Properties

Label 9576.2.a.bv.1.2
Level $9576$
Weight $2$
Character 9576.1
Self dual yes
Analytic conductor $76.465$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 9576 = 2^{3} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9576.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(76.4647449756\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 9576.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.23607 q^{5} +1.00000 q^{7} +O(q^{10})\) \(q+3.23607 q^{5} +1.00000 q^{7} +2.00000 q^{11} +4.47214 q^{13} -3.23607 q^{17} -1.00000 q^{19} -2.00000 q^{23} +5.47214 q^{25} +7.70820 q^{29} -10.4721 q^{31} +3.23607 q^{35} -0.472136 q^{37} -0.472136 q^{41} +8.00000 q^{43} +11.7082 q^{47} +1.00000 q^{49} -6.76393 q^{53} +6.47214 q^{55} -8.94427 q^{59} +13.4164 q^{61} +14.4721 q^{65} -10.4721 q^{67} +5.70820 q^{71} +3.52786 q^{73} +2.00000 q^{77} +4.00000 q^{79} +0.291796 q^{83} -10.4721 q^{85} +4.47214 q^{89} +4.47214 q^{91} -3.23607 q^{95} +9.41641 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{5} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{5} + 2 q^{7} + 4 q^{11} - 2 q^{17} - 2 q^{19} - 4 q^{23} + 2 q^{25} + 2 q^{29} - 12 q^{31} + 2 q^{35} + 8 q^{37} + 8 q^{41} + 16 q^{43} + 10 q^{47} + 2 q^{49} - 18 q^{53} + 4 q^{55} + 20 q^{65} - 12 q^{67} - 2 q^{71} + 16 q^{73} + 4 q^{77} + 8 q^{79} + 14 q^{83} - 12 q^{85} - 2 q^{95} - 8 q^{97}+O(q^{100}) \) 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
\(3\) 0 0
\(4\) 0 0
\(5\) 3.23607 1.44721 0.723607 0.690212i \(-0.242483\pi\)
0.723607 + 0.690212i \(0.242483\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) 0 0
\(13\) 4.47214 1.24035 0.620174 0.784465i \(-0.287062\pi\)
0.620174 + 0.784465i \(0.287062\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −3.23607 −0.784862 −0.392431 0.919781i \(-0.628366\pi\)
−0.392431 + 0.919781i \(0.628366\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −2.00000 −0.417029 −0.208514 0.978019i \(-0.566863\pi\)
−0.208514 + 0.978019i \(0.566863\pi\)
\(24\) 0 0
\(25\) 5.47214 1.09443
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.70820 1.43138 0.715689 0.698419i \(-0.246113\pi\)
0.715689 + 0.698419i \(0.246113\pi\)
\(30\) 0 0
\(31\) −10.4721 −1.88085 −0.940426 0.340000i \(-0.889573\pi\)
−0.940426 + 0.340000i \(0.889573\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 3.23607 0.546995
\(36\) 0 0
\(37\) −0.472136 −0.0776187 −0.0388093 0.999247i \(-0.512356\pi\)
−0.0388093 + 0.999247i \(0.512356\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −0.472136 −0.0737352 −0.0368676 0.999320i \(-0.511738\pi\)
−0.0368676 + 0.999320i \(0.511738\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 11.7082 1.70782 0.853909 0.520423i \(-0.174226\pi\)
0.853909 + 0.520423i \(0.174226\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −6.76393 −0.929098 −0.464549 0.885548i \(-0.653783\pi\)
−0.464549 + 0.885548i \(0.653783\pi\)
\(54\) 0 0
\(55\) 6.47214 0.872703
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −8.94427 −1.16445 −0.582223 0.813029i \(-0.697817\pi\)
−0.582223 + 0.813029i \(0.697817\pi\)
\(60\) 0 0
\(61\) 13.4164 1.71780 0.858898 0.512148i \(-0.171150\pi\)
0.858898 + 0.512148i \(0.171150\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 14.4721 1.79505
\(66\) 0 0
\(67\) −10.4721 −1.27938 −0.639688 0.768635i \(-0.720936\pi\)
−0.639688 + 0.768635i \(0.720936\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 5.70820 0.677439 0.338720 0.940887i \(-0.390006\pi\)
0.338720 + 0.940887i \(0.390006\pi\)
\(72\) 0 0
\(73\) 3.52786 0.412905 0.206453 0.978457i \(-0.433808\pi\)
0.206453 + 0.978457i \(0.433808\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.00000 0.227921
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.291796 0.0320288 0.0160144 0.999872i \(-0.494902\pi\)
0.0160144 + 0.999872i \(0.494902\pi\)
\(84\) 0 0
\(85\) −10.4721 −1.13586
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 4.47214 0.474045 0.237023 0.971504i \(-0.423828\pi\)
0.237023 + 0.971504i \(0.423828\pi\)
\(90\) 0 0
\(91\) 4.47214 0.468807
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.23607 −0.332014
\(96\) 0 0
\(97\) 9.41641 0.956091 0.478046 0.878335i \(-0.341345\pi\)
0.478046 + 0.878335i \(0.341345\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 15.2361 1.51605 0.758023 0.652228i \(-0.226166\pi\)
0.758023 + 0.652228i \(0.226166\pi\)
\(102\) 0 0
\(103\) 4.00000 0.394132 0.197066 0.980390i \(-0.436859\pi\)
0.197066 + 0.980390i \(0.436859\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −4.18034 −0.404129 −0.202064 0.979372i \(-0.564765\pi\)
−0.202064 + 0.979372i \(0.564765\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.76393 0.260009 0.130004 0.991513i \(-0.458501\pi\)
0.130004 + 0.991513i \(0.458501\pi\)
\(114\) 0 0
\(115\) −6.47214 −0.603530
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −3.23607 −0.296650
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.52786 0.136656
\(126\) 0 0
\(127\) 11.4164 1.01304 0.506521 0.862228i \(-0.330931\pi\)
0.506521 + 0.862228i \(0.330931\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 10.7639 0.940449 0.470225 0.882547i \(-0.344173\pi\)
0.470225 + 0.882547i \(0.344173\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.00000 0.341743 0.170872 0.985293i \(-0.445342\pi\)
0.170872 + 0.985293i \(0.445342\pi\)
\(138\) 0 0
\(139\) 18.4721 1.56679 0.783393 0.621527i \(-0.213487\pi\)
0.783393 + 0.621527i \(0.213487\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 8.94427 0.747958
\(144\) 0 0
\(145\) 24.9443 2.07151
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −22.4721 −1.84099 −0.920495 0.390755i \(-0.872214\pi\)
−0.920495 + 0.390755i \(0.872214\pi\)
\(150\) 0 0
\(151\) 4.00000 0.325515 0.162758 0.986666i \(-0.447961\pi\)
0.162758 + 0.986666i \(0.447961\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −33.8885 −2.72199
\(156\) 0 0
\(157\) −12.4721 −0.995385 −0.497692 0.867354i \(-0.665819\pi\)
−0.497692 + 0.867354i \(0.665819\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −2.00000 −0.157622
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −3.41641 −0.264370 −0.132185 0.991225i \(-0.542199\pi\)
−0.132185 + 0.991225i \(0.542199\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 11.5279 0.876447 0.438224 0.898866i \(-0.355608\pi\)
0.438224 + 0.898866i \(0.355608\pi\)
\(174\) 0 0
\(175\) 5.47214 0.413655
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −5.70820 −0.426651 −0.213326 0.976981i \(-0.568430\pi\)
−0.213326 + 0.976981i \(0.568430\pi\)
\(180\) 0 0
\(181\) −12.4721 −0.927047 −0.463523 0.886085i \(-0.653415\pi\)
−0.463523 + 0.886085i \(0.653415\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.52786 −0.112331
\(186\) 0 0
\(187\) −6.47214 −0.473289
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 10.0000 0.723575 0.361787 0.932261i \(-0.382167\pi\)
0.361787 + 0.932261i \(0.382167\pi\)
\(192\) 0 0
\(193\) 0.472136 0.0339851 0.0169925 0.999856i \(-0.494591\pi\)
0.0169925 + 0.999856i \(0.494591\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) −3.05573 −0.216615 −0.108307 0.994117i \(-0.534543\pi\)
−0.108307 + 0.994117i \(0.534543\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 7.70820 0.541010
\(204\) 0 0
\(205\) −1.52786 −0.106711
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) 2.47214 0.170189 0.0850944 0.996373i \(-0.472881\pi\)
0.0850944 + 0.996373i \(0.472881\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 25.8885 1.76558
\(216\) 0 0
\(217\) −10.4721 −0.710895
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −14.4721 −0.973501
\(222\) 0 0
\(223\) −22.4721 −1.50485 −0.752423 0.658680i \(-0.771115\pi\)
−0.752423 + 0.658680i \(0.771115\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.4721 −0.960549 −0.480275 0.877118i \(-0.659463\pi\)
−0.480275 + 0.877118i \(0.659463\pi\)
\(228\) 0 0
\(229\) −2.94427 −0.194563 −0.0972815 0.995257i \(-0.531015\pi\)
−0.0972815 + 0.995257i \(0.531015\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 19.4164 1.27201 0.636006 0.771684i \(-0.280586\pi\)
0.636006 + 0.771684i \(0.280586\pi\)
\(234\) 0 0
\(235\) 37.8885 2.47158
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 13.4164 0.867835 0.433918 0.900953i \(-0.357131\pi\)
0.433918 + 0.900953i \(0.357131\pi\)
\(240\) 0 0
\(241\) −5.41641 −0.348902 −0.174451 0.984666i \(-0.555815\pi\)
−0.174451 + 0.984666i \(0.555815\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.23607 0.206745
\(246\) 0 0
\(247\) −4.47214 −0.284555
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −17.2361 −1.08793 −0.543965 0.839108i \(-0.683078\pi\)
−0.543965 + 0.839108i \(0.683078\pi\)
\(252\) 0 0
\(253\) −4.00000 −0.251478
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 14.9443 0.932198 0.466099 0.884733i \(-0.345659\pi\)
0.466099 + 0.884733i \(0.345659\pi\)
\(258\) 0 0
\(259\) −0.472136 −0.0293371
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 11.5279 0.710839 0.355419 0.934707i \(-0.384338\pi\)
0.355419 + 0.934707i \(0.384338\pi\)
\(264\) 0 0
\(265\) −21.8885 −1.34460
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.00000 0.121942 0.0609711 0.998140i \(-0.480580\pi\)
0.0609711 + 0.998140i \(0.480580\pi\)
\(270\) 0 0
\(271\) −19.4164 −1.17946 −0.589731 0.807599i \(-0.700766\pi\)
−0.589731 + 0.807599i \(0.700766\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 10.9443 0.659964
\(276\) 0 0
\(277\) −5.41641 −0.325440 −0.162720 0.986672i \(-0.552027\pi\)
−0.162720 + 0.986672i \(0.552027\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 6.76393 0.403502 0.201751 0.979437i \(-0.435337\pi\)
0.201751 + 0.979437i \(0.435337\pi\)
\(282\) 0 0
\(283\) −16.9443 −1.00723 −0.503616 0.863927i \(-0.667997\pi\)
−0.503616 + 0.863927i \(0.667997\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.472136 −0.0278693
\(288\) 0 0
\(289\) −6.52786 −0.383992
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 16.4721 0.962312 0.481156 0.876635i \(-0.340217\pi\)
0.481156 + 0.876635i \(0.340217\pi\)
\(294\) 0 0
\(295\) −28.9443 −1.68520
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −8.94427 −0.517261
\(300\) 0 0
\(301\) 8.00000 0.461112
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 43.4164 2.48602
\(306\) 0 0
\(307\) −26.4721 −1.51084 −0.755422 0.655238i \(-0.772568\pi\)
−0.755422 + 0.655238i \(0.772568\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 32.6525 1.85155 0.925776 0.378072i \(-0.123413\pi\)
0.925776 + 0.378072i \(0.123413\pi\)
\(312\) 0 0
\(313\) −21.4164 −1.21053 −0.605263 0.796025i \(-0.706932\pi\)
−0.605263 + 0.796025i \(0.706932\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 16.6525 0.935296 0.467648 0.883915i \(-0.345101\pi\)
0.467648 + 0.883915i \(0.345101\pi\)
\(318\) 0 0
\(319\) 15.4164 0.863153
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.23607 0.180060
\(324\) 0 0
\(325\) 24.4721 1.35747
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 11.7082 0.645494
\(330\) 0 0
\(331\) −28.9443 −1.59092 −0.795461 0.606005i \(-0.792771\pi\)
−0.795461 + 0.606005i \(0.792771\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −33.8885 −1.85153
\(336\) 0 0
\(337\) 10.9443 0.596172 0.298086 0.954539i \(-0.403652\pi\)
0.298086 + 0.954539i \(0.403652\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −20.9443 −1.13420
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −14.3607 −0.770922 −0.385461 0.922724i \(-0.625958\pi\)
−0.385461 + 0.922724i \(0.625958\pi\)
\(348\) 0 0
\(349\) 17.0557 0.912972 0.456486 0.889731i \(-0.349108\pi\)
0.456486 + 0.889731i \(0.349108\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7.81966 0.416199 0.208099 0.978108i \(-0.433272\pi\)
0.208099 + 0.978108i \(0.433272\pi\)
\(354\) 0 0
\(355\) 18.4721 0.980399
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −2.94427 −0.155393 −0.0776964 0.996977i \(-0.524756\pi\)
−0.0776964 + 0.996977i \(0.524756\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 11.4164 0.597562
\(366\) 0 0
\(367\) 3.05573 0.159508 0.0797539 0.996815i \(-0.474587\pi\)
0.0797539 + 0.996815i \(0.474587\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −6.76393 −0.351166
\(372\) 0 0
\(373\) −3.88854 −0.201341 −0.100671 0.994920i \(-0.532099\pi\)
−0.100671 + 0.994920i \(0.532099\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 34.4721 1.77541
\(378\) 0 0
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 10.4721 0.535101 0.267551 0.963544i \(-0.413786\pi\)
0.267551 + 0.963544i \(0.413786\pi\)
\(384\) 0 0
\(385\) 6.47214 0.329851
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −20.3607 −1.03233 −0.516164 0.856490i \(-0.672640\pi\)
−0.516164 + 0.856490i \(0.672640\pi\)
\(390\) 0 0
\(391\) 6.47214 0.327310
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 12.9443 0.651297
\(396\) 0 0
\(397\) 15.8885 0.797423 0.398712 0.917076i \(-0.369457\pi\)
0.398712 + 0.917076i \(0.369457\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9.23607 0.461227 0.230614 0.973045i \(-0.425927\pi\)
0.230614 + 0.973045i \(0.425927\pi\)
\(402\) 0 0
\(403\) −46.8328 −2.33291
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −0.944272 −0.0468058
\(408\) 0 0
\(409\) −27.3050 −1.35014 −0.675071 0.737752i \(-0.735887\pi\)
−0.675071 + 0.737752i \(0.735887\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −8.94427 −0.440119
\(414\) 0 0
\(415\) 0.944272 0.0463525
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −21.5967 −1.05507 −0.527535 0.849533i \(-0.676884\pi\)
−0.527535 + 0.849533i \(0.676884\pi\)
\(420\) 0 0
\(421\) 24.4721 1.19270 0.596349 0.802725i \(-0.296617\pi\)
0.596349 + 0.802725i \(0.296617\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −17.7082 −0.858974
\(426\) 0 0
\(427\) 13.4164 0.649265
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.65248 0.127765 0.0638826 0.997957i \(-0.479652\pi\)
0.0638826 + 0.997957i \(0.479652\pi\)
\(432\) 0 0
\(433\) 37.4164 1.79812 0.899059 0.437828i \(-0.144252\pi\)
0.899059 + 0.437828i \(0.144252\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.00000 0.0956730
\(438\) 0 0
\(439\) −32.3607 −1.54449 −0.772245 0.635324i \(-0.780866\pi\)
−0.772245 + 0.635324i \(0.780866\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 13.4164 0.637433 0.318716 0.947850i \(-0.396748\pi\)
0.318716 + 0.947850i \(0.396748\pi\)
\(444\) 0 0
\(445\) 14.4721 0.686045
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −18.7639 −0.885525 −0.442762 0.896639i \(-0.646001\pi\)
−0.442762 + 0.896639i \(0.646001\pi\)
\(450\) 0 0
\(451\) −0.944272 −0.0444640
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 14.4721 0.678464
\(456\) 0 0
\(457\) −5.41641 −0.253369 −0.126684 0.991943i \(-0.540434\pi\)
−0.126684 + 0.991943i \(0.540434\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 30.0689 1.40045 0.700224 0.713923i \(-0.253084\pi\)
0.700224 + 0.713923i \(0.253084\pi\)
\(462\) 0 0
\(463\) −6.11146 −0.284023 −0.142012 0.989865i \(-0.545357\pi\)
−0.142012 + 0.989865i \(0.545357\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −25.2361 −1.16779 −0.583893 0.811831i \(-0.698471\pi\)
−0.583893 + 0.811831i \(0.698471\pi\)
\(468\) 0 0
\(469\) −10.4721 −0.483558
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 16.0000 0.735681
\(474\) 0 0
\(475\) −5.47214 −0.251079
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 12.2918 0.561626 0.280813 0.959762i \(-0.409396\pi\)
0.280813 + 0.959762i \(0.409396\pi\)
\(480\) 0 0
\(481\) −2.11146 −0.0962741
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 30.4721 1.38367
\(486\) 0 0
\(487\) −12.5836 −0.570217 −0.285108 0.958495i \(-0.592030\pi\)
−0.285108 + 0.958495i \(0.592030\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 31.3050 1.41277 0.706386 0.707826i \(-0.250324\pi\)
0.706386 + 0.707826i \(0.250324\pi\)
\(492\) 0 0
\(493\) −24.9443 −1.12343
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 5.70820 0.256048
\(498\) 0 0
\(499\) −29.8885 −1.33799 −0.668997 0.743265i \(-0.733276\pi\)
−0.668997 + 0.743265i \(0.733276\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 15.7082 0.700394 0.350197 0.936676i \(-0.386115\pi\)
0.350197 + 0.936676i \(0.386115\pi\)
\(504\) 0 0
\(505\) 49.3050 2.19404
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −7.88854 −0.349654 −0.174827 0.984599i \(-0.555937\pi\)
−0.174827 + 0.984599i \(0.555937\pi\)
\(510\) 0 0
\(511\) 3.52786 0.156064
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 12.9443 0.570393
\(516\) 0 0
\(517\) 23.4164 1.02985
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −43.8885 −1.92279 −0.961396 0.275169i \(-0.911266\pi\)
−0.961396 + 0.275169i \(0.911266\pi\)
\(522\) 0 0
\(523\) −21.3050 −0.931600 −0.465800 0.884890i \(-0.654233\pi\)
−0.465800 + 0.884890i \(0.654233\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 33.8885 1.47621
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.11146 −0.0914573
\(534\) 0 0
\(535\) −13.5279 −0.584861
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.00000 0.0861461
\(540\) 0 0
\(541\) 22.0000 0.945854 0.472927 0.881102i \(-0.343197\pi\)
0.472927 + 0.881102i \(0.343197\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 32.3607 1.38618
\(546\) 0 0
\(547\) 32.0000 1.36822 0.684111 0.729378i \(-0.260191\pi\)
0.684111 + 0.729378i \(0.260191\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −7.70820 −0.328381
\(552\) 0 0
\(553\) 4.00000 0.170097
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 29.3050 1.24169 0.620845 0.783933i \(-0.286789\pi\)
0.620845 + 0.783933i \(0.286789\pi\)
\(558\) 0 0
\(559\) 35.7771 1.51321
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −9.52786 −0.401552 −0.200776 0.979637i \(-0.564346\pi\)
−0.200776 + 0.979637i \(0.564346\pi\)
\(564\) 0 0
\(565\) 8.94427 0.376288
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 4.87539 0.204387 0.102193 0.994765i \(-0.467414\pi\)
0.102193 + 0.994765i \(0.467414\pi\)
\(570\) 0 0
\(571\) 21.8885 0.916007 0.458004 0.888950i \(-0.348565\pi\)
0.458004 + 0.888950i \(0.348565\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −10.9443 −0.456408
\(576\) 0 0
\(577\) −32.4721 −1.35183 −0.675916 0.736978i \(-0.736252\pi\)
−0.675916 + 0.736978i \(0.736252\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0.291796 0.0121057
\(582\) 0 0
\(583\) −13.5279 −0.560267
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.87539 0.201229 0.100614 0.994925i \(-0.467919\pi\)
0.100614 + 0.994925i \(0.467919\pi\)
\(588\) 0 0
\(589\) 10.4721 0.431497
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −20.5410 −0.843519 −0.421759 0.906708i \(-0.638587\pi\)
−0.421759 + 0.906708i \(0.638587\pi\)
\(594\) 0 0
\(595\) −10.4721 −0.429316
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −11.5967 −0.473830 −0.236915 0.971530i \(-0.576136\pi\)
−0.236915 + 0.971530i \(0.576136\pi\)
\(600\) 0 0
\(601\) −35.3050 −1.44012 −0.720060 0.693912i \(-0.755886\pi\)
−0.720060 + 0.693912i \(0.755886\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −22.6525 −0.920954
\(606\) 0 0
\(607\) −28.9443 −1.17481 −0.587406 0.809292i \(-0.699851\pi\)
−0.587406 + 0.809292i \(0.699851\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 52.3607 2.11829
\(612\) 0 0
\(613\) −2.36068 −0.0953470 −0.0476735 0.998863i \(-0.515181\pi\)
−0.0476735 + 0.998863i \(0.515181\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −29.8885 −1.20327 −0.601634 0.798772i \(-0.705483\pi\)
−0.601634 + 0.798772i \(0.705483\pi\)
\(618\) 0 0
\(619\) 8.58359 0.345004 0.172502 0.985009i \(-0.444815\pi\)
0.172502 + 0.985009i \(0.444815\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 4.47214 0.179172
\(624\) 0 0
\(625\) −22.4164 −0.896656
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.52786 0.0609199
\(630\) 0 0
\(631\) −8.94427 −0.356066 −0.178033 0.984025i \(-0.556973\pi\)
−0.178033 + 0.984025i \(0.556973\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 36.9443 1.46609
\(636\) 0 0
\(637\) 4.47214 0.177192
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −22.7639 −0.899121 −0.449561 0.893250i \(-0.648419\pi\)
−0.449561 + 0.893250i \(0.648419\pi\)
\(642\) 0 0
\(643\) −32.9443 −1.29920 −0.649598 0.760278i \(-0.725063\pi\)
−0.649598 + 0.760278i \(0.725063\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −4.29180 −0.168728 −0.0843640 0.996435i \(-0.526886\pi\)
−0.0843640 + 0.996435i \(0.526886\pi\)
\(648\) 0 0
\(649\) −17.8885 −0.702187
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −40.7214 −1.59355 −0.796775 0.604276i \(-0.793462\pi\)
−0.796775 + 0.604276i \(0.793462\pi\)
\(654\) 0 0
\(655\) 34.8328 1.36103
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 35.2361 1.37260 0.686301 0.727317i \(-0.259233\pi\)
0.686301 + 0.727317i \(0.259233\pi\)
\(660\) 0 0
\(661\) 44.2492 1.72110 0.860548 0.509370i \(-0.170121\pi\)
0.860548 + 0.509370i \(0.170121\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −3.23607 −0.125489
\(666\) 0 0
\(667\) −15.4164 −0.596926
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 26.8328 1.03587
\(672\) 0 0
\(673\) 26.3607 1.01613 0.508065 0.861319i \(-0.330361\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30.0000 1.15299 0.576497 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) 0 0
\(679\) 9.41641 0.361369
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 23.2361 0.889103 0.444552 0.895753i \(-0.353363\pi\)
0.444552 + 0.895753i \(0.353363\pi\)
\(684\) 0 0
\(685\) 12.9443 0.494575
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −30.2492 −1.15240
\(690\) 0 0
\(691\) 20.3607 0.774557 0.387278 0.921963i \(-0.373415\pi\)
0.387278 + 0.921963i \(0.373415\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 59.7771 2.26747
\(696\) 0 0
\(697\) 1.52786 0.0578720
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −43.7771 −1.65344 −0.826719 0.562615i \(-0.809795\pi\)
−0.826719 + 0.562615i \(0.809795\pi\)
\(702\) 0 0
\(703\) 0.472136 0.0178069
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 15.2361 0.573011
\(708\) 0 0
\(709\) −27.3050 −1.02546 −0.512729 0.858550i \(-0.671366\pi\)
−0.512729 + 0.858550i \(0.671366\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 20.9443 0.784369
\(714\) 0 0
\(715\) 28.9443 1.08245
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 37.2361 1.38867 0.694336 0.719651i \(-0.255698\pi\)
0.694336 + 0.719651i \(0.255698\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 42.1803 1.56654
\(726\) 0 0
\(727\) −3.41641 −0.126708 −0.0633538 0.997991i \(-0.520180\pi\)
−0.0633538 + 0.997991i \(0.520180\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −25.8885 −0.957522
\(732\) 0 0
\(733\) 10.5836 0.390914 0.195457 0.980712i \(-0.437381\pi\)
0.195457 + 0.980712i \(0.437381\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −20.9443 −0.771492
\(738\) 0 0
\(739\) 24.0000 0.882854 0.441427 0.897297i \(-0.354472\pi\)
0.441427 + 0.897297i \(0.354472\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.403252 −0.0147939 −0.00739695 0.999973i \(-0.502355\pi\)
−0.00739695 + 0.999973i \(0.502355\pi\)
\(744\) 0 0
\(745\) −72.7214 −2.66430
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −4.18034 −0.152746
\(750\) 0 0
\(751\) −15.0557 −0.549391 −0.274696 0.961531i \(-0.588577\pi\)
−0.274696 + 0.961531i \(0.588577\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 12.9443 0.471090
\(756\) 0 0
\(757\) 19.8885 0.722861 0.361431 0.932399i \(-0.382288\pi\)
0.361431 + 0.932399i \(0.382288\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −20.7639 −0.752692 −0.376346 0.926479i \(-0.622820\pi\)
−0.376346 + 0.926479i \(0.622820\pi\)
\(762\) 0 0
\(763\) 10.0000 0.362024
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −40.0000 −1.44432
\(768\) 0 0
\(769\) 28.4721 1.02673 0.513366 0.858170i \(-0.328398\pi\)
0.513366 + 0.858170i \(0.328398\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 36.2492 1.30379 0.651897 0.758308i \(-0.273973\pi\)
0.651897 + 0.758308i \(0.273973\pi\)
\(774\) 0 0
\(775\) −57.3050 −2.05845
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0.472136 0.0169160
\(780\) 0 0
\(781\) 11.4164 0.408511
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −40.3607 −1.44053
\(786\) 0 0
\(787\) −30.4721 −1.08621 −0.543107 0.839663i \(-0.682752\pi\)
−0.543107 + 0.839663i \(0.682752\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 2.76393 0.0982741
\(792\) 0 0
\(793\) 60.0000 2.13066
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 5.41641 0.191859 0.0959295 0.995388i \(-0.469418\pi\)
0.0959295 + 0.995388i \(0.469418\pi\)
\(798\) 0 0
\(799\) −37.8885 −1.34040
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 7.05573 0.248991
\(804\) 0 0
\(805\) −6.47214 −0.228113
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −33.8885 −1.19146 −0.595729 0.803186i \(-0.703137\pi\)
−0.595729 + 0.803186i \(0.703137\pi\)
\(810\) 0 0
\(811\) −20.9443 −0.735453 −0.367726 0.929934i \(-0.619864\pi\)
−0.367726 + 0.929934i \(0.619864\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −51.7771 −1.81367
\(816\) 0 0
\(817\) −8.00000 −0.279885
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −50.2492 −1.75371 −0.876855 0.480755i \(-0.840363\pi\)
−0.876855 + 0.480755i \(0.840363\pi\)
\(822\) 0 0
\(823\) 10.8328 0.377608 0.188804 0.982015i \(-0.439539\pi\)
0.188804 + 0.982015i \(0.439539\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −31.2361 −1.08618 −0.543092 0.839673i \(-0.682747\pi\)
−0.543092 + 0.839673i \(0.682747\pi\)
\(828\) 0 0
\(829\) −25.4164 −0.882748 −0.441374 0.897323i \(-0.645509\pi\)
−0.441374 + 0.897323i \(0.645509\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −3.23607 −0.112123
\(834\) 0 0
\(835\) −11.0557 −0.382599
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −8.94427 −0.308791 −0.154395 0.988009i \(-0.549343\pi\)
−0.154395 + 0.988009i \(0.549343\pi\)
\(840\) 0 0
\(841\) 30.4164 1.04884
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 22.6525 0.779269
\(846\) 0 0
\(847\) −7.00000 −0.240523
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0.944272 0.0323692
\(852\) 0 0
\(853\) 41.7771 1.43042 0.715210 0.698909i \(-0.246331\pi\)
0.715210 + 0.698909i \(0.246331\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 48.2492 1.64816 0.824081 0.566472i \(-0.191692\pi\)
0.824081 + 0.566472i \(0.191692\pi\)
\(858\) 0 0
\(859\) −24.9443 −0.851088 −0.425544 0.904938i \(-0.639917\pi\)
−0.425544 + 0.904938i \(0.639917\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −6.87539 −0.234041 −0.117020 0.993130i \(-0.537334\pi\)
−0.117020 + 0.993130i \(0.537334\pi\)
\(864\) 0 0
\(865\) 37.3050 1.26841
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 8.00000 0.271381
\(870\) 0 0
\(871\) −46.8328 −1.58687
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 1.52786 0.0516512
\(876\) 0 0
\(877\) −24.8328 −0.838545 −0.419272 0.907861i \(-0.637715\pi\)
−0.419272 + 0.907861i \(0.637715\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 23.8197 0.802505 0.401252 0.915968i \(-0.368575\pi\)
0.401252 + 0.915968i \(0.368575\pi\)
\(882\) 0 0
\(883\) −29.8885 −1.00583 −0.502915 0.864336i \(-0.667739\pi\)
−0.502915 + 0.864336i \(0.667739\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 51.4164 1.72639 0.863197 0.504867i \(-0.168459\pi\)
0.863197 + 0.504867i \(0.168459\pi\)
\(888\) 0 0
\(889\) 11.4164 0.382894
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −11.7082 −0.391800
\(894\) 0 0
\(895\) −18.4721 −0.617455
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −80.7214 −2.69221
\(900\) 0 0
\(901\) 21.8885 0.729213
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −40.3607 −1.34163
\(906\) 0 0
\(907\) −34.4721 −1.14463 −0.572314 0.820034i \(-0.693954\pi\)
−0.572314 + 0.820034i \(0.693954\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −40.5410 −1.34318 −0.671592 0.740921i \(-0.734389\pi\)
−0.671592 + 0.740921i \(0.734389\pi\)
\(912\) 0 0
\(913\) 0.583592 0.0193141
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 10.7639 0.355456
\(918\) 0 0
\(919\) 35.7771 1.18018 0.590089 0.807338i \(-0.299093\pi\)
0.590089 + 0.807338i \(0.299093\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 25.5279 0.840260
\(924\) 0 0
\(925\) −2.58359 −0.0849480
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 55.5967 1.82407 0.912035 0.410112i \(-0.134510\pi\)
0.912035 + 0.410112i \(0.134510\pi\)
\(930\) 0 0
\(931\) −1.00000 −0.0327737
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −20.9443 −0.684951
\(936\) 0 0
\(937\) 51.8885 1.69512 0.847562 0.530696i \(-0.178069\pi\)
0.847562 + 0.530696i \(0.178069\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 40.8328 1.33111 0.665556 0.746348i \(-0.268195\pi\)
0.665556 + 0.746348i \(0.268195\pi\)
\(942\) 0 0
\(943\) 0.944272 0.0307497
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 26.0000 0.844886 0.422443 0.906389i \(-0.361173\pi\)
0.422443 + 0.906389i \(0.361173\pi\)
\(948\) 0 0
\(949\) 15.7771 0.512146
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −44.6525 −1.44644 −0.723218 0.690620i \(-0.757338\pi\)
−0.723218 + 0.690620i \(0.757338\pi\)
\(954\) 0 0
\(955\) 32.3607 1.04717
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 4.00000 0.129167
\(960\) 0 0
\(961\) 78.6656 2.53760
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 1.52786 0.0491837
\(966\) 0 0
\(967\) −34.8328 −1.12015 −0.560074 0.828443i \(-0.689227\pi\)
−0.560074 + 0.828443i \(0.689227\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −6.83282 −0.219275 −0.109638 0.993972i \(-0.534969\pi\)
−0.109638 + 0.993972i \(0.534969\pi\)
\(972\) 0 0
\(973\) 18.4721 0.592189
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 8.06888 0.258146 0.129073 0.991635i \(-0.458800\pi\)
0.129073 + 0.991635i \(0.458800\pi\)
\(978\) 0 0
\(979\) 8.94427 0.285860
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 40.7214 1.29881 0.649405 0.760443i \(-0.275018\pi\)
0.649405 + 0.760443i \(0.275018\pi\)
\(984\) 0 0
\(985\) 38.8328 1.23732
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −16.0000 −0.508770
\(990\) 0 0
\(991\) 7.63932 0.242671 0.121336 0.992612i \(-0.461282\pi\)
0.121336 + 0.992612i \(0.461282\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −9.88854 −0.313488
\(996\) 0 0
\(997\) −7.52786 −0.238410 −0.119205 0.992870i \(-0.538035\pi\)
−0.119205 + 0.992870i \(0.538035\pi\)
\(998\) 0 0
\(999\) 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 9576.2.a.bv.1.2 yes 2
3.2 odd 2 9576.2.a.bi.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9576.2.a.bi.1.1 2 3.2 odd 2
9576.2.a.bv.1.2 yes 2 1.1 even 1 trivial