Properties

Label 7600.2.a.bm.1.3
Level $7600$
Weight $2$
Character 7600.1
Self dual yes
Analytic conductor $60.686$
Analytic rank $1$
Dimension $3$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(60.6863055362\)
Analytic rank: \(1\)
Dimension: \(3\)
Coefficient field: 3.3.257.1
Defining polynomial: \(x^{3} - x^{2} - 4 x + 3\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 950)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(2.19869\) of defining polynomial
Character \(\chi\) \(=\) 7600.1

$q$-expansion

\(f(q)\) \(=\) \(q+3.03293 q^{3} -2.46980 q^{7} +6.19869 q^{9} +O(q^{10})\) \(q+3.03293 q^{3} -2.46980 q^{7} +6.19869 q^{9} -0.728896 q^{11} -6.23163 q^{13} +0.563139 q^{17} +1.00000 q^{19} -7.49073 q^{21} -4.63555 q^{23} +9.70142 q^{27} +10.2316 q^{29} -6.06587 q^{31} -2.21069 q^{33} -5.72890 q^{37} -18.9001 q^{39} +4.79476 q^{41} -8.06587 q^{43} -8.12628 q^{47} -0.900112 q^{49} +1.70796 q^{51} -1.53020 q^{53} +3.03293 q^{57} +5.76183 q^{59} +10.9396 q^{61} -15.3095 q^{63} -12.9330 q^{67} -14.0593 q^{69} +4.39738 q^{71} -4.09334 q^{73} +1.80022 q^{77} -15.3370 q^{79} +10.8277 q^{81} -7.85517 q^{83} +31.0318 q^{87} -10.0000 q^{89} +15.3908 q^{91} -18.3974 q^{93} +11.0055 q^{97} -4.51820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3q - 2q^{3} - 2q^{7} + 13q^{9} + O(q^{10}) \) \( 3q - 2q^{3} - 2q^{7} + 13q^{9} - 2q^{11} - 2q^{13} - 4q^{17} + 3q^{19} - 11q^{21} - 14q^{23} + 7q^{27} + 14q^{29} + 4q^{31} + 4q^{33} - 17q^{37} - 29q^{39} - 8q^{41} - 2q^{43} - 13q^{47} + 25q^{49} + 11q^{51} - 10q^{53} - 2q^{57} + 6q^{59} + 22q^{61} - 2q^{63} + 8q^{69} + 2q^{71} - 12q^{73} - 50q^{77} - 24q^{79} - q^{81} - 12q^{83} + 21q^{87} - 30q^{89} + 7q^{91} - 44q^{93} - 24q^{99} + O(q^{100}) \)

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
\(3\) 3.03293 1.75107 0.875533 0.483159i \(-0.160511\pi\)
0.875533 + 0.483159i \(0.160511\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.46980 −0.933495 −0.466747 0.884391i \(-0.654574\pi\)
−0.466747 + 0.884391i \(0.654574\pi\)
\(8\) 0 0
\(9\) 6.19869 2.06623
\(10\) 0 0
\(11\) −0.728896 −0.219770 −0.109885 0.993944i \(-0.535048\pi\)
−0.109885 + 0.993944i \(0.535048\pi\)
\(12\) 0 0
\(13\) −6.23163 −1.72834 −0.864171 0.503198i \(-0.832157\pi\)
−0.864171 + 0.503198i \(0.832157\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0.563139 0.136581 0.0682907 0.997665i \(-0.478245\pi\)
0.0682907 + 0.997665i \(0.478245\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −7.49073 −1.63461
\(22\) 0 0
\(23\) −4.63555 −0.966579 −0.483290 0.875460i \(-0.660558\pi\)
−0.483290 + 0.875460i \(0.660558\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 9.70142 1.86704
\(28\) 0 0
\(29\) 10.2316 1.89997 0.949983 0.312303i \(-0.101100\pi\)
0.949983 + 0.312303i \(0.101100\pi\)
\(30\) 0 0
\(31\) −6.06587 −1.08946 −0.544731 0.838611i \(-0.683368\pi\)
−0.544731 + 0.838611i \(0.683368\pi\)
\(32\) 0 0
\(33\) −2.21069 −0.384832
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −5.72890 −0.941825 −0.470912 0.882180i \(-0.656075\pi\)
−0.470912 + 0.882180i \(0.656075\pi\)
\(38\) 0 0
\(39\) −18.9001 −3.02644
\(40\) 0 0
\(41\) 4.79476 0.748816 0.374408 0.927264i \(-0.377846\pi\)
0.374408 + 0.927264i \(0.377846\pi\)
\(42\) 0 0
\(43\) −8.06587 −1.23003 −0.615017 0.788514i \(-0.710851\pi\)
−0.615017 + 0.788514i \(0.710851\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −8.12628 −1.18534 −0.592670 0.805446i \(-0.701926\pi\)
−0.592670 + 0.805446i \(0.701926\pi\)
\(48\) 0 0
\(49\) −0.900112 −0.128587
\(50\) 0 0
\(51\) 1.70796 0.239163
\(52\) 0 0
\(53\) −1.53020 −0.210190 −0.105095 0.994462i \(-0.533515\pi\)
−0.105095 + 0.994462i \(0.533515\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.03293 0.401722
\(58\) 0 0
\(59\) 5.76183 0.750126 0.375063 0.926999i \(-0.377621\pi\)
0.375063 + 0.926999i \(0.377621\pi\)
\(60\) 0 0
\(61\) 10.9396 1.40067 0.700336 0.713814i \(-0.253034\pi\)
0.700336 + 0.713814i \(0.253034\pi\)
\(62\) 0 0
\(63\) −15.3095 −1.92882
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −12.9330 −1.58002 −0.790012 0.613092i \(-0.789926\pi\)
−0.790012 + 0.613092i \(0.789926\pi\)
\(68\) 0 0
\(69\) −14.0593 −1.69254
\(70\) 0 0
\(71\) 4.39738 0.521873 0.260937 0.965356i \(-0.415969\pi\)
0.260937 + 0.965356i \(0.415969\pi\)
\(72\) 0 0
\(73\) −4.09334 −0.479090 −0.239545 0.970885i \(-0.576998\pi\)
−0.239545 + 0.970885i \(0.576998\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.80022 0.205155
\(78\) 0 0
\(79\) −15.3370 −1.72554 −0.862772 0.505593i \(-0.831274\pi\)
−0.862772 + 0.505593i \(0.831274\pi\)
\(80\) 0 0
\(81\) 10.8277 1.20308
\(82\) 0 0
\(83\) −7.85517 −0.862217 −0.431109 0.902300i \(-0.641877\pi\)
−0.431109 + 0.902300i \(0.641877\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 31.0318 3.32696
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 15.3908 1.61340
\(92\) 0 0
\(93\) −18.3974 −1.90772
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 11.0055 1.11744 0.558718 0.829358i \(-0.311294\pi\)
0.558718 + 0.829358i \(0.311294\pi\)
\(98\) 0 0
\(99\) −4.51820 −0.454096
\(100\) 0 0
\(101\) −9.73436 −0.968605 −0.484302 0.874901i \(-0.660926\pi\)
−0.484302 + 0.874901i \(0.660926\pi\)
\(102\) 0 0
\(103\) 8.33151 0.820928 0.410464 0.911877i \(-0.365367\pi\)
0.410464 + 0.911877i \(0.365367\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 15.0264 1.45266 0.726328 0.687348i \(-0.241225\pi\)
0.726328 + 0.687348i \(0.241225\pi\)
\(108\) 0 0
\(109\) −13.6619 −1.30858 −0.654288 0.756245i \(-0.727032\pi\)
−0.654288 + 0.756245i \(0.727032\pi\)
\(110\) 0 0
\(111\) −17.3754 −1.64920
\(112\) 0 0
\(113\) 1.20524 0.113379 0.0566895 0.998392i \(-0.481945\pi\)
0.0566895 + 0.998392i \(0.481945\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −38.6279 −3.57115
\(118\) 0 0
\(119\) −1.39084 −0.127498
\(120\) 0 0
\(121\) −10.4687 −0.951701
\(122\) 0 0
\(123\) 14.5422 1.31123
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −9.52366 −0.845088 −0.422544 0.906342i \(-0.638863\pi\)
−0.422544 + 0.906342i \(0.638863\pi\)
\(128\) 0 0
\(129\) −24.4633 −2.15387
\(130\) 0 0
\(131\) 17.4028 1.52049 0.760247 0.649635i \(-0.225078\pi\)
0.760247 + 0.649635i \(0.225078\pi\)
\(132\) 0 0
\(133\) −2.46980 −0.214158
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.25910 0.193008 0.0965040 0.995333i \(-0.469234\pi\)
0.0965040 + 0.995333i \(0.469234\pi\)
\(138\) 0 0
\(139\) −16.8606 −1.43010 −0.715050 0.699073i \(-0.753596\pi\)
−0.715050 + 0.699073i \(0.753596\pi\)
\(140\) 0 0
\(141\) −24.6465 −2.07561
\(142\) 0 0
\(143\) 4.54221 0.379838
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −2.72998 −0.225165
\(148\) 0 0
\(149\) −13.0055 −1.06545 −0.532724 0.846289i \(-0.678832\pi\)
−0.532724 + 0.846289i \(0.678832\pi\)
\(150\) 0 0
\(151\) −17.5895 −1.43142 −0.715708 0.698400i \(-0.753896\pi\)
−0.715708 + 0.698400i \(0.753896\pi\)
\(152\) 0 0
\(153\) 3.49073 0.282209
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 9.52366 0.760071 0.380035 0.924972i \(-0.375912\pi\)
0.380035 + 0.924972i \(0.375912\pi\)
\(158\) 0 0
\(159\) −4.64101 −0.368056
\(160\) 0 0
\(161\) 11.4489 0.902297
\(162\) 0 0
\(163\) −13.1921 −1.03329 −0.516644 0.856200i \(-0.672819\pi\)
−0.516644 + 0.856200i \(0.672819\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.81331 −0.140318 −0.0701591 0.997536i \(-0.522351\pi\)
−0.0701591 + 0.997536i \(0.522351\pi\)
\(168\) 0 0
\(169\) 25.8332 1.98717
\(170\) 0 0
\(171\) 6.19869 0.474026
\(172\) 0 0
\(173\) −12.5237 −0.952156 −0.476078 0.879403i \(-0.657942\pi\)
−0.476078 + 0.879403i \(0.657942\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 17.4753 1.31352
\(178\) 0 0
\(179\) −1.39738 −0.104445 −0.0522226 0.998635i \(-0.516631\pi\)
−0.0522226 + 0.998635i \(0.516631\pi\)
\(180\) 0 0
\(181\) 5.72890 0.425825 0.212913 0.977071i \(-0.431705\pi\)
0.212913 + 0.977071i \(0.431705\pi\)
\(182\) 0 0
\(183\) 33.1791 2.45267
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −0.410470 −0.0300165
\(188\) 0 0
\(189\) −23.9605 −1.74287
\(190\) 0 0
\(191\) 27.0198 1.95509 0.977544 0.210733i \(-0.0675849\pi\)
0.977544 + 0.210733i \(0.0675849\pi\)
\(192\) 0 0
\(193\) −23.0713 −1.66071 −0.830355 0.557234i \(-0.811862\pi\)
−0.830355 + 0.557234i \(0.811862\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.794765 0.0566247 0.0283123 0.999599i \(-0.490987\pi\)
0.0283123 + 0.999599i \(0.490987\pi\)
\(198\) 0 0
\(199\) −8.07241 −0.572238 −0.286119 0.958194i \(-0.592365\pi\)
−0.286119 + 0.958194i \(0.592365\pi\)
\(200\) 0 0
\(201\) −39.2251 −2.76672
\(202\) 0 0
\(203\) −25.2700 −1.77361
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −28.7344 −1.99718
\(208\) 0 0
\(209\) −0.728896 −0.0504188
\(210\) 0 0
\(211\) 11.6410 0.801400 0.400700 0.916209i \(-0.368767\pi\)
0.400700 + 0.916209i \(0.368767\pi\)
\(212\) 0 0
\(213\) 13.3370 0.913834
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 14.9815 1.01701
\(218\) 0 0
\(219\) −12.4148 −0.838917
\(220\) 0 0
\(221\) −3.50927 −0.236059
\(222\) 0 0
\(223\) 15.6554 1.04836 0.524182 0.851607i \(-0.324371\pi\)
0.524182 + 0.851607i \(0.324371\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4.80131 −0.318674 −0.159337 0.987224i \(-0.550936\pi\)
−0.159337 + 0.987224i \(0.550936\pi\)
\(228\) 0 0
\(229\) 2.79476 0.184683 0.0923416 0.995727i \(-0.470565\pi\)
0.0923416 + 0.995727i \(0.470565\pi\)
\(230\) 0 0
\(231\) 5.45996 0.359239
\(232\) 0 0
\(233\) 11.5422 0.756155 0.378078 0.925774i \(-0.376585\pi\)
0.378078 + 0.925774i \(0.376585\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −46.5160 −3.02154
\(238\) 0 0
\(239\) 26.2251 1.69636 0.848180 0.529708i \(-0.177699\pi\)
0.848180 + 0.529708i \(0.177699\pi\)
\(240\) 0 0
\(241\) −12.0659 −0.777231 −0.388615 0.921400i \(-0.627047\pi\)
−0.388615 + 0.921400i \(0.627047\pi\)
\(242\) 0 0
\(243\) 3.73544 0.239629
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −6.23163 −0.396509
\(248\) 0 0
\(249\) −23.8242 −1.50980
\(250\) 0 0
\(251\) −13.5237 −0.853606 −0.426803 0.904345i \(-0.640360\pi\)
−0.426803 + 0.904345i \(0.640360\pi\)
\(252\) 0 0
\(253\) 3.37884 0.212426
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 22.7398 1.41847 0.709235 0.704972i \(-0.249040\pi\)
0.709235 + 0.704972i \(0.249040\pi\)
\(258\) 0 0
\(259\) 14.1492 0.879188
\(260\) 0 0
\(261\) 63.4227 3.92577
\(262\) 0 0
\(263\) 6.67395 0.411533 0.205767 0.978601i \(-0.434031\pi\)
0.205767 + 0.978601i \(0.434031\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −30.3293 −1.85613
\(268\) 0 0
\(269\) −29.7398 −1.81327 −0.906634 0.421917i \(-0.861357\pi\)
−0.906634 + 0.421917i \(0.861357\pi\)
\(270\) 0 0
\(271\) −1.11189 −0.0675426 −0.0337713 0.999430i \(-0.510752\pi\)
−0.0337713 + 0.999430i \(0.510752\pi\)
\(272\) 0 0
\(273\) 46.6794 2.82517
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 13.1263 0.788682 0.394341 0.918964i \(-0.370973\pi\)
0.394341 + 0.918964i \(0.370973\pi\)
\(278\) 0 0
\(279\) −37.6004 −2.25108
\(280\) 0 0
\(281\) 22.9265 1.36768 0.683840 0.729632i \(-0.260309\pi\)
0.683840 + 0.729632i \(0.260309\pi\)
\(282\) 0 0
\(283\) −0.860634 −0.0511594 −0.0255797 0.999673i \(-0.508143\pi\)
−0.0255797 + 0.999673i \(0.508143\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −11.8421 −0.699016
\(288\) 0 0
\(289\) −16.6829 −0.981346
\(290\) 0 0
\(291\) 33.3788 1.95670
\(292\) 0 0
\(293\) 19.8212 1.15796 0.578982 0.815340i \(-0.303450\pi\)
0.578982 + 0.815340i \(0.303450\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −7.07133 −0.410320
\(298\) 0 0
\(299\) 28.8870 1.67058
\(300\) 0 0
\(301\) 19.9210 1.14823
\(302\) 0 0
\(303\) −29.5237 −1.69609
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 16.8661 0.962599 0.481299 0.876556i \(-0.340165\pi\)
0.481299 + 0.876556i \(0.340165\pi\)
\(308\) 0 0
\(309\) 25.2689 1.43750
\(310\) 0 0
\(311\) −10.3250 −0.585475 −0.292738 0.956193i \(-0.594566\pi\)
−0.292738 + 0.956193i \(0.594566\pi\)
\(312\) 0 0
\(313\) −15.7684 −0.891281 −0.445641 0.895212i \(-0.647024\pi\)
−0.445641 + 0.895212i \(0.647024\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.17230 −0.122009 −0.0610043 0.998138i \(-0.519430\pi\)
−0.0610043 + 0.998138i \(0.519430\pi\)
\(318\) 0 0
\(319\) −7.45779 −0.417556
\(320\) 0 0
\(321\) 45.5741 2.54370
\(322\) 0 0
\(323\) 0.563139 0.0313339
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −41.4358 −2.29140
\(328\) 0 0
\(329\) 20.0702 1.10651
\(330\) 0 0
\(331\) −11.9791 −0.658429 −0.329215 0.944255i \(-0.606784\pi\)
−0.329215 + 0.944255i \(0.606784\pi\)
\(332\) 0 0
\(333\) −35.5117 −1.94603
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −11.1921 −0.609675 −0.304838 0.952404i \(-0.598602\pi\)
−0.304838 + 0.952404i \(0.598602\pi\)
\(338\) 0 0
\(339\) 3.65540 0.198534
\(340\) 0 0
\(341\) 4.42139 0.239432
\(342\) 0 0
\(343\) 19.5117 1.05353
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 20.3843 1.09429 0.547143 0.837039i \(-0.315715\pi\)
0.547143 + 0.837039i \(0.315715\pi\)
\(348\) 0 0
\(349\) −0.252557 −0.0135191 −0.00675954 0.999977i \(-0.502152\pi\)
−0.00675954 + 0.999977i \(0.502152\pi\)
\(350\) 0 0
\(351\) −60.4556 −3.22688
\(352\) 0 0
\(353\) −28.6434 −1.52453 −0.762267 0.647263i \(-0.775914\pi\)
−0.762267 + 0.647263i \(0.775914\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −4.21832 −0.223257
\(358\) 0 0
\(359\) 18.5741 0.980301 0.490151 0.871638i \(-0.336942\pi\)
0.490151 + 0.871638i \(0.336942\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −31.7509 −1.66649
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 4.79476 0.250285 0.125142 0.992139i \(-0.460061\pi\)
0.125142 + 0.992139i \(0.460061\pi\)
\(368\) 0 0
\(369\) 29.7213 1.54723
\(370\) 0 0
\(371\) 3.77929 0.196211
\(372\) 0 0
\(373\) 15.9485 0.825783 0.412892 0.910780i \(-0.364519\pi\)
0.412892 + 0.910780i \(0.364519\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −63.7597 −3.28379
\(378\) 0 0
\(379\) 16.8013 0.863025 0.431513 0.902107i \(-0.357980\pi\)
0.431513 + 0.902107i \(0.357980\pi\)
\(380\) 0 0
\(381\) −28.8846 −1.47980
\(382\) 0 0
\(383\) −26.7948 −1.36915 −0.684574 0.728943i \(-0.740012\pi\)
−0.684574 + 0.728943i \(0.740012\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −49.9978 −2.54153
\(388\) 0 0
\(389\) 18.3424 0.929998 0.464999 0.885311i \(-0.346055\pi\)
0.464999 + 0.885311i \(0.346055\pi\)
\(390\) 0 0
\(391\) −2.61046 −0.132017
\(392\) 0 0
\(393\) 52.7817 2.66248
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 21.2162 1.06481 0.532404 0.846490i \(-0.321289\pi\)
0.532404 + 0.846490i \(0.321289\pi\)
\(398\) 0 0
\(399\) −7.49073 −0.375005
\(400\) 0 0
\(401\) −27.8661 −1.39157 −0.695783 0.718252i \(-0.744943\pi\)
−0.695783 + 0.718252i \(0.744943\pi\)
\(402\) 0 0
\(403\) 37.8002 1.88296
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 4.17577 0.206985
\(408\) 0 0
\(409\) −18.0899 −0.894487 −0.447243 0.894412i \(-0.647594\pi\)
−0.447243 + 0.894412i \(0.647594\pi\)
\(410\) 0 0
\(411\) 6.85171 0.337970
\(412\) 0 0
\(413\) −14.2305 −0.700239
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −51.1372 −2.50420
\(418\) 0 0
\(419\) 15.3370 0.749260 0.374630 0.927174i \(-0.377770\pi\)
0.374630 + 0.927174i \(0.377770\pi\)
\(420\) 0 0
\(421\) −8.42486 −0.410602 −0.205301 0.978699i \(-0.565817\pi\)
−0.205301 + 0.978699i \(0.565817\pi\)
\(422\) 0 0
\(423\) −50.3723 −2.44918
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −27.0185 −1.30752
\(428\) 0 0
\(429\) 13.7762 0.665122
\(430\) 0 0
\(431\) −16.2766 −0.784014 −0.392007 0.919962i \(-0.628219\pi\)
−0.392007 + 0.919962i \(0.628219\pi\)
\(432\) 0 0
\(433\) −18.1976 −0.874521 −0.437261 0.899335i \(-0.644051\pi\)
−0.437261 + 0.899335i \(0.644051\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −4.63555 −0.221749
\(438\) 0 0
\(439\) −20.4214 −0.974660 −0.487330 0.873218i \(-0.662029\pi\)
−0.487330 + 0.873218i \(0.662029\pi\)
\(440\) 0 0
\(441\) −5.57952 −0.265691
\(442\) 0 0
\(443\) −21.6685 −1.02950 −0.514750 0.857340i \(-0.672115\pi\)
−0.514750 + 0.857340i \(0.672115\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −39.4447 −1.86567
\(448\) 0 0
\(449\) 23.8133 1.12382 0.561910 0.827198i \(-0.310067\pi\)
0.561910 + 0.827198i \(0.310067\pi\)
\(450\) 0 0
\(451\) −3.49489 −0.164568
\(452\) 0 0
\(453\) −53.3479 −2.50650
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 9.15813 0.428399 0.214200 0.976790i \(-0.431286\pi\)
0.214200 + 0.976790i \(0.431286\pi\)
\(458\) 0 0
\(459\) 5.46325 0.255003
\(460\) 0 0
\(461\) −7.78931 −0.362784 −0.181392 0.983411i \(-0.558060\pi\)
−0.181392 + 0.983411i \(0.558060\pi\)
\(462\) 0 0
\(463\) −0.405011 −0.0188225 −0.00941123 0.999956i \(-0.502996\pi\)
−0.00941123 + 0.999956i \(0.502996\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 1.95814 0.0906118 0.0453059 0.998973i \(-0.485574\pi\)
0.0453059 + 0.998973i \(0.485574\pi\)
\(468\) 0 0
\(469\) 31.9420 1.47494
\(470\) 0 0
\(471\) 28.8846 1.33093
\(472\) 0 0
\(473\) 5.87918 0.270325
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −9.48527 −0.434301
\(478\) 0 0
\(479\) 22.9210 1.04729 0.523645 0.851937i \(-0.324572\pi\)
0.523645 + 0.851937i \(0.324572\pi\)
\(480\) 0 0
\(481\) 35.7003 1.62780
\(482\) 0 0
\(483\) 34.7237 1.57998
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 23.9450 1.08505 0.542527 0.840038i \(-0.317468\pi\)
0.542527 + 0.840038i \(0.317468\pi\)
\(488\) 0 0
\(489\) −40.0109 −1.80936
\(490\) 0 0
\(491\) −3.86826 −0.174572 −0.0872861 0.996183i \(-0.527819\pi\)
−0.0872861 + 0.996183i \(0.527819\pi\)
\(492\) 0 0
\(493\) 5.76183 0.259500
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −10.8606 −0.487166
\(498\) 0 0
\(499\) 7.92104 0.354595 0.177297 0.984157i \(-0.443265\pi\)
0.177297 + 0.984157i \(0.443265\pi\)
\(500\) 0 0
\(501\) −5.49966 −0.245706
\(502\) 0 0
\(503\) 16.6949 0.744388 0.372194 0.928155i \(-0.378606\pi\)
0.372194 + 0.928155i \(0.378606\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 78.3503 3.47966
\(508\) 0 0
\(509\) 24.4028 1.08164 0.540818 0.841139i \(-0.318115\pi\)
0.540818 + 0.841139i \(0.318115\pi\)
\(510\) 0 0
\(511\) 10.1097 0.447228
\(512\) 0 0
\(513\) 9.70142 0.428328
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 5.92321 0.260503
\(518\) 0 0
\(519\) −37.9834 −1.66729
\(520\) 0 0
\(521\) 26.0659 1.14197 0.570983 0.820962i \(-0.306562\pi\)
0.570983 + 0.820962i \(0.306562\pi\)
\(522\) 0 0
\(523\) −17.8726 −0.781516 −0.390758 0.920493i \(-0.627787\pi\)
−0.390758 + 0.920493i \(0.627787\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −3.41593 −0.148800
\(528\) 0 0
\(529\) −1.51166 −0.0657243
\(530\) 0 0
\(531\) 35.7158 1.54993
\(532\) 0 0
\(533\) −29.8792 −1.29421
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −4.23817 −0.182891
\(538\) 0 0
\(539\) 0.656088 0.0282597
\(540\) 0 0
\(541\) 23.0604 0.991444 0.495722 0.868481i \(-0.334903\pi\)
0.495722 + 0.868481i \(0.334903\pi\)
\(542\) 0 0
\(543\) 17.3754 0.745648
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 27.7584 1.18686 0.593431 0.804885i \(-0.297773\pi\)
0.593431 + 0.804885i \(0.297773\pi\)
\(548\) 0 0
\(549\) 67.8111 2.89411
\(550\) 0 0
\(551\) 10.2316 0.435882
\(552\) 0 0
\(553\) 37.8792 1.61079
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.60808 −0.364736 −0.182368 0.983230i \(-0.558376\pi\)
−0.182368 + 0.983230i \(0.558376\pi\)
\(558\) 0 0
\(559\) 50.2635 2.12592
\(560\) 0 0
\(561\) −1.24493 −0.0525609
\(562\) 0 0
\(563\) −7.93959 −0.334614 −0.167307 0.985905i \(-0.553507\pi\)
−0.167307 + 0.985905i \(0.553507\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −26.7422 −1.12307
\(568\) 0 0
\(569\) −1.65757 −0.0694889 −0.0347444 0.999396i \(-0.511062\pi\)
−0.0347444 + 0.999396i \(0.511062\pi\)
\(570\) 0 0
\(571\) 14.0528 0.588091 0.294045 0.955791i \(-0.404998\pi\)
0.294045 + 0.955791i \(0.404998\pi\)
\(572\) 0 0
\(573\) 81.9494 3.42349
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −1.36445 −0.0568027 −0.0284014 0.999597i \(-0.509042\pi\)
−0.0284014 + 0.999597i \(0.509042\pi\)
\(578\) 0 0
\(579\) −69.9738 −2.90801
\(580\) 0 0
\(581\) 19.4007 0.804876
\(582\) 0 0
\(583\) 1.11536 0.0461935
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 24.6609 1.01786 0.508931 0.860807i \(-0.330041\pi\)
0.508931 + 0.860807i \(0.330041\pi\)
\(588\) 0 0
\(589\) −6.06587 −0.249940
\(590\) 0 0
\(591\) 2.41047 0.0991535
\(592\) 0 0
\(593\) −0.747443 −0.0306938 −0.0153469 0.999882i \(-0.504885\pi\)
−0.0153469 + 0.999882i \(0.504885\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −24.4831 −1.00203
\(598\) 0 0
\(599\) −1.40501 −0.0574072 −0.0287036 0.999588i \(-0.509138\pi\)
−0.0287036 + 0.999588i \(0.509138\pi\)
\(600\) 0 0
\(601\) 29.7453 1.21334 0.606668 0.794956i \(-0.292506\pi\)
0.606668 + 0.794956i \(0.292506\pi\)
\(602\) 0 0
\(603\) −80.1680 −3.26469
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −5.66849 −0.230077 −0.115038 0.993361i \(-0.536699\pi\)
−0.115038 + 0.993361i \(0.536699\pi\)
\(608\) 0 0
\(609\) −76.6423 −3.10570
\(610\) 0 0
\(611\) 50.6399 2.04867
\(612\) 0 0
\(613\) −2.99454 −0.120948 −0.0604742 0.998170i \(-0.519261\pi\)
−0.0604742 + 0.998170i \(0.519261\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −32.3370 −1.30184 −0.650919 0.759147i \(-0.725616\pi\)
−0.650919 + 0.759147i \(0.725616\pi\)
\(618\) 0 0
\(619\) 20.9265 0.841107 0.420554 0.907268i \(-0.361836\pi\)
0.420554 + 0.907268i \(0.361836\pi\)
\(620\) 0 0
\(621\) −44.9714 −1.80464
\(622\) 0 0
\(623\) 24.6980 0.989503
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −2.21069 −0.0882866
\(628\) 0 0
\(629\) −3.22617 −0.128636
\(630\) 0 0
\(631\) −22.8002 −0.907663 −0.453831 0.891088i \(-0.649943\pi\)
−0.453831 + 0.891088i \(0.649943\pi\)
\(632\) 0 0
\(633\) 35.3064 1.40330
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 5.60916 0.222243
\(638\) 0 0
\(639\) 27.2580 1.07831
\(640\) 0 0
\(641\) 36.3184 1.43449 0.717246 0.696820i \(-0.245402\pi\)
0.717246 + 0.696820i \(0.245402\pi\)
\(642\) 0 0
\(643\) −13.6135 −0.536865 −0.268433 0.963298i \(-0.586506\pi\)
−0.268433 + 0.963298i \(0.586506\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.0724126 0.00284683 0.00142342 0.999999i \(-0.499547\pi\)
0.00142342 + 0.999999i \(0.499547\pi\)
\(648\) 0 0
\(649\) −4.19978 −0.164856
\(650\) 0 0
\(651\) 45.4378 1.78085
\(652\) 0 0
\(653\) −43.5346 −1.70364 −0.851820 0.523835i \(-0.824501\pi\)
−0.851820 + 0.523835i \(0.824501\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −25.3734 −0.989910
\(658\) 0 0
\(659\) 33.4512 1.30308 0.651538 0.758616i \(-0.274124\pi\)
0.651538 + 0.758616i \(0.274124\pi\)
\(660\) 0 0
\(661\) −2.89465 −0.112589 −0.0562945 0.998414i \(-0.517929\pi\)
−0.0562945 + 0.998414i \(0.517929\pi\)
\(662\) 0 0
\(663\) −10.6434 −0.413355
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −47.4292 −1.83647
\(668\) 0 0
\(669\) 47.4818 1.83575
\(670\) 0 0
\(671\) −7.97382 −0.307826
\(672\) 0 0
\(673\) 42.8475 1.65165 0.825826 0.563925i \(-0.190709\pi\)
0.825826 + 0.563925i \(0.190709\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 34.4567 1.32428 0.662139 0.749381i \(-0.269649\pi\)
0.662139 + 0.749381i \(0.269649\pi\)
\(678\) 0 0
\(679\) −27.1812 −1.04312
\(680\) 0 0
\(681\) −14.5621 −0.558019
\(682\) 0 0
\(683\) 2.73436 0.104627 0.0523136 0.998631i \(-0.483340\pi\)
0.0523136 + 0.998631i \(0.483340\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 8.47634 0.323393
\(688\) 0 0
\(689\) 9.53566 0.363280
\(690\) 0 0
\(691\) 4.74198 0.180394 0.0901968 0.995924i \(-0.471250\pi\)
0.0901968 + 0.995924i \(0.471250\pi\)
\(692\) 0 0
\(693\) 11.1590 0.423897
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 2.70012 0.102274
\(698\) 0 0
\(699\) 35.0068 1.32408
\(700\) 0 0
\(701\) 33.1372 1.25157 0.625787 0.779994i \(-0.284778\pi\)
0.625787 + 0.779994i \(0.284778\pi\)
\(702\) 0 0
\(703\) −5.72890 −0.216069
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 24.0419 0.904187
\(708\) 0 0
\(709\) 5.37884 0.202006 0.101003 0.994886i \(-0.467795\pi\)
0.101003 + 0.994886i \(0.467795\pi\)
\(710\) 0 0
\(711\) −95.0692 −3.56537
\(712\) 0 0
\(713\) 28.1187 1.05305
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 79.5390 2.97044
\(718\) 0 0
\(719\) −33.0857 −1.23389 −0.616944 0.787007i \(-0.711630\pi\)
−0.616944 + 0.787007i \(0.711630\pi\)
\(720\) 0 0
\(721\) −20.5771 −0.766332
\(722\) 0 0
\(723\) −36.5950 −1.36098
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −2.62463 −0.0973423 −0.0486711 0.998815i \(-0.515499\pi\)
−0.0486711 + 0.998815i \(0.515499\pi\)
\(728\) 0 0
\(729\) −21.1538 −0.783472
\(730\) 0 0
\(731\) −4.54221 −0.168000
\(732\) 0 0
\(733\) 0.608077 0.0224598 0.0112299 0.999937i \(-0.496425\pi\)
0.0112299 + 0.999937i \(0.496425\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 9.42685 0.347242
\(738\) 0 0
\(739\) −36.3974 −1.33890 −0.669450 0.742857i \(-0.733470\pi\)
−0.669450 + 0.742857i \(0.733470\pi\)
\(740\) 0 0
\(741\) −18.9001 −0.694313
\(742\) 0 0
\(743\) 23.0713 0.846405 0.423202 0.906035i \(-0.360906\pi\)
0.423202 + 0.906035i \(0.360906\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −48.6918 −1.78154
\(748\) 0 0
\(749\) −37.1121 −1.35605
\(750\) 0 0
\(751\) −4.75290 −0.173436 −0.0867179 0.996233i \(-0.527638\pi\)
−0.0867179 + 0.996233i \(0.527638\pi\)
\(752\) 0 0
\(753\) −41.0164 −1.49472
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 26.8057 0.974269 0.487135 0.873327i \(-0.338042\pi\)
0.487135 + 0.873327i \(0.338042\pi\)
\(758\) 0 0
\(759\) 10.2478 0.371971
\(760\) 0 0
\(761\) 25.4478 0.922481 0.461241 0.887275i \(-0.347404\pi\)
0.461241 + 0.887275i \(0.347404\pi\)
\(762\) 0 0
\(763\) 33.7422 1.22155
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −35.9056 −1.29648
\(768\) 0 0
\(769\) −14.6421 −0.528007 −0.264004 0.964522i \(-0.585043\pi\)
−0.264004 + 0.964522i \(0.585043\pi\)
\(770\) 0 0
\(771\) 68.9684 2.48384
\(772\) 0 0
\(773\) −16.8462 −0.605917 −0.302959 0.953004i \(-0.597974\pi\)
−0.302959 + 0.953004i \(0.597974\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 42.9136 1.53952
\(778\) 0 0
\(779\) 4.79476 0.171790
\(780\) 0 0
\(781\) −3.20524 −0.114692
\(782\) 0 0
\(783\) 99.2613 3.54731
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) −18.7367 −0.667893 −0.333946 0.942592i \(-0.608380\pi\)
−0.333946 + 0.942592i \(0.608380\pi\)
\(788\) 0 0
\(789\) 20.2416 0.720621
\(790\) 0 0
\(791\) −2.97668 −0.105839
\(792\) 0 0
\(793\) −68.1714 −2.42084
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −37.9900 −1.34567 −0.672837 0.739791i \(-0.734925\pi\)
−0.672837 + 0.739791i \(0.734925\pi\)
\(798\) 0 0
\(799\) −4.57623 −0.161895
\(800\) 0 0
\(801\) −61.9869 −2.19020
\(802\) 0 0
\(803\) 2.98362 0.105290
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) −90.1989 −3.17515
\(808\) 0 0
\(809\) 21.8857 0.769461 0.384731 0.923029i \(-0.374294\pi\)
0.384731 + 0.923029i \(0.374294\pi\)
\(810\) 0 0
\(811\) −37.8595 −1.32943 −0.664714 0.747098i \(-0.731447\pi\)
−0.664714 + 0.747098i \(0.731447\pi\)
\(812\) 0 0
\(813\) −3.37229 −0.118271
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −8.06587 −0.282189
\(818\) 0 0
\(819\) 95.4031 3.33365
\(820\) 0 0
\(821\) −20.1976 −0.704901 −0.352451 0.935830i \(-0.614652\pi\)
−0.352451 + 0.935830i \(0.614652\pi\)
\(822\) 0 0
\(823\) 4.34590 0.151489 0.0757443 0.997127i \(-0.475867\pi\)
0.0757443 + 0.997127i \(0.475867\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 56.8375 1.97643 0.988217 0.153057i \(-0.0489119\pi\)
0.988217 + 0.153057i \(0.0489119\pi\)
\(828\) 0 0
\(829\) −17.4543 −0.606214 −0.303107 0.952957i \(-0.598024\pi\)
−0.303107 + 0.952957i \(0.598024\pi\)
\(830\) 0 0
\(831\) 39.8111 1.38103
\(832\) 0 0
\(833\) −0.506888 −0.0175626
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −58.8475 −2.03407
\(838\) 0 0
\(839\) −1.77622 −0.0613219 −0.0306609 0.999530i \(-0.509761\pi\)
−0.0306609 + 0.999530i \(0.509761\pi\)
\(840\) 0 0
\(841\) 75.6862 2.60987
\(842\) 0 0
\(843\) 69.5346 2.39490
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 25.8556 0.888408
\(848\) 0 0
\(849\) −2.61025 −0.0895834
\(850\) 0 0
\(851\) 26.5566 0.910348
\(852\) 0 0
\(853\) −16.1187 −0.551892 −0.275946 0.961173i \(-0.588991\pi\)
−0.275946 + 0.961173i \(0.588991\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −47.2031 −1.61243 −0.806213 0.591625i \(-0.798486\pi\)
−0.806213 + 0.591625i \(0.798486\pi\)
\(858\) 0 0
\(859\) −37.3239 −1.27347 −0.636737 0.771081i \(-0.719716\pi\)
−0.636737 + 0.771081i \(0.719716\pi\)
\(860\) 0 0
\(861\) −35.9163 −1.22402
\(862\) 0 0
\(863\) 1.33697 0.0455111 0.0227555 0.999741i \(-0.492756\pi\)
0.0227555 + 0.999741i \(0.492756\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −50.5981 −1.71840
\(868\) 0 0
\(869\) 11.1791 0.379224
\(870\) 0 0
\(871\) 80.5939 2.73082
\(872\) 0 0
\(873\) 68.2194 2.30888
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 13.1647 0.444539 0.222270 0.974985i \(-0.428653\pi\)
0.222270 + 0.974985i \(0.428653\pi\)
\(878\) 0 0
\(879\) 60.1163 2.02767
\(880\) 0 0
\(881\) −10.2052 −0.343823 −0.171912 0.985112i \(-0.554994\pi\)
−0.171912 + 0.985112i \(0.554994\pi\)
\(882\) 0 0
\(883\) −1.49966 −0.0504674 −0.0252337 0.999682i \(-0.508033\pi\)
−0.0252337 + 0.999682i \(0.508033\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 46.9505 1.57644 0.788222 0.615391i \(-0.211002\pi\)
0.788222 + 0.615391i \(0.211002\pi\)
\(888\) 0 0
\(889\) 23.5215 0.788886
\(890\) 0 0
\(891\) −7.89227 −0.264401
\(892\) 0 0
\(893\) −8.12628 −0.271936
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 87.6125 2.92529
\(898\) 0 0
\(899\) −62.0637 −2.06994
\(900\) 0 0
\(901\) −0.861719 −0.0287080
\(902\) 0 0
\(903\) 60.4192 2.01063
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −16.3668 −0.543452 −0.271726 0.962375i \(-0.587594\pi\)
−0.271726 + 0.962375i \(0.587594\pi\)
\(908\) 0 0
\(909\) −60.3403 −2.00136
\(910\) 0 0
\(911\) −32.3293 −1.07112 −0.535559 0.844498i \(-0.679899\pi\)
−0.535559 + 0.844498i \(0.679899\pi\)
\(912\) 0 0
\(913\) 5.72561 0.189490
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −42.9815 −1.41937
\(918\) 0 0
\(919\) 22.8157 0.752620 0.376310 0.926494i \(-0.377193\pi\)
0.376310 + 0.926494i \(0.377193\pi\)
\(920\) 0 0
\(921\) 51.1538 1.68557
\(922\) 0 0
\(923\) −27.4028 −0.901976
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 51.6445 1.69623
\(928\) 0 0
\(929\) −27.2436 −0.893834 −0.446917 0.894575i \(-0.647478\pi\)
−0.446917 + 0.894575i \(0.647478\pi\)
\(930\) 0 0
\(931\) −0.900112 −0.0295000
\(932\) 0 0
\(933\) −31.3150 −1.02521
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −51.5006 −1.68245 −0.841225 0.540685i \(-0.818165\pi\)
−0.841225 + 0.540685i \(0.818165\pi\)
\(938\) 0 0
\(939\) −47.8244 −1.56069
\(940\) 0 0
\(941\) −40.8541 −1.33181 −0.665903 0.746039i \(-0.731953\pi\)
−0.665903 + 0.746039i \(0.731953\pi\)
\(942\) 0 0
\(943\) −22.2264 −0.723791
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −38.2526 −1.24304 −0.621521 0.783398i \(-0.713485\pi\)
−0.621521 + 0.783398i \(0.713485\pi\)
\(948\) 0 0
\(949\) 25.5082 0.828031
\(950\) 0 0
\(951\) −6.58845 −0.213645
\(952\) 0 0
\(953\) 54.1187 1.75308 0.876538 0.481334i \(-0.159847\pi\)
0.876538 + 0.481334i \(0.159847\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −22.6190 −0.731168
\(958\) 0 0
\(959\) −5.57952 −0.180172
\(960\) 0 0
\(961\) 5.79476 0.186928
\(962\) 0 0
\(963\) 93.1440 3.00152
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −28.4214 −0.913970 −0.456985 0.889474i \(-0.651071\pi\)
−0.456985 + 0.889474i \(0.651071\pi\)
\(968\) 0 0
\(969\) 1.70796 0.0548677
\(970\) 0 0
\(971\) −30.8057 −0.988601 −0.494301 0.869291i \(-0.664576\pi\)
−0.494301 + 0.869291i \(0.664576\pi\)
\(972\) 0 0
\(973\) 41.6423 1.33499
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 37.6554 1.20470 0.602351 0.798231i \(-0.294231\pi\)
0.602351 + 0.798231i \(0.294231\pi\)
\(978\) 0 0
\(979\) 7.28896 0.232956
\(980\) 0 0
\(981\) −84.6862 −2.70382
\(982\) 0 0
\(983\) 38.7948 1.23736 0.618680 0.785643i \(-0.287668\pi\)
0.618680 + 0.785643i \(0.287668\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 60.8717 1.93757
\(988\) 0 0
\(989\) 37.3898 1.18893
\(990\) 0 0
\(991\) 15.0295 0.477427 0.238713 0.971090i \(-0.423274\pi\)
0.238713 + 0.971090i \(0.423274\pi\)
\(992\) 0 0
\(993\) −36.3317 −1.15295
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1.18123 0.0374099 0.0187050 0.999825i \(-0.494046\pi\)
0.0187050 + 0.999825i \(0.494046\pi\)
\(998\) 0 0
\(999\) −55.5784 −1.75842
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 7600.2.a.bm.1.3 3
4.3 odd 2 950.2.a.m.1.1 yes 3
5.4 even 2 7600.2.a.cb.1.1 3
12.11 even 2 8550.2.a.cj.1.2 3
20.3 even 4 950.2.b.g.799.1 6
20.7 even 4 950.2.b.g.799.6 6
20.19 odd 2 950.2.a.k.1.3 3
60.59 even 2 8550.2.a.co.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
950.2.a.k.1.3 3 20.19 odd 2
950.2.a.m.1.1 yes 3 4.3 odd 2
950.2.b.g.799.1 6 20.3 even 4
950.2.b.g.799.6 6 20.7 even 4
7600.2.a.bm.1.3 3 1.1 even 1 trivial
7600.2.a.cb.1.1 3 5.4 even 2
8550.2.a.cj.1.2 3 12.11 even 2
8550.2.a.co.1.2 3 60.59 even 2