Properties

Label 1932.2.a.c.1.2
Level $1932$
Weight $2$
Character 1932.1
Self dual yes
Analytic conductor $15.427$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 1932 = 2^{2} \cdot 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1932.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(15.4270976705\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
Defining polynomial: \( x^{2} - x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.30278\) of defining polynomial
Character \(\chi\) \(=\) 1932.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{3} -0.697224 q^{5} -1.00000 q^{7} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -0.697224 q^{5} -1.00000 q^{7} +1.00000 q^{9} +5.60555 q^{11} +2.30278 q^{13} +0.697224 q^{15} -0.394449 q^{17} -0.394449 q^{19} +1.00000 q^{21} -1.00000 q^{23} -4.51388 q^{25} -1.00000 q^{27} -5.60555 q^{29} -3.60555 q^{31} -5.60555 q^{33} +0.697224 q^{35} +5.60555 q^{37} -2.30278 q^{39} +3.60555 q^{41} +4.30278 q^{43} -0.697224 q^{45} -4.60555 q^{47} +1.00000 q^{49} +0.394449 q^{51} +5.90833 q^{53} -3.90833 q^{55} +0.394449 q^{57} +3.90833 q^{59} +4.90833 q^{61} -1.00000 q^{63} -1.60555 q^{65} +13.3028 q^{67} +1.00000 q^{69} +12.9083 q^{71} +11.0000 q^{73} +4.51388 q^{75} -5.60555 q^{77} +13.4222 q^{79} +1.00000 q^{81} +16.2111 q^{83} +0.275019 q^{85} +5.60555 q^{87} -15.5139 q^{89} -2.30278 q^{91} +3.60555 q^{93} +0.275019 q^{95} +3.78890 q^{97} +5.60555 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{3} - 5 q^{5} - 2 q^{7} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{3} - 5 q^{5} - 2 q^{7} + 2 q^{9} + 4 q^{11} + q^{13} + 5 q^{15} - 8 q^{17} - 8 q^{19} + 2 q^{21} - 2 q^{23} + 9 q^{25} - 2 q^{27} - 4 q^{29} - 4 q^{33} + 5 q^{35} + 4 q^{37} - q^{39} + 5 q^{43} - 5 q^{45} - 2 q^{47} + 2 q^{49} + 8 q^{51} + q^{53} + 3 q^{55} + 8 q^{57} - 3 q^{59} - q^{61} - 2 q^{63} + 4 q^{65} + 23 q^{67} + 2 q^{69} + 15 q^{71} + 22 q^{73} - 9 q^{75} - 4 q^{77} - 2 q^{79} + 2 q^{81} + 18 q^{83} + 33 q^{85} + 4 q^{87} - 13 q^{89} - q^{91} + 33 q^{95} + 22 q^{97} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) −0.697224 −0.311808 −0.155904 0.987772i \(-0.549829\pi\)
−0.155904 + 0.987772i \(0.549829\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.60555 1.69014 0.845069 0.534658i \(-0.179559\pi\)
0.845069 + 0.534658i \(0.179559\pi\)
\(12\) 0 0
\(13\) 2.30278 0.638675 0.319338 0.947641i \(-0.396540\pi\)
0.319338 + 0.947641i \(0.396540\pi\)
\(14\) 0 0
\(15\) 0.697224 0.180023
\(16\) 0 0
\(17\) −0.394449 −0.0956679 −0.0478339 0.998855i \(-0.515232\pi\)
−0.0478339 + 0.998855i \(0.515232\pi\)
\(18\) 0 0
\(19\) −0.394449 −0.0904927 −0.0452464 0.998976i \(-0.514407\pi\)
−0.0452464 + 0.998976i \(0.514407\pi\)
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) −1.00000 −0.208514
\(24\) 0 0
\(25\) −4.51388 −0.902776
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −5.60555 −1.04092 −0.520462 0.853885i \(-0.674240\pi\)
−0.520462 + 0.853885i \(0.674240\pi\)
\(30\) 0 0
\(31\) −3.60555 −0.647576 −0.323788 0.946130i \(-0.604956\pi\)
−0.323788 + 0.946130i \(0.604956\pi\)
\(32\) 0 0
\(33\) −5.60555 −0.975801
\(34\) 0 0
\(35\) 0.697224 0.117852
\(36\) 0 0
\(37\) 5.60555 0.921547 0.460773 0.887518i \(-0.347572\pi\)
0.460773 + 0.887518i \(0.347572\pi\)
\(38\) 0 0
\(39\) −2.30278 −0.368739
\(40\) 0 0
\(41\) 3.60555 0.563093 0.281546 0.959548i \(-0.409153\pi\)
0.281546 + 0.959548i \(0.409153\pi\)
\(42\) 0 0
\(43\) 4.30278 0.656167 0.328084 0.944649i \(-0.393597\pi\)
0.328084 + 0.944649i \(0.393597\pi\)
\(44\) 0 0
\(45\) −0.697224 −0.103936
\(46\) 0 0
\(47\) −4.60555 −0.671789 −0.335894 0.941900i \(-0.609039\pi\)
−0.335894 + 0.941900i \(0.609039\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0.394449 0.0552339
\(52\) 0 0
\(53\) 5.90833 0.811571 0.405786 0.913968i \(-0.366998\pi\)
0.405786 + 0.913968i \(0.366998\pi\)
\(54\) 0 0
\(55\) −3.90833 −0.526999
\(56\) 0 0
\(57\) 0.394449 0.0522460
\(58\) 0 0
\(59\) 3.90833 0.508821 0.254410 0.967096i \(-0.418119\pi\)
0.254410 + 0.967096i \(0.418119\pi\)
\(60\) 0 0
\(61\) 4.90833 0.628447 0.314223 0.949349i \(-0.398256\pi\)
0.314223 + 0.949349i \(0.398256\pi\)
\(62\) 0 0
\(63\) −1.00000 −0.125988
\(64\) 0 0
\(65\) −1.60555 −0.199144
\(66\) 0 0
\(67\) 13.3028 1.62519 0.812596 0.582827i \(-0.198053\pi\)
0.812596 + 0.582827i \(0.198053\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) 12.9083 1.53194 0.765968 0.642878i \(-0.222260\pi\)
0.765968 + 0.642878i \(0.222260\pi\)
\(72\) 0 0
\(73\) 11.0000 1.28745 0.643726 0.765256i \(-0.277388\pi\)
0.643726 + 0.765256i \(0.277388\pi\)
\(74\) 0 0
\(75\) 4.51388 0.521218
\(76\) 0 0
\(77\) −5.60555 −0.638812
\(78\) 0 0
\(79\) 13.4222 1.51012 0.755058 0.655658i \(-0.227609\pi\)
0.755058 + 0.655658i \(0.227609\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 16.2111 1.77940 0.889700 0.456546i \(-0.150914\pi\)
0.889700 + 0.456546i \(0.150914\pi\)
\(84\) 0 0
\(85\) 0.275019 0.0298300
\(86\) 0 0
\(87\) 5.60555 0.600978
\(88\) 0 0
\(89\) −15.5139 −1.64447 −0.822234 0.569150i \(-0.807272\pi\)
−0.822234 + 0.569150i \(0.807272\pi\)
\(90\) 0 0
\(91\) −2.30278 −0.241396
\(92\) 0 0
\(93\) 3.60555 0.373878
\(94\) 0 0
\(95\) 0.275019 0.0282164
\(96\) 0 0
\(97\) 3.78890 0.384704 0.192352 0.981326i \(-0.438388\pi\)
0.192352 + 0.981326i \(0.438388\pi\)
\(98\) 0 0
\(99\) 5.60555 0.563379
\(100\) 0 0
\(101\) −12.5139 −1.24518 −0.622589 0.782549i \(-0.713919\pi\)
−0.622589 + 0.782549i \(0.713919\pi\)
\(102\) 0 0
\(103\) 2.78890 0.274798 0.137399 0.990516i \(-0.456126\pi\)
0.137399 + 0.990516i \(0.456126\pi\)
\(104\) 0 0
\(105\) −0.697224 −0.0680421
\(106\) 0 0
\(107\) 0.302776 0.0292704 0.0146352 0.999893i \(-0.495341\pi\)
0.0146352 + 0.999893i \(0.495341\pi\)
\(108\) 0 0
\(109\) −4.51388 −0.432351 −0.216176 0.976355i \(-0.569358\pi\)
−0.216176 + 0.976355i \(0.569358\pi\)
\(110\) 0 0
\(111\) −5.60555 −0.532055
\(112\) 0 0
\(113\) 5.30278 0.498843 0.249422 0.968395i \(-0.419760\pi\)
0.249422 + 0.968395i \(0.419760\pi\)
\(114\) 0 0
\(115\) 0.697224 0.0650165
\(116\) 0 0
\(117\) 2.30278 0.212892
\(118\) 0 0
\(119\) 0.394449 0.0361591
\(120\) 0 0
\(121\) 20.4222 1.85656
\(122\) 0 0
\(123\) −3.60555 −0.325102
\(124\) 0 0
\(125\) 6.63331 0.593301
\(126\) 0 0
\(127\) 18.1194 1.60784 0.803920 0.594738i \(-0.202744\pi\)
0.803920 + 0.594738i \(0.202744\pi\)
\(128\) 0 0
\(129\) −4.30278 −0.378838
\(130\) 0 0
\(131\) −6.81665 −0.595574 −0.297787 0.954632i \(-0.596248\pi\)
−0.297787 + 0.954632i \(0.596248\pi\)
\(132\) 0 0
\(133\) 0.394449 0.0342030
\(134\) 0 0
\(135\) 0.697224 0.0600075
\(136\) 0 0
\(137\) −5.60555 −0.478915 −0.239457 0.970907i \(-0.576970\pi\)
−0.239457 + 0.970907i \(0.576970\pi\)
\(138\) 0 0
\(139\) −15.1194 −1.28241 −0.641207 0.767368i \(-0.721566\pi\)
−0.641207 + 0.767368i \(0.721566\pi\)
\(140\) 0 0
\(141\) 4.60555 0.387857
\(142\) 0 0
\(143\) 12.9083 1.07945
\(144\) 0 0
\(145\) 3.90833 0.324569
\(146\) 0 0
\(147\) −1.00000 −0.0824786
\(148\) 0 0
\(149\) −15.3944 −1.26116 −0.630581 0.776123i \(-0.717183\pi\)
−0.630581 + 0.776123i \(0.717183\pi\)
\(150\) 0 0
\(151\) 8.60555 0.700310 0.350155 0.936692i \(-0.386129\pi\)
0.350155 + 0.936692i \(0.386129\pi\)
\(152\) 0 0
\(153\) −0.394449 −0.0318893
\(154\) 0 0
\(155\) 2.51388 0.201920
\(156\) 0 0
\(157\) 11.8167 0.943072 0.471536 0.881847i \(-0.343700\pi\)
0.471536 + 0.881847i \(0.343700\pi\)
\(158\) 0 0
\(159\) −5.90833 −0.468561
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) −9.11943 −0.714289 −0.357144 0.934049i \(-0.616250\pi\)
−0.357144 + 0.934049i \(0.616250\pi\)
\(164\) 0 0
\(165\) 3.90833 0.304263
\(166\) 0 0
\(167\) −14.0278 −1.08550 −0.542750 0.839894i \(-0.682617\pi\)
−0.542750 + 0.839894i \(0.682617\pi\)
\(168\) 0 0
\(169\) −7.69722 −0.592094
\(170\) 0 0
\(171\) −0.394449 −0.0301642
\(172\) 0 0
\(173\) −6.39445 −0.486161 −0.243080 0.970006i \(-0.578158\pi\)
−0.243080 + 0.970006i \(0.578158\pi\)
\(174\) 0 0
\(175\) 4.51388 0.341217
\(176\) 0 0
\(177\) −3.90833 −0.293768
\(178\) 0 0
\(179\) 24.9361 1.86381 0.931905 0.362702i \(-0.118146\pi\)
0.931905 + 0.362702i \(0.118146\pi\)
\(180\) 0 0
\(181\) −19.0000 −1.41226 −0.706129 0.708083i \(-0.749560\pi\)
−0.706129 + 0.708083i \(0.749560\pi\)
\(182\) 0 0
\(183\) −4.90833 −0.362834
\(184\) 0 0
\(185\) −3.90833 −0.287346
\(186\) 0 0
\(187\) −2.21110 −0.161692
\(188\) 0 0
\(189\) 1.00000 0.0727393
\(190\) 0 0
\(191\) −8.60555 −0.622676 −0.311338 0.950299i \(-0.600777\pi\)
−0.311338 + 0.950299i \(0.600777\pi\)
\(192\) 0 0
\(193\) 21.0278 1.51361 0.756806 0.653640i \(-0.226759\pi\)
0.756806 + 0.653640i \(0.226759\pi\)
\(194\) 0 0
\(195\) 1.60555 0.114976
\(196\) 0 0
\(197\) −25.9361 −1.84787 −0.923935 0.382550i \(-0.875046\pi\)
−0.923935 + 0.382550i \(0.875046\pi\)
\(198\) 0 0
\(199\) −1.90833 −0.135278 −0.0676389 0.997710i \(-0.521547\pi\)
−0.0676389 + 0.997710i \(0.521547\pi\)
\(200\) 0 0
\(201\) −13.3028 −0.938305
\(202\) 0 0
\(203\) 5.60555 0.393433
\(204\) 0 0
\(205\) −2.51388 −0.175577
\(206\) 0 0
\(207\) −1.00000 −0.0695048
\(208\) 0 0
\(209\) −2.21110 −0.152945
\(210\) 0 0
\(211\) 25.6056 1.76276 0.881379 0.472409i \(-0.156615\pi\)
0.881379 + 0.472409i \(0.156615\pi\)
\(212\) 0 0
\(213\) −12.9083 −0.884464
\(214\) 0 0
\(215\) −3.00000 −0.204598
\(216\) 0 0
\(217\) 3.60555 0.244761
\(218\) 0 0
\(219\) −11.0000 −0.743311
\(220\) 0 0
\(221\) −0.908327 −0.0611007
\(222\) 0 0
\(223\) 17.7250 1.18695 0.593476 0.804852i \(-0.297755\pi\)
0.593476 + 0.804852i \(0.297755\pi\)
\(224\) 0 0
\(225\) −4.51388 −0.300925
\(226\) 0 0
\(227\) 11.9083 0.790383 0.395192 0.918599i \(-0.370678\pi\)
0.395192 + 0.918599i \(0.370678\pi\)
\(228\) 0 0
\(229\) 3.11943 0.206138 0.103069 0.994674i \(-0.467134\pi\)
0.103069 + 0.994674i \(0.467134\pi\)
\(230\) 0 0
\(231\) 5.60555 0.368818
\(232\) 0 0
\(233\) 7.11943 0.466409 0.233205 0.972428i \(-0.425079\pi\)
0.233205 + 0.972428i \(0.425079\pi\)
\(234\) 0 0
\(235\) 3.21110 0.209469
\(236\) 0 0
\(237\) −13.4222 −0.871866
\(238\) 0 0
\(239\) 5.90833 0.382178 0.191089 0.981573i \(-0.438798\pi\)
0.191089 + 0.981573i \(0.438798\pi\)
\(240\) 0 0
\(241\) 8.21110 0.528924 0.264462 0.964396i \(-0.414806\pi\)
0.264462 + 0.964396i \(0.414806\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) −0.697224 −0.0445440
\(246\) 0 0
\(247\) −0.908327 −0.0577955
\(248\) 0 0
\(249\) −16.2111 −1.02734
\(250\) 0 0
\(251\) 4.18335 0.264050 0.132025 0.991246i \(-0.457852\pi\)
0.132025 + 0.991246i \(0.457852\pi\)
\(252\) 0 0
\(253\) −5.60555 −0.352418
\(254\) 0 0
\(255\) −0.275019 −0.0172224
\(256\) 0 0
\(257\) 25.8167 1.61040 0.805199 0.593004i \(-0.202058\pi\)
0.805199 + 0.593004i \(0.202058\pi\)
\(258\) 0 0
\(259\) −5.60555 −0.348312
\(260\) 0 0
\(261\) −5.60555 −0.346975
\(262\) 0 0
\(263\) −9.42221 −0.580998 −0.290499 0.956875i \(-0.593821\pi\)
−0.290499 + 0.956875i \(0.593821\pi\)
\(264\) 0 0
\(265\) −4.11943 −0.253055
\(266\) 0 0
\(267\) 15.5139 0.949434
\(268\) 0 0
\(269\) 12.1194 0.738935 0.369467 0.929244i \(-0.379540\pi\)
0.369467 + 0.929244i \(0.379540\pi\)
\(270\) 0 0
\(271\) −0.577795 −0.0350985 −0.0175493 0.999846i \(-0.505586\pi\)
−0.0175493 + 0.999846i \(0.505586\pi\)
\(272\) 0 0
\(273\) 2.30278 0.139370
\(274\) 0 0
\(275\) −25.3028 −1.52581
\(276\) 0 0
\(277\) 24.5416 1.47456 0.737282 0.675585i \(-0.236109\pi\)
0.737282 + 0.675585i \(0.236109\pi\)
\(278\) 0 0
\(279\) −3.60555 −0.215859
\(280\) 0 0
\(281\) 6.60555 0.394054 0.197027 0.980398i \(-0.436871\pi\)
0.197027 + 0.980398i \(0.436871\pi\)
\(282\) 0 0
\(283\) 25.3028 1.50409 0.752047 0.659110i \(-0.229067\pi\)
0.752047 + 0.659110i \(0.229067\pi\)
\(284\) 0 0
\(285\) −0.275019 −0.0162907
\(286\) 0 0
\(287\) −3.60555 −0.212829
\(288\) 0 0
\(289\) −16.8444 −0.990848
\(290\) 0 0
\(291\) −3.78890 −0.222109
\(292\) 0 0
\(293\) −18.7889 −1.09766 −0.548830 0.835934i \(-0.684926\pi\)
−0.548830 + 0.835934i \(0.684926\pi\)
\(294\) 0 0
\(295\) −2.72498 −0.158655
\(296\) 0 0
\(297\) −5.60555 −0.325267
\(298\) 0 0
\(299\) −2.30278 −0.133173
\(300\) 0 0
\(301\) −4.30278 −0.248008
\(302\) 0 0
\(303\) 12.5139 0.718904
\(304\) 0 0
\(305\) −3.42221 −0.195955
\(306\) 0 0
\(307\) −25.6056 −1.46139 −0.730693 0.682706i \(-0.760803\pi\)
−0.730693 + 0.682706i \(0.760803\pi\)
\(308\) 0 0
\(309\) −2.78890 −0.158655
\(310\) 0 0
\(311\) 10.1194 0.573820 0.286910 0.957958i \(-0.407372\pi\)
0.286910 + 0.957958i \(0.407372\pi\)
\(312\) 0 0
\(313\) −30.4222 −1.71956 −0.859782 0.510661i \(-0.829401\pi\)
−0.859782 + 0.510661i \(0.829401\pi\)
\(314\) 0 0
\(315\) 0.697224 0.0392841
\(316\) 0 0
\(317\) −12.6972 −0.713147 −0.356574 0.934267i \(-0.616055\pi\)
−0.356574 + 0.934267i \(0.616055\pi\)
\(318\) 0 0
\(319\) −31.4222 −1.75931
\(320\) 0 0
\(321\) −0.302776 −0.0168993
\(322\) 0 0
\(323\) 0.155590 0.00865725
\(324\) 0 0
\(325\) −10.3944 −0.576580
\(326\) 0 0
\(327\) 4.51388 0.249618
\(328\) 0 0
\(329\) 4.60555 0.253912
\(330\) 0 0
\(331\) −2.00000 −0.109930 −0.0549650 0.998488i \(-0.517505\pi\)
−0.0549650 + 0.998488i \(0.517505\pi\)
\(332\) 0 0
\(333\) 5.60555 0.307182
\(334\) 0 0
\(335\) −9.27502 −0.506748
\(336\) 0 0
\(337\) 16.7250 0.911068 0.455534 0.890218i \(-0.349448\pi\)
0.455534 + 0.890218i \(0.349448\pi\)
\(338\) 0 0
\(339\) −5.30278 −0.288007
\(340\) 0 0
\(341\) −20.2111 −1.09449
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 0 0
\(345\) −0.697224 −0.0375373
\(346\) 0 0
\(347\) 0.211103 0.0113326 0.00566629 0.999984i \(-0.498196\pi\)
0.00566629 + 0.999984i \(0.498196\pi\)
\(348\) 0 0
\(349\) 0.697224 0.0373216 0.0186608 0.999826i \(-0.494060\pi\)
0.0186608 + 0.999826i \(0.494060\pi\)
\(350\) 0 0
\(351\) −2.30278 −0.122913
\(352\) 0 0
\(353\) 15.6056 0.830600 0.415300 0.909685i \(-0.363677\pi\)
0.415300 + 0.909685i \(0.363677\pi\)
\(354\) 0 0
\(355\) −9.00000 −0.477670
\(356\) 0 0
\(357\) −0.394449 −0.0208764
\(358\) 0 0
\(359\) 9.90833 0.522941 0.261471 0.965211i \(-0.415793\pi\)
0.261471 + 0.965211i \(0.415793\pi\)
\(360\) 0 0
\(361\) −18.8444 −0.991811
\(362\) 0 0
\(363\) −20.4222 −1.07189
\(364\) 0 0
\(365\) −7.66947 −0.401438
\(366\) 0 0
\(367\) 25.5139 1.33181 0.665907 0.746035i \(-0.268045\pi\)
0.665907 + 0.746035i \(0.268045\pi\)
\(368\) 0 0
\(369\) 3.60555 0.187698
\(370\) 0 0
\(371\) −5.90833 −0.306745
\(372\) 0 0
\(373\) 11.1833 0.579052 0.289526 0.957170i \(-0.406502\pi\)
0.289526 + 0.957170i \(0.406502\pi\)
\(374\) 0 0
\(375\) −6.63331 −0.342543
\(376\) 0 0
\(377\) −12.9083 −0.664813
\(378\) 0 0
\(379\) −10.4222 −0.535353 −0.267676 0.963509i \(-0.586256\pi\)
−0.267676 + 0.963509i \(0.586256\pi\)
\(380\) 0 0
\(381\) −18.1194 −0.928286
\(382\) 0 0
\(383\) −26.6333 −1.36090 −0.680449 0.732795i \(-0.738215\pi\)
−0.680449 + 0.732795i \(0.738215\pi\)
\(384\) 0 0
\(385\) 3.90833 0.199187
\(386\) 0 0
\(387\) 4.30278 0.218722
\(388\) 0 0
\(389\) −12.6333 −0.640534 −0.320267 0.947327i \(-0.603773\pi\)
−0.320267 + 0.947327i \(0.603773\pi\)
\(390\) 0 0
\(391\) 0.394449 0.0199481
\(392\) 0 0
\(393\) 6.81665 0.343855
\(394\) 0 0
\(395\) −9.35829 −0.470867
\(396\) 0 0
\(397\) −8.60555 −0.431900 −0.215950 0.976404i \(-0.569285\pi\)
−0.215950 + 0.976404i \(0.569285\pi\)
\(398\) 0 0
\(399\) −0.394449 −0.0197471
\(400\) 0 0
\(401\) −26.6333 −1.33000 −0.665002 0.746842i \(-0.731569\pi\)
−0.665002 + 0.746842i \(0.731569\pi\)
\(402\) 0 0
\(403\) −8.30278 −0.413591
\(404\) 0 0
\(405\) −0.697224 −0.0346454
\(406\) 0 0
\(407\) 31.4222 1.55754
\(408\) 0 0
\(409\) 8.39445 0.415079 0.207539 0.978227i \(-0.433454\pi\)
0.207539 + 0.978227i \(0.433454\pi\)
\(410\) 0 0
\(411\) 5.60555 0.276501
\(412\) 0 0
\(413\) −3.90833 −0.192316
\(414\) 0 0
\(415\) −11.3028 −0.554831
\(416\) 0 0
\(417\) 15.1194 0.740402
\(418\) 0 0
\(419\) −11.9083 −0.581760 −0.290880 0.956760i \(-0.593948\pi\)
−0.290880 + 0.956760i \(0.593948\pi\)
\(420\) 0 0
\(421\) −7.09167 −0.345627 −0.172813 0.984955i \(-0.555286\pi\)
−0.172813 + 0.984955i \(0.555286\pi\)
\(422\) 0 0
\(423\) −4.60555 −0.223930
\(424\) 0 0
\(425\) 1.78049 0.0863666
\(426\) 0 0
\(427\) −4.90833 −0.237531
\(428\) 0 0
\(429\) −12.9083 −0.623220
\(430\) 0 0
\(431\) −4.30278 −0.207257 −0.103629 0.994616i \(-0.533045\pi\)
−0.103629 + 0.994616i \(0.533045\pi\)
\(432\) 0 0
\(433\) 23.8167 1.14456 0.572278 0.820060i \(-0.306060\pi\)
0.572278 + 0.820060i \(0.306060\pi\)
\(434\) 0 0
\(435\) −3.90833 −0.187390
\(436\) 0 0
\(437\) 0.394449 0.0188690
\(438\) 0 0
\(439\) −27.6056 −1.31754 −0.658771 0.752344i \(-0.728923\pi\)
−0.658771 + 0.752344i \(0.728923\pi\)
\(440\) 0 0
\(441\) 1.00000 0.0476190
\(442\) 0 0
\(443\) −6.78890 −0.322550 −0.161275 0.986909i \(-0.551561\pi\)
−0.161275 + 0.986909i \(0.551561\pi\)
\(444\) 0 0
\(445\) 10.8167 0.512759
\(446\) 0 0
\(447\) 15.3944 0.728132
\(448\) 0 0
\(449\) −7.11943 −0.335987 −0.167993 0.985788i \(-0.553729\pi\)
−0.167993 + 0.985788i \(0.553729\pi\)
\(450\) 0 0
\(451\) 20.2111 0.951704
\(452\) 0 0
\(453\) −8.60555 −0.404324
\(454\) 0 0
\(455\) 1.60555 0.0752694
\(456\) 0 0
\(457\) −20.6972 −0.968175 −0.484088 0.875020i \(-0.660848\pi\)
−0.484088 + 0.875020i \(0.660848\pi\)
\(458\) 0 0
\(459\) 0.394449 0.0184113
\(460\) 0 0
\(461\) −26.0917 −1.21521 −0.607605 0.794239i \(-0.707870\pi\)
−0.607605 + 0.794239i \(0.707870\pi\)
\(462\) 0 0
\(463\) 17.0000 0.790057 0.395029 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) 0 0
\(465\) −2.51388 −0.116578
\(466\) 0 0
\(467\) −23.8444 −1.10339 −0.551694 0.834047i \(-0.686018\pi\)
−0.551694 + 0.834047i \(0.686018\pi\)
\(468\) 0 0
\(469\) −13.3028 −0.614265
\(470\) 0 0
\(471\) −11.8167 −0.544483
\(472\) 0 0
\(473\) 24.1194 1.10901
\(474\) 0 0
\(475\) 1.78049 0.0816946
\(476\) 0 0
\(477\) 5.90833 0.270524
\(478\) 0 0
\(479\) −27.2389 −1.24458 −0.622288 0.782789i \(-0.713797\pi\)
−0.622288 + 0.782789i \(0.713797\pi\)
\(480\) 0 0
\(481\) 12.9083 0.588569
\(482\) 0 0
\(483\) −1.00000 −0.0455016
\(484\) 0 0
\(485\) −2.64171 −0.119954
\(486\) 0 0
\(487\) 4.21110 0.190823 0.0954116 0.995438i \(-0.469583\pi\)
0.0954116 + 0.995438i \(0.469583\pi\)
\(488\) 0 0
\(489\) 9.11943 0.412395
\(490\) 0 0
\(491\) 34.9083 1.57539 0.787695 0.616065i \(-0.211274\pi\)
0.787695 + 0.616065i \(0.211274\pi\)
\(492\) 0 0
\(493\) 2.21110 0.0995831
\(494\) 0 0
\(495\) −3.90833 −0.175666
\(496\) 0 0
\(497\) −12.9083 −0.579018
\(498\) 0 0
\(499\) 12.8806 0.576614 0.288307 0.957538i \(-0.406908\pi\)
0.288307 + 0.957538i \(0.406908\pi\)
\(500\) 0 0
\(501\) 14.0278 0.626714
\(502\) 0 0
\(503\) 21.1194 0.941669 0.470834 0.882222i \(-0.343953\pi\)
0.470834 + 0.882222i \(0.343953\pi\)
\(504\) 0 0
\(505\) 8.72498 0.388257
\(506\) 0 0
\(507\) 7.69722 0.341846
\(508\) 0 0
\(509\) −19.3944 −0.859644 −0.429822 0.902914i \(-0.641424\pi\)
−0.429822 + 0.902914i \(0.641424\pi\)
\(510\) 0 0
\(511\) −11.0000 −0.486611
\(512\) 0 0
\(513\) 0.394449 0.0174153
\(514\) 0 0
\(515\) −1.94449 −0.0856843
\(516\) 0 0
\(517\) −25.8167 −1.13542
\(518\) 0 0
\(519\) 6.39445 0.280685
\(520\) 0 0
\(521\) 4.78890 0.209805 0.104903 0.994482i \(-0.466547\pi\)
0.104903 + 0.994482i \(0.466547\pi\)
\(522\) 0 0
\(523\) 31.2111 1.36477 0.682383 0.730995i \(-0.260944\pi\)
0.682383 + 0.730995i \(0.260944\pi\)
\(524\) 0 0
\(525\) −4.51388 −0.197002
\(526\) 0 0
\(527\) 1.42221 0.0619522
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) 3.90833 0.169607
\(532\) 0 0
\(533\) 8.30278 0.359633
\(534\) 0 0
\(535\) −0.211103 −0.00912676
\(536\) 0 0
\(537\) −24.9361 −1.07607
\(538\) 0 0
\(539\) 5.60555 0.241448
\(540\) 0 0
\(541\) 27.0278 1.16201 0.581007 0.813899i \(-0.302659\pi\)
0.581007 + 0.813899i \(0.302659\pi\)
\(542\) 0 0
\(543\) 19.0000 0.815368
\(544\) 0 0
\(545\) 3.14719 0.134811
\(546\) 0 0
\(547\) −28.3305 −1.21133 −0.605663 0.795721i \(-0.707092\pi\)
−0.605663 + 0.795721i \(0.707092\pi\)
\(548\) 0 0
\(549\) 4.90833 0.209482
\(550\) 0 0
\(551\) 2.21110 0.0941961
\(552\) 0 0
\(553\) −13.4222 −0.570770
\(554\) 0 0
\(555\) 3.90833 0.165899
\(556\) 0 0
\(557\) 16.1833 0.685710 0.342855 0.939388i \(-0.388606\pi\)
0.342855 + 0.939388i \(0.388606\pi\)
\(558\) 0 0
\(559\) 9.90833 0.419078
\(560\) 0 0
\(561\) 2.21110 0.0933528
\(562\) 0 0
\(563\) −38.5416 −1.62434 −0.812168 0.583423i \(-0.801713\pi\)
−0.812168 + 0.583423i \(0.801713\pi\)
\(564\) 0 0
\(565\) −3.69722 −0.155543
\(566\) 0 0
\(567\) −1.00000 −0.0419961
\(568\) 0 0
\(569\) −14.7889 −0.619983 −0.309991 0.950739i \(-0.600326\pi\)
−0.309991 + 0.950739i \(0.600326\pi\)
\(570\) 0 0
\(571\) −29.7889 −1.24663 −0.623313 0.781972i \(-0.714214\pi\)
−0.623313 + 0.781972i \(0.714214\pi\)
\(572\) 0 0
\(573\) 8.60555 0.359502
\(574\) 0 0
\(575\) 4.51388 0.188242
\(576\) 0 0
\(577\) 14.0000 0.582828 0.291414 0.956597i \(-0.405874\pi\)
0.291414 + 0.956597i \(0.405874\pi\)
\(578\) 0 0
\(579\) −21.0278 −0.873884
\(580\) 0 0
\(581\) −16.2111 −0.672550
\(582\) 0 0
\(583\) 33.1194 1.37167
\(584\) 0 0
\(585\) −1.60555 −0.0663814
\(586\) 0 0
\(587\) −35.5139 −1.46581 −0.732907 0.680329i \(-0.761837\pi\)
−0.732907 + 0.680329i \(0.761837\pi\)
\(588\) 0 0
\(589\) 1.42221 0.0586009
\(590\) 0 0
\(591\) 25.9361 1.06687
\(592\) 0 0
\(593\) 21.3944 0.878565 0.439282 0.898349i \(-0.355233\pi\)
0.439282 + 0.898349i \(0.355233\pi\)
\(594\) 0 0
\(595\) −0.275019 −0.0112747
\(596\) 0 0
\(597\) 1.90833 0.0781026
\(598\) 0 0
\(599\) 26.5416 1.08446 0.542231 0.840230i \(-0.317580\pi\)
0.542231 + 0.840230i \(0.317580\pi\)
\(600\) 0 0
\(601\) −27.5416 −1.12345 −0.561723 0.827325i \(-0.689861\pi\)
−0.561723 + 0.827325i \(0.689861\pi\)
\(602\) 0 0
\(603\) 13.3028 0.541731
\(604\) 0 0
\(605\) −14.2389 −0.578892
\(606\) 0 0
\(607\) −20.5416 −0.833759 −0.416880 0.908962i \(-0.636876\pi\)
−0.416880 + 0.908962i \(0.636876\pi\)
\(608\) 0 0
\(609\) −5.60555 −0.227148
\(610\) 0 0
\(611\) −10.6056 −0.429055
\(612\) 0 0
\(613\) −28.6333 −1.15649 −0.578244 0.815864i \(-0.696262\pi\)
−0.578244 + 0.815864i \(0.696262\pi\)
\(614\) 0 0
\(615\) 2.51388 0.101369
\(616\) 0 0
\(617\) 20.3028 0.817359 0.408679 0.912678i \(-0.365989\pi\)
0.408679 + 0.912678i \(0.365989\pi\)
\(618\) 0 0
\(619\) 40.3028 1.61991 0.809953 0.586495i \(-0.199493\pi\)
0.809953 + 0.586495i \(0.199493\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 15.5139 0.621550
\(624\) 0 0
\(625\) 17.9445 0.717779
\(626\) 0 0
\(627\) 2.21110 0.0883029
\(628\) 0 0
\(629\) −2.21110 −0.0881624
\(630\) 0 0
\(631\) 16.3944 0.652653 0.326326 0.945257i \(-0.394189\pi\)
0.326326 + 0.945257i \(0.394189\pi\)
\(632\) 0 0
\(633\) −25.6056 −1.01773
\(634\) 0 0
\(635\) −12.6333 −0.501338
\(636\) 0 0
\(637\) 2.30278 0.0912393
\(638\) 0 0
\(639\) 12.9083 0.510646
\(640\) 0 0
\(641\) −30.5416 −1.20632 −0.603161 0.797619i \(-0.706092\pi\)
−0.603161 + 0.797619i \(0.706092\pi\)
\(642\) 0 0
\(643\) 19.0917 0.752902 0.376451 0.926437i \(-0.377144\pi\)
0.376451 + 0.926437i \(0.377144\pi\)
\(644\) 0 0
\(645\) 3.00000 0.118125
\(646\) 0 0
\(647\) −16.5139 −0.649228 −0.324614 0.945847i \(-0.605234\pi\)
−0.324614 + 0.945847i \(0.605234\pi\)
\(648\) 0 0
\(649\) 21.9083 0.859977
\(650\) 0 0
\(651\) −3.60555 −0.141313
\(652\) 0 0
\(653\) 17.9083 0.700807 0.350403 0.936599i \(-0.386044\pi\)
0.350403 + 0.936599i \(0.386044\pi\)
\(654\) 0 0
\(655\) 4.75274 0.185705
\(656\) 0 0
\(657\) 11.0000 0.429151
\(658\) 0 0
\(659\) −13.1833 −0.513550 −0.256775 0.966471i \(-0.582660\pi\)
−0.256775 + 0.966471i \(0.582660\pi\)
\(660\) 0 0
\(661\) −5.42221 −0.210899 −0.105450 0.994425i \(-0.533628\pi\)
−0.105450 + 0.994425i \(0.533628\pi\)
\(662\) 0 0
\(663\) 0.908327 0.0352765
\(664\) 0 0
\(665\) −0.275019 −0.0106648
\(666\) 0 0
\(667\) 5.60555 0.217048
\(668\) 0 0
\(669\) −17.7250 −0.685287
\(670\) 0 0
\(671\) 27.5139 1.06216
\(672\) 0 0
\(673\) 5.00000 0.192736 0.0963679 0.995346i \(-0.469277\pi\)
0.0963679 + 0.995346i \(0.469277\pi\)
\(674\) 0 0
\(675\) 4.51388 0.173739
\(676\) 0 0
\(677\) −30.1194 −1.15758 −0.578792 0.815475i \(-0.696476\pi\)
−0.578792 + 0.815475i \(0.696476\pi\)
\(678\) 0 0
\(679\) −3.78890 −0.145405
\(680\) 0 0
\(681\) −11.9083 −0.456328
\(682\) 0 0
\(683\) −30.6333 −1.17215 −0.586075 0.810256i \(-0.699328\pi\)
−0.586075 + 0.810256i \(0.699328\pi\)
\(684\) 0 0
\(685\) 3.90833 0.149329
\(686\) 0 0
\(687\) −3.11943 −0.119014
\(688\) 0 0
\(689\) 13.6056 0.518330
\(690\) 0 0
\(691\) −3.09167 −0.117613 −0.0588064 0.998269i \(-0.518729\pi\)
−0.0588064 + 0.998269i \(0.518729\pi\)
\(692\) 0 0
\(693\) −5.60555 −0.212937
\(694\) 0 0
\(695\) 10.5416 0.399867
\(696\) 0 0
\(697\) −1.42221 −0.0538699
\(698\) 0 0
\(699\) −7.11943 −0.269282
\(700\) 0 0
\(701\) 18.9361 0.715206 0.357603 0.933874i \(-0.383594\pi\)
0.357603 + 0.933874i \(0.383594\pi\)
\(702\) 0 0
\(703\) −2.21110 −0.0833933
\(704\) 0 0
\(705\) −3.21110 −0.120937
\(706\) 0 0
\(707\) 12.5139 0.470633
\(708\) 0 0
\(709\) −20.1194 −0.755601 −0.377801 0.925887i \(-0.623319\pi\)
−0.377801 + 0.925887i \(0.623319\pi\)
\(710\) 0 0
\(711\) 13.4222 0.503372
\(712\) 0 0
\(713\) 3.60555 0.135029
\(714\) 0 0
\(715\) −9.00000 −0.336581
\(716\) 0 0
\(717\) −5.90833 −0.220651
\(718\) 0 0
\(719\) 41.8444 1.56053 0.780267 0.625447i \(-0.215083\pi\)
0.780267 + 0.625447i \(0.215083\pi\)
\(720\) 0 0
\(721\) −2.78890 −0.103864
\(722\) 0 0
\(723\) −8.21110 −0.305374
\(724\) 0 0
\(725\) 25.3028 0.939721
\(726\) 0 0
\(727\) −6.39445 −0.237157 −0.118578 0.992945i \(-0.537834\pi\)
−0.118578 + 0.992945i \(0.537834\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −1.69722 −0.0627741
\(732\) 0 0
\(733\) −37.0278 −1.36765 −0.683826 0.729645i \(-0.739685\pi\)
−0.683826 + 0.729645i \(0.739685\pi\)
\(734\) 0 0
\(735\) 0.697224 0.0257175
\(736\) 0 0
\(737\) 74.5694 2.74680
\(738\) 0 0
\(739\) −36.8167 −1.35432 −0.677161 0.735835i \(-0.736790\pi\)
−0.677161 + 0.735835i \(0.736790\pi\)
\(740\) 0 0
\(741\) 0.908327 0.0333682
\(742\) 0 0
\(743\) 27.4861 1.00837 0.504184 0.863596i \(-0.331793\pi\)
0.504184 + 0.863596i \(0.331793\pi\)
\(744\) 0 0
\(745\) 10.7334 0.393241
\(746\) 0 0
\(747\) 16.2111 0.593133
\(748\) 0 0
\(749\) −0.302776 −0.0110632
\(750\) 0 0
\(751\) −42.9361 −1.56676 −0.783380 0.621543i \(-0.786506\pi\)
−0.783380 + 0.621543i \(0.786506\pi\)
\(752\) 0 0
\(753\) −4.18335 −0.152450
\(754\) 0 0
\(755\) −6.00000 −0.218362
\(756\) 0 0
\(757\) 20.8167 0.756594 0.378297 0.925684i \(-0.376510\pi\)
0.378297 + 0.925684i \(0.376510\pi\)
\(758\) 0 0
\(759\) 5.60555 0.203469
\(760\) 0 0
\(761\) −15.6333 −0.566707 −0.283353 0.959016i \(-0.591447\pi\)
−0.283353 + 0.959016i \(0.591447\pi\)
\(762\) 0 0
\(763\) 4.51388 0.163413
\(764\) 0 0
\(765\) 0.275019 0.00994334
\(766\) 0 0
\(767\) 9.00000 0.324971
\(768\) 0 0
\(769\) 11.8167 0.426119 0.213060 0.977039i \(-0.431657\pi\)
0.213060 + 0.977039i \(0.431657\pi\)
\(770\) 0 0
\(771\) −25.8167 −0.929764
\(772\) 0 0
\(773\) −2.21110 −0.0795278 −0.0397639 0.999209i \(-0.512661\pi\)
−0.0397639 + 0.999209i \(0.512661\pi\)
\(774\) 0 0
\(775\) 16.2750 0.584616
\(776\) 0 0
\(777\) 5.60555 0.201098
\(778\) 0 0
\(779\) −1.42221 −0.0509558
\(780\) 0 0
\(781\) 72.3583 2.58918
\(782\) 0 0
\(783\) 5.60555 0.200326
\(784\) 0 0
\(785\) −8.23886 −0.294057
\(786\) 0 0
\(787\) −31.1194 −1.10929 −0.554644 0.832088i \(-0.687146\pi\)
−0.554644 + 0.832088i \(0.687146\pi\)
\(788\) 0 0
\(789\) 9.42221 0.335439
\(790\) 0 0
\(791\) −5.30278 −0.188545
\(792\) 0 0
\(793\) 11.3028 0.401373
\(794\) 0 0
\(795\) 4.11943 0.146101
\(796\) 0 0
\(797\) −49.8167 −1.76460 −0.882298 0.470691i \(-0.844005\pi\)
−0.882298 + 0.470691i \(0.844005\pi\)
\(798\) 0 0
\(799\) 1.81665 0.0642686
\(800\) 0 0
\(801\) −15.5139 −0.548156
\(802\) 0 0
\(803\) 61.6611 2.17597
\(804\) 0 0
\(805\) −0.697224 −0.0245739
\(806\) 0 0
\(807\) −12.1194 −0.426624
\(808\) 0 0
\(809\) 25.5139 0.897020 0.448510 0.893778i \(-0.351955\pi\)
0.448510 + 0.893778i \(0.351955\pi\)
\(810\) 0 0
\(811\) 10.6333 0.373386 0.186693 0.982418i \(-0.440223\pi\)
0.186693 + 0.982418i \(0.440223\pi\)
\(812\) 0 0
\(813\) 0.577795 0.0202642
\(814\) 0 0
\(815\) 6.35829 0.222721
\(816\) 0 0
\(817\) −1.69722 −0.0593784
\(818\) 0 0
\(819\) −2.30278 −0.0804655
\(820\) 0 0
\(821\) −17.4500 −0.609008 −0.304504 0.952511i \(-0.598491\pi\)
−0.304504 + 0.952511i \(0.598491\pi\)
\(822\) 0 0
\(823\) −48.5139 −1.69109 −0.845544 0.533906i \(-0.820724\pi\)
−0.845544 + 0.533906i \(0.820724\pi\)
\(824\) 0 0
\(825\) 25.3028 0.880930
\(826\) 0 0
\(827\) 22.6972 0.789260 0.394630 0.918840i \(-0.370873\pi\)
0.394630 + 0.918840i \(0.370873\pi\)
\(828\) 0 0
\(829\) 1.18335 0.0410993 0.0205497 0.999789i \(-0.493458\pi\)
0.0205497 + 0.999789i \(0.493458\pi\)
\(830\) 0 0
\(831\) −24.5416 −0.851340
\(832\) 0 0
\(833\) −0.394449 −0.0136668
\(834\) 0 0
\(835\) 9.78049 0.338468
\(836\) 0 0
\(837\) 3.60555 0.124626
\(838\) 0 0
\(839\) −28.5416 −0.985367 −0.492683 0.870209i \(-0.663984\pi\)
−0.492683 + 0.870209i \(0.663984\pi\)
\(840\) 0 0
\(841\) 2.42221 0.0835243
\(842\) 0 0
\(843\) −6.60555 −0.227507
\(844\) 0 0
\(845\) 5.36669 0.184620
\(846\) 0 0
\(847\) −20.4222 −0.701715
\(848\) 0 0
\(849\) −25.3028 −0.868389
\(850\) 0 0
\(851\) −5.60555 −0.192156
\(852\) 0 0
\(853\) −2.60555 −0.0892124 −0.0446062 0.999005i \(-0.514203\pi\)
−0.0446062 + 0.999005i \(0.514203\pi\)
\(854\) 0 0
\(855\) 0.275019 0.00940546
\(856\) 0 0
\(857\) 9.02776 0.308382 0.154191 0.988041i \(-0.450723\pi\)
0.154191 + 0.988041i \(0.450723\pi\)
\(858\) 0 0
\(859\) 28.0555 0.957242 0.478621 0.878022i \(-0.341137\pi\)
0.478621 + 0.878022i \(0.341137\pi\)
\(860\) 0 0
\(861\) 3.60555 0.122877
\(862\) 0 0
\(863\) −11.8167 −0.402244 −0.201122 0.979566i \(-0.564459\pi\)
−0.201122 + 0.979566i \(0.564459\pi\)
\(864\) 0 0
\(865\) 4.45837 0.151589
\(866\) 0 0
\(867\) 16.8444 0.572066
\(868\) 0 0
\(869\) 75.2389 2.55230
\(870\) 0 0
\(871\) 30.6333 1.03797
\(872\) 0 0
\(873\) 3.78890 0.128235
\(874\) 0 0
\(875\) −6.63331 −0.224247
\(876\) 0 0
\(877\) −32.0000 −1.08056 −0.540282 0.841484i \(-0.681682\pi\)
−0.540282 + 0.841484i \(0.681682\pi\)
\(878\) 0 0
\(879\) 18.7889 0.633734
\(880\) 0 0
\(881\) −2.23886 −0.0754291 −0.0377145 0.999289i \(-0.512008\pi\)
−0.0377145 + 0.999289i \(0.512008\pi\)
\(882\) 0 0
\(883\) −6.90833 −0.232484 −0.116242 0.993221i \(-0.537085\pi\)
−0.116242 + 0.993221i \(0.537085\pi\)
\(884\) 0 0
\(885\) 2.72498 0.0915992
\(886\) 0 0
\(887\) −1.51388 −0.0508311 −0.0254155 0.999677i \(-0.508091\pi\)
−0.0254155 + 0.999677i \(0.508091\pi\)
\(888\) 0 0
\(889\) −18.1194 −0.607706
\(890\) 0 0
\(891\) 5.60555 0.187793
\(892\) 0 0
\(893\) 1.81665 0.0607920
\(894\) 0 0
\(895\) −17.3860 −0.581151
\(896\) 0 0
\(897\) 2.30278 0.0768874
\(898\) 0 0
\(899\) 20.2111 0.674078
\(900\) 0 0
\(901\) −2.33053 −0.0776413
\(902\) 0 0
\(903\) 4.30278 0.143187
\(904\) 0 0
\(905\) 13.2473 0.440354
\(906\) 0 0
\(907\) −49.7250 −1.65109 −0.825545 0.564336i \(-0.809132\pi\)
−0.825545 + 0.564336i \(0.809132\pi\)
\(908\) 0 0
\(909\) −12.5139 −0.415059
\(910\) 0 0
\(911\) 24.6056 0.815218 0.407609 0.913156i \(-0.366363\pi\)
0.407609 + 0.913156i \(0.366363\pi\)
\(912\) 0 0
\(913\) 90.8722 3.00743
\(914\) 0 0
\(915\) 3.42221 0.113135
\(916\) 0 0
\(917\) 6.81665 0.225106
\(918\) 0 0
\(919\) 8.02776 0.264811 0.132406 0.991196i \(-0.457730\pi\)
0.132406 + 0.991196i \(0.457730\pi\)
\(920\) 0 0
\(921\) 25.6056 0.843732
\(922\) 0 0
\(923\) 29.7250 0.978410
\(924\) 0 0
\(925\) −25.3028 −0.831950
\(926\) 0 0
\(927\) 2.78890 0.0915994
\(928\) 0 0
\(929\) −34.6972 −1.13838 −0.569190 0.822206i \(-0.692743\pi\)
−0.569190 + 0.822206i \(0.692743\pi\)
\(930\) 0 0
\(931\) −0.394449 −0.0129275
\(932\) 0 0
\(933\) −10.1194 −0.331295
\(934\) 0 0
\(935\) 1.54163 0.0504168
\(936\) 0 0
\(937\) −5.97224 −0.195105 −0.0975523 0.995230i \(-0.531101\pi\)
−0.0975523 + 0.995230i \(0.531101\pi\)
\(938\) 0 0
\(939\) 30.4222 0.992791
\(940\) 0 0
\(941\) −5.21110 −0.169877 −0.0849385 0.996386i \(-0.527069\pi\)
−0.0849385 + 0.996386i \(0.527069\pi\)
\(942\) 0 0
\(943\) −3.60555 −0.117413
\(944\) 0 0
\(945\) −0.697224 −0.0226807
\(946\) 0 0
\(947\) −18.8444 −0.612361 −0.306181 0.951973i \(-0.599051\pi\)
−0.306181 + 0.951973i \(0.599051\pi\)
\(948\) 0 0
\(949\) 25.3305 0.822264
\(950\) 0 0
\(951\) 12.6972 0.411736
\(952\) 0 0
\(953\) 26.7250 0.865707 0.432854 0.901464i \(-0.357507\pi\)
0.432854 + 0.901464i \(0.357507\pi\)
\(954\) 0 0
\(955\) 6.00000 0.194155
\(956\) 0 0
\(957\) 31.4222 1.01574
\(958\) 0 0
\(959\) 5.60555 0.181013
\(960\) 0 0
\(961\) −18.0000 −0.580645
\(962\) 0 0
\(963\) 0.302776 0.00975681
\(964\) 0 0
\(965\) −14.6611 −0.471956
\(966\) 0 0
\(967\) −16.0555 −0.516310 −0.258155 0.966103i \(-0.583115\pi\)
−0.258155 + 0.966103i \(0.583115\pi\)
\(968\) 0 0
\(969\) −0.155590 −0.00499826
\(970\) 0 0
\(971\) 6.06392 0.194600 0.0973002 0.995255i \(-0.468979\pi\)
0.0973002 + 0.995255i \(0.468979\pi\)
\(972\) 0 0
\(973\) 15.1194 0.484707
\(974\) 0 0
\(975\) 10.3944 0.332889
\(976\) 0 0
\(977\) −13.6972 −0.438213 −0.219107 0.975701i \(-0.570314\pi\)
−0.219107 + 0.975701i \(0.570314\pi\)
\(978\) 0 0
\(979\) −86.9638 −2.77938
\(980\) 0 0
\(981\) −4.51388 −0.144117
\(982\) 0 0
\(983\) 2.57779 0.0822189 0.0411094 0.999155i \(-0.486911\pi\)
0.0411094 + 0.999155i \(0.486911\pi\)
\(984\) 0 0
\(985\) 18.0833 0.576181
\(986\) 0 0
\(987\) −4.60555 −0.146596
\(988\) 0 0
\(989\) −4.30278 −0.136820
\(990\) 0 0
\(991\) −30.9638 −0.983599 −0.491799 0.870709i \(-0.663661\pi\)
−0.491799 + 0.870709i \(0.663661\pi\)
\(992\) 0 0
\(993\) 2.00000 0.0634681
\(994\) 0 0
\(995\) 1.33053 0.0421807
\(996\) 0 0
\(997\) −3.18335 −0.100818 −0.0504088 0.998729i \(-0.516052\pi\)
−0.0504088 + 0.998729i \(0.516052\pi\)
\(998\) 0 0
\(999\) −5.60555 −0.177352
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 1932.2.a.c.1.2 2
3.2 odd 2 5796.2.a.m.1.1 2
4.3 odd 2 7728.2.a.bf.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1932.2.a.c.1.2 2 1.1 even 1 trivial
5796.2.a.m.1.1 2 3.2 odd 2
7728.2.a.bf.1.2 2 4.3 odd 2