\(931\) 102.963 3.37447
\(932\) 0 0
\(933\) 33.3404 1.09151
\(934\) 0 0
\(935\) −12.9890 −0.424786
\(936\) 0 0
\(937\) −5.57744 −0.182207 −0.0911035 0.995841i \(-0.529039\pi\)
−0.0911035 + 0.995841i \(0.529039\pi\)
\(938\) 0 0
\(939\) 60.9465 1.98891
\(940\) 0 0
\(941\) 19.7230 0.642951 0.321475 0.946918i \(-0.395821\pi\)
0.321475 + 0.946918i \(0.395821\pi\)
\(942\) 0 0
\(943\) 7.01581 0.228466
\(944\) 0 0
\(945\) 4.24267 0.138014
\(946\) 0 0
\(947\) −24.4631 −0.794943 −0.397471 0.917615i \(-0.630112\pi\)
−0.397471 + 0.917615i \(0.630112\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 16.2141 0.525779
\(952\) 0 0
\(953\) 55.5402 1.79912 0.899562 0.436794i \(-0.143886\pi\)
0.899562 + 0.436794i \(0.143886\pi\)
\(954\) 0 0
\(955\) −22.0068 −0.712125
\(956\) 0 0
\(957\) 54.9090 1.77496
\(958\) 0 0
\(959\) 22.2443 0.718306
\(960\) 0 0
\(961\) 40.2494 1.29837
\(962\) 0 0
\(963\) −2.96544 −0.0955600
\(964\) 0 0
\(965\) 6.46062 0.207975
\(966\) 0 0
\(967\) −18.1787 −0.584589 −0.292294 0.956328i \(-0.594419\pi\)
−0.292294 + 0.956328i \(0.594419\pi\)
\(968\) 0 0
\(969\) −97.7739 −3.14095
\(970\) 0 0
\(971\) −42.7938 −1.37332 −0.686660 0.726979i \(-0.740924\pi\)
−0.686660 + 0.726979i \(0.740924\pi\)
\(972\) 0 0
\(973\) −102.233 −3.27743
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 27.7715 0.888488 0.444244 0.895906i \(-0.353472\pi\)
0.444244 + 0.895906i \(0.353472\pi\)
\(978\) 0 0
\(979\) 7.71480 0.246566
\(980\) 0 0
\(981\) −5.19406 −0.165834
\(982\) 0 0
\(983\) 26.1593 0.834351 0.417176 0.908826i \(-0.363020\pi\)
0.417176 + 0.908826i \(0.363020\pi\)
\(984\) 0 0
\(985\) 19.2295 0.612701
\(986\) 0 0
\(987\) 93.5588 2.97801
\(988\) 0 0
\(989\) −25.6913 −0.816936
\(990\) 0 0
\(991\) 50.2217 1.59535 0.797673 0.603090i \(-0.206064\pi\)
0.797673 + 0.603090i \(0.206064\pi\)
\(992\) 0 0
\(993\) −55.0459 −1.74683
\(994\) 0 0
\(995\) −16.3145 −0.517205
\(996\) 0 0
\(997\) 44.5985 1.41245 0.706224 0.707989i \(-0.250397\pi\)
0.706224 + 0.707989i \(0.250397\pi\)
\(998\) 0 0
\(999\) −6.51599 −0.206157
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 3380.2.a.r.1.2 9
13.5 odd 4 3380.2.f.j.3041.4 18
13.8 odd 4 3380.2.f.j.3041.3 18
13.12 even 2 3380.2.a.s.1.2 yes 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3380.2.a.r.1.2 9 1.1 even 1 trivial
3380.2.a.s.1.2 yes 9 13.12 even 2
3380.2.f.j.3041.3 18 13.8 odd 4
3380.2.f.j.3041.4 18 13.5 odd 4