Properties

Label 4598.2.a.e.1.1
Level $4598$
Weight $2$
Character 4598.1
Self dual yes
Analytic conductor $36.715$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4598.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(36.7152148494\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4598.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -3.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -3.00000 q^{7} -1.00000 q^{8} -3.00000 q^{9} -1.00000 q^{13} +3.00000 q^{14} +1.00000 q^{16} -5.00000 q^{17} +3.00000 q^{18} -1.00000 q^{19} +5.00000 q^{23} -5.00000 q^{25} +1.00000 q^{26} -3.00000 q^{28} -6.00000 q^{29} +2.00000 q^{31} -1.00000 q^{32} +5.00000 q^{34} -3.00000 q^{36} -3.00000 q^{37} +1.00000 q^{38} +2.00000 q^{41} +4.00000 q^{43} -5.00000 q^{46} -3.00000 q^{47} +2.00000 q^{49} +5.00000 q^{50} -1.00000 q^{52} +2.00000 q^{53} +3.00000 q^{56} +6.00000 q^{58} +1.00000 q^{59} -2.00000 q^{62} +9.00000 q^{63} +1.00000 q^{64} +3.00000 q^{67} -5.00000 q^{68} -4.00000 q^{71} +3.00000 q^{72} -15.0000 q^{73} +3.00000 q^{74} -1.00000 q^{76} -10.0000 q^{79} +9.00000 q^{81} -2.00000 q^{82} -4.00000 q^{86} +6.00000 q^{89} +3.00000 q^{91} +5.00000 q^{92} +3.00000 q^{94} +2.00000 q^{97} -2.00000 q^{98} +O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(6\) 0 0
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) −1.00000 −0.353553
\(9\) −3.00000 −1.00000
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) 3.00000 0.801784
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −5.00000 −1.21268 −0.606339 0.795206i \(-0.707363\pi\)
−0.606339 + 0.795206i \(0.707363\pi\)
\(18\) 3.00000 0.707107
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.00000 1.04257 0.521286 0.853382i \(-0.325452\pi\)
0.521286 + 0.853382i \(0.325452\pi\)
\(24\) 0 0
\(25\) −5.00000 −1.00000
\(26\) 1.00000 0.196116
\(27\) 0 0
\(28\) −3.00000 −0.566947
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 5.00000 0.857493
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) −3.00000 −0.493197 −0.246598 0.969118i \(-0.579313\pi\)
−0.246598 + 0.969118i \(0.579313\pi\)
\(38\) 1.00000 0.162221
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −5.00000 −0.737210
\(47\) −3.00000 −0.437595 −0.218797 0.975770i \(-0.570213\pi\)
−0.218797 + 0.975770i \(0.570213\pi\)
\(48\) 0 0
\(49\) 2.00000 0.285714
\(50\) 5.00000 0.707107
\(51\) 0 0
\(52\) −1.00000 −0.138675
\(53\) 2.00000 0.274721 0.137361 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 3.00000 0.400892
\(57\) 0 0
\(58\) 6.00000 0.787839
\(59\) 1.00000 0.130189 0.0650945 0.997879i \(-0.479265\pi\)
0.0650945 + 0.997879i \(0.479265\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) −2.00000 −0.254000
\(63\) 9.00000 1.13389
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 3.00000 0.366508 0.183254 0.983066i \(-0.441337\pi\)
0.183254 + 0.983066i \(0.441337\pi\)
\(68\) −5.00000 −0.606339
\(69\) 0 0
\(70\) 0 0
\(71\) −4.00000 −0.474713 −0.237356 0.971423i \(-0.576281\pi\)
−0.237356 + 0.971423i \(0.576281\pi\)
\(72\) 3.00000 0.353553
\(73\) −15.0000 −1.75562 −0.877809 0.479012i \(-0.840995\pi\)
−0.877809 + 0.479012i \(0.840995\pi\)
\(74\) 3.00000 0.348743
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 0 0
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 9.00000 1.00000
\(82\) −2.00000 −0.220863
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) 0 0
\(89\) 6.00000 0.635999 0.317999 0.948091i \(-0.396989\pi\)
0.317999 + 0.948091i \(0.396989\pi\)
\(90\) 0 0
\(91\) 3.00000 0.314485
\(92\) 5.00000 0.521286
\(93\) 0 0
\(94\) 3.00000 0.309426
\(95\) 0 0
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) −2.00000 −0.202031
\(99\) 0 0
\(100\) −5.00000 −0.500000
\(101\) −10.0000 −0.995037 −0.497519 0.867453i \(-0.665755\pi\)
−0.497519 + 0.867453i \(0.665755\pi\)
\(102\) 0 0
\(103\) 14.0000 1.37946 0.689730 0.724066i \(-0.257729\pi\)
0.689730 + 0.724066i \(0.257729\pi\)
\(104\) 1.00000 0.0980581
\(105\) 0 0
\(106\) −2.00000 −0.194257
\(107\) 3.00000 0.290021 0.145010 0.989430i \(-0.453678\pi\)
0.145010 + 0.989430i \(0.453678\pi\)
\(108\) 0 0
\(109\) 17.0000 1.62830 0.814152 0.580651i \(-0.197202\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −3.00000 −0.283473
\(113\) 16.0000 1.50515 0.752577 0.658505i \(-0.228811\pi\)
0.752577 + 0.658505i \(0.228811\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 3.00000 0.277350
\(118\) −1.00000 −0.0920575
\(119\) 15.0000 1.37505
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) 2.00000 0.179605
\(125\) 0 0
\(126\) −9.00000 −0.801784
\(127\) 10.0000 0.887357 0.443678 0.896186i \(-0.353673\pi\)
0.443678 + 0.896186i \(0.353673\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 0 0
\(133\) 3.00000 0.260133
\(134\) −3.00000 −0.259161
\(135\) 0 0
\(136\) 5.00000 0.428746
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 4.00000 0.335673
\(143\) 0 0
\(144\) −3.00000 −0.250000
\(145\) 0 0
\(146\) 15.0000 1.24141
\(147\) 0 0
\(148\) −3.00000 −0.246598
\(149\) −20.0000 −1.63846 −0.819232 0.573462i \(-0.805600\pi\)
−0.819232 + 0.573462i \(0.805600\pi\)
\(150\) 0 0
\(151\) −6.00000 −0.488273 −0.244137 0.969741i \(-0.578505\pi\)
−0.244137 + 0.969741i \(0.578505\pi\)
\(152\) 1.00000 0.0811107
\(153\) 15.0000 1.21268
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 12.0000 0.957704 0.478852 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) 10.0000 0.795557
\(159\) 0 0
\(160\) 0 0
\(161\) −15.0000 −1.18217
\(162\) −9.00000 −0.707107
\(163\) 4.00000 0.313304 0.156652 0.987654i \(-0.449930\pi\)
0.156652 + 0.987654i \(0.449930\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) 0 0
\(167\) −8.00000 −0.619059 −0.309529 0.950890i \(-0.600171\pi\)
−0.309529 + 0.950890i \(0.600171\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) 0 0
\(171\) 3.00000 0.229416
\(172\) 4.00000 0.304997
\(173\) 15.0000 1.14043 0.570214 0.821496i \(-0.306860\pi\)
0.570214 + 0.821496i \(0.306860\pi\)
\(174\) 0 0
\(175\) 15.0000 1.13389
\(176\) 0 0
\(177\) 0 0
\(178\) −6.00000 −0.449719
\(179\) −21.0000 −1.56961 −0.784807 0.619740i \(-0.787238\pi\)
−0.784807 + 0.619740i \(0.787238\pi\)
\(180\) 0 0
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) −3.00000 −0.222375
\(183\) 0 0
\(184\) −5.00000 −0.368605
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −3.00000 −0.218797
\(189\) 0 0
\(190\) 0 0
\(191\) 9.00000 0.651217 0.325609 0.945505i \(-0.394431\pi\)
0.325609 + 0.945505i \(0.394431\pi\)
\(192\) 0 0
\(193\) 20.0000 1.43963 0.719816 0.694165i \(-0.244226\pi\)
0.719816 + 0.694165i \(0.244226\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) 2.00000 0.142494 0.0712470 0.997459i \(-0.477302\pi\)
0.0712470 + 0.997459i \(0.477302\pi\)
\(198\) 0 0
\(199\) 7.00000 0.496217 0.248108 0.968732i \(-0.420191\pi\)
0.248108 + 0.968732i \(0.420191\pi\)
\(200\) 5.00000 0.353553
\(201\) 0 0
\(202\) 10.0000 0.703598
\(203\) 18.0000 1.26335
\(204\) 0 0
\(205\) 0 0
\(206\) −14.0000 −0.975426
\(207\) −15.0000 −1.04257
\(208\) −1.00000 −0.0693375
\(209\) 0 0
\(210\) 0 0
\(211\) −28.0000 −1.92760 −0.963800 0.266627i \(-0.914091\pi\)
−0.963800 + 0.266627i \(0.914091\pi\)
\(212\) 2.00000 0.137361
\(213\) 0 0
\(214\) −3.00000 −0.205076
\(215\) 0 0
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) −17.0000 −1.15139
\(219\) 0 0
\(220\) 0 0
\(221\) 5.00000 0.336336
\(222\) 0 0
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 3.00000 0.200446
\(225\) 15.0000 1.00000
\(226\) −16.0000 −1.06430
\(227\) −13.0000 −0.862840 −0.431420 0.902151i \(-0.641987\pi\)
−0.431420 + 0.902151i \(0.641987\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 19.0000 1.24473 0.622366 0.782727i \(-0.286172\pi\)
0.622366 + 0.782727i \(0.286172\pi\)
\(234\) −3.00000 −0.196116
\(235\) 0 0
\(236\) 1.00000 0.0650945
\(237\) 0 0
\(238\) −15.0000 −0.972306
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 10.0000 0.644157 0.322078 0.946713i \(-0.395619\pi\)
0.322078 + 0.946713i \(0.395619\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 1.00000 0.0636285
\(248\) −2.00000 −0.127000
\(249\) 0 0
\(250\) 0 0
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 9.00000 0.566947
\(253\) 0 0
\(254\) −10.0000 −0.627456
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 2.00000 0.124757 0.0623783 0.998053i \(-0.480131\pi\)
0.0623783 + 0.998053i \(0.480131\pi\)
\(258\) 0 0
\(259\) 9.00000 0.559233
\(260\) 0 0
\(261\) 18.0000 1.11417
\(262\) −12.0000 −0.741362
\(263\) −8.00000 −0.493301 −0.246651 0.969104i \(-0.579330\pi\)
−0.246651 + 0.969104i \(0.579330\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −3.00000 −0.183942
\(267\) 0 0
\(268\) 3.00000 0.183254
\(269\) 9.00000 0.548740 0.274370 0.961624i \(-0.411531\pi\)
0.274370 + 0.961624i \(0.411531\pi\)
\(270\) 0 0
\(271\) −29.0000 −1.76162 −0.880812 0.473466i \(-0.843003\pi\)
−0.880812 + 0.473466i \(0.843003\pi\)
\(272\) −5.00000 −0.303170
\(273\) 0 0
\(274\) −3.00000 −0.181237
\(275\) 0 0
\(276\) 0 0
\(277\) −22.0000 −1.32185 −0.660926 0.750451i \(-0.729836\pi\)
−0.660926 + 0.750451i \(0.729836\pi\)
\(278\) −14.0000 −0.839664
\(279\) −6.00000 −0.359211
\(280\) 0 0
\(281\) 24.0000 1.43172 0.715860 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) 0 0
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) −4.00000 −0.237356
\(285\) 0 0
\(286\) 0 0
\(287\) −6.00000 −0.354169
\(288\) 3.00000 0.176777
\(289\) 8.00000 0.470588
\(290\) 0 0
\(291\) 0 0
\(292\) −15.0000 −0.877809
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.00000 0.174371
\(297\) 0 0
\(298\) 20.0000 1.15857
\(299\) −5.00000 −0.289157
\(300\) 0 0
\(301\) −12.0000 −0.691669
\(302\) 6.00000 0.345261
\(303\) 0 0
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) −15.0000 −0.857493
\(307\) −7.00000 −0.399511 −0.199756 0.979846i \(-0.564015\pi\)
−0.199756 + 0.979846i \(0.564015\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −17.0000 −0.963982 −0.481991 0.876176i \(-0.660086\pi\)
−0.481991 + 0.876176i \(0.660086\pi\)
\(312\) 0 0
\(313\) 1.00000 0.0565233 0.0282617 0.999601i \(-0.491003\pi\)
0.0282617 + 0.999601i \(0.491003\pi\)
\(314\) −12.0000 −0.677199
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −11.0000 −0.617822 −0.308911 0.951091i \(-0.599964\pi\)
−0.308911 + 0.951091i \(0.599964\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 15.0000 0.835917
\(323\) 5.00000 0.278207
\(324\) 9.00000 0.500000
\(325\) 5.00000 0.277350
\(326\) −4.00000 −0.221540
\(327\) 0 0
\(328\) −2.00000 −0.110432
\(329\) 9.00000 0.496186
\(330\) 0 0
\(331\) 7.00000 0.384755 0.192377 0.981321i \(-0.438380\pi\)
0.192377 + 0.981321i \(0.438380\pi\)
\(332\) 0 0
\(333\) 9.00000 0.493197
\(334\) 8.00000 0.437741
\(335\) 0 0
\(336\) 0 0
\(337\) 4.00000 0.217894 0.108947 0.994048i \(-0.465252\pi\)
0.108947 + 0.994048i \(0.465252\pi\)
\(338\) 12.0000 0.652714
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) −3.00000 −0.162221
\(343\) 15.0000 0.809924
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) −15.0000 −0.806405
\(347\) 16.0000 0.858925 0.429463 0.903085i \(-0.358703\pi\)
0.429463 + 0.903085i \(0.358703\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) −15.0000 −0.801784
\(351\) 0 0
\(352\) 0 0
\(353\) −30.0000 −1.59674 −0.798369 0.602168i \(-0.794304\pi\)
−0.798369 + 0.602168i \(0.794304\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 6.00000 0.317999
\(357\) 0 0
\(358\) 21.0000 1.10988
\(359\) 1.00000 0.0527780 0.0263890 0.999652i \(-0.491599\pi\)
0.0263890 + 0.999652i \(0.491599\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 2.00000 0.105118
\(363\) 0 0
\(364\) 3.00000 0.157243
\(365\) 0 0
\(366\) 0 0
\(367\) 19.0000 0.991792 0.495896 0.868382i \(-0.334840\pi\)
0.495896 + 0.868382i \(0.334840\pi\)
\(368\) 5.00000 0.260643
\(369\) −6.00000 −0.312348
\(370\) 0 0
\(371\) −6.00000 −0.311504
\(372\) 0 0
\(373\) 10.0000 0.517780 0.258890 0.965907i \(-0.416643\pi\)
0.258890 + 0.965907i \(0.416643\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 3.00000 0.154713
\(377\) 6.00000 0.309016
\(378\) 0 0
\(379\) 25.0000 1.28416 0.642082 0.766636i \(-0.278071\pi\)
0.642082 + 0.766636i \(0.278071\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −9.00000 −0.460480
\(383\) 6.00000 0.306586 0.153293 0.988181i \(-0.451012\pi\)
0.153293 + 0.988181i \(0.451012\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −20.0000 −1.01797
\(387\) −12.0000 −0.609994
\(388\) 2.00000 0.101535
\(389\) 10.0000 0.507020 0.253510 0.967333i \(-0.418415\pi\)
0.253510 + 0.967333i \(0.418415\pi\)
\(390\) 0 0
\(391\) −25.0000 −1.26430
\(392\) −2.00000 −0.101015
\(393\) 0 0
\(394\) −2.00000 −0.100759
\(395\) 0 0
\(396\) 0 0
\(397\) 12.0000 0.602263 0.301131 0.953583i \(-0.402636\pi\)
0.301131 + 0.953583i \(0.402636\pi\)
\(398\) −7.00000 −0.350878
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 12.0000 0.599251 0.299626 0.954057i \(-0.403138\pi\)
0.299626 + 0.954057i \(0.403138\pi\)
\(402\) 0 0
\(403\) −2.00000 −0.0996271
\(404\) −10.0000 −0.497519
\(405\) 0 0
\(406\) −18.0000 −0.893325
\(407\) 0 0
\(408\) 0 0
\(409\) 28.0000 1.38451 0.692255 0.721653i \(-0.256617\pi\)
0.692255 + 0.721653i \(0.256617\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 14.0000 0.689730
\(413\) −3.00000 −0.147620
\(414\) 15.0000 0.737210
\(415\) 0 0
\(416\) 1.00000 0.0490290
\(417\) 0 0
\(418\) 0 0
\(419\) −4.00000 −0.195413 −0.0977064 0.995215i \(-0.531151\pi\)
−0.0977064 + 0.995215i \(0.531151\pi\)
\(420\) 0 0
\(421\) 35.0000 1.70580 0.852898 0.522078i \(-0.174843\pi\)
0.852898 + 0.522078i \(0.174843\pi\)
\(422\) 28.0000 1.36302
\(423\) 9.00000 0.437595
\(424\) −2.00000 −0.0971286
\(425\) 25.0000 1.21268
\(426\) 0 0
\(427\) 0 0
\(428\) 3.00000 0.145010
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) 2.00000 0.0961139 0.0480569 0.998845i \(-0.484697\pi\)
0.0480569 + 0.998845i \(0.484697\pi\)
\(434\) 6.00000 0.288009
\(435\) 0 0
\(436\) 17.0000 0.814152
\(437\) −5.00000 −0.239182
\(438\) 0 0
\(439\) −26.0000 −1.24091 −0.620456 0.784241i \(-0.713053\pi\)
−0.620456 + 0.784241i \(0.713053\pi\)
\(440\) 0 0
\(441\) −6.00000 −0.285714
\(442\) −5.00000 −0.237826
\(443\) −38.0000 −1.80543 −0.902717 0.430234i \(-0.858431\pi\)
−0.902717 + 0.430234i \(0.858431\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 8.00000 0.378811
\(447\) 0 0
\(448\) −3.00000 −0.141737
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) −15.0000 −0.707107
\(451\) 0 0
\(452\) 16.0000 0.752577
\(453\) 0 0
\(454\) 13.0000 0.610120
\(455\) 0 0
\(456\) 0 0
\(457\) 13.0000 0.608114 0.304057 0.952654i \(-0.401659\pi\)
0.304057 + 0.952654i \(0.401659\pi\)
\(458\) −22.0000 −1.02799
\(459\) 0 0
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) 8.00000 0.371792 0.185896 0.982569i \(-0.440481\pi\)
0.185896 + 0.982569i \(0.440481\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −19.0000 −0.880158
\(467\) −14.0000 −0.647843 −0.323921 0.946084i \(-0.605001\pi\)
−0.323921 + 0.946084i \(0.605001\pi\)
\(468\) 3.00000 0.138675
\(469\) −9.00000 −0.415581
\(470\) 0 0
\(471\) 0 0
\(472\) −1.00000 −0.0460287
\(473\) 0 0
\(474\) 0 0
\(475\) 5.00000 0.229416
\(476\) 15.0000 0.687524
\(477\) −6.00000 −0.274721
\(478\) −24.0000 −1.09773
\(479\) −5.00000 −0.228456 −0.114228 0.993455i \(-0.536439\pi\)
−0.114228 + 0.993455i \(0.536439\pi\)
\(480\) 0 0
\(481\) 3.00000 0.136788
\(482\) −10.0000 −0.455488
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −12.0000 −0.543772 −0.271886 0.962329i \(-0.587647\pi\)
−0.271886 + 0.962329i \(0.587647\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) 0 0
\(493\) 30.0000 1.35113
\(494\) −1.00000 −0.0449921
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 12.0000 0.538274
\(498\) 0 0
\(499\) −4.00000 −0.179065 −0.0895323 0.995984i \(-0.528537\pi\)
−0.0895323 + 0.995984i \(0.528537\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 18.0000 0.803379
\(503\) 21.0000 0.936344 0.468172 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) −9.00000 −0.400892
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 10.0000 0.443678
\(509\) −35.0000 −1.55135 −0.775674 0.631134i \(-0.782590\pi\)
−0.775674 + 0.631134i \(0.782590\pi\)
\(510\) 0 0
\(511\) 45.0000 1.99068
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −2.00000 −0.0882162
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) −9.00000 −0.395437
\(519\) 0 0
\(520\) 0 0
\(521\) 24.0000 1.05146 0.525730 0.850652i \(-0.323792\pi\)
0.525730 + 0.850652i \(0.323792\pi\)
\(522\) −18.0000 −0.787839
\(523\) 27.0000 1.18063 0.590314 0.807174i \(-0.299004\pi\)
0.590314 + 0.807174i \(0.299004\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) −10.0000 −0.435607
\(528\) 0 0
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) −3.00000 −0.130189
\(532\) 3.00000 0.130066
\(533\) −2.00000 −0.0866296
\(534\) 0 0
\(535\) 0 0
\(536\) −3.00000 −0.129580
\(537\) 0 0
\(538\) −9.00000 −0.388018
\(539\) 0 0
\(540\) 0 0
\(541\) −2.00000 −0.0859867 −0.0429934 0.999075i \(-0.513689\pi\)
−0.0429934 + 0.999075i \(0.513689\pi\)
\(542\) 29.0000 1.24566
\(543\) 0 0
\(544\) 5.00000 0.214373
\(545\) 0 0
\(546\) 0 0
\(547\) 11.0000 0.470326 0.235163 0.971956i \(-0.424438\pi\)
0.235163 + 0.971956i \(0.424438\pi\)
\(548\) 3.00000 0.128154
\(549\) 0 0
\(550\) 0 0
\(551\) 6.00000 0.255609
\(552\) 0 0
\(553\) 30.0000 1.27573
\(554\) 22.0000 0.934690
\(555\) 0 0
\(556\) 14.0000 0.593732
\(557\) 36.0000 1.52537 0.762684 0.646771i \(-0.223881\pi\)
0.762684 + 0.646771i \(0.223881\pi\)
\(558\) 6.00000 0.254000
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 0 0
\(562\) −24.0000 −1.01238
\(563\) 41.0000 1.72794 0.863972 0.503540i \(-0.167969\pi\)
0.863972 + 0.503540i \(0.167969\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −14.0000 −0.588464
\(567\) −27.0000 −1.13389
\(568\) 4.00000 0.167836
\(569\) −8.00000 −0.335377 −0.167689 0.985840i \(-0.553630\pi\)
−0.167689 + 0.985840i \(0.553630\pi\)
\(570\) 0 0
\(571\) 34.0000 1.42286 0.711428 0.702759i \(-0.248049\pi\)
0.711428 + 0.702759i \(0.248049\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 6.00000 0.250435
\(575\) −25.0000 −1.04257
\(576\) −3.00000 −0.125000
\(577\) −13.0000 −0.541197 −0.270599 0.962692i \(-0.587222\pi\)
−0.270599 + 0.962692i \(0.587222\pi\)
\(578\) −8.00000 −0.332756
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 15.0000 0.620704
\(585\) 0 0
\(586\) 6.00000 0.247858
\(587\) −26.0000 −1.07313 −0.536567 0.843857i \(-0.680279\pi\)
−0.536567 + 0.843857i \(0.680279\pi\)
\(588\) 0 0
\(589\) −2.00000 −0.0824086
\(590\) 0 0
\(591\) 0 0
\(592\) −3.00000 −0.123299
\(593\) 35.0000 1.43728 0.718639 0.695383i \(-0.244765\pi\)
0.718639 + 0.695383i \(0.244765\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −20.0000 −0.819232
\(597\) 0 0
\(598\) 5.00000 0.204465
\(599\) −30.0000 −1.22577 −0.612883 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) −18.0000 −0.734235 −0.367118 0.930175i \(-0.619655\pi\)
−0.367118 + 0.930175i \(0.619655\pi\)
\(602\) 12.0000 0.489083
\(603\) −9.00000 −0.366508
\(604\) −6.00000 −0.244137
\(605\) 0 0
\(606\) 0 0
\(607\) 34.0000 1.38002 0.690009 0.723801i \(-0.257607\pi\)
0.690009 + 0.723801i \(0.257607\pi\)
\(608\) 1.00000 0.0405554
\(609\) 0 0
\(610\) 0 0
\(611\) 3.00000 0.121367
\(612\) 15.0000 0.606339
\(613\) 40.0000 1.61558 0.807792 0.589467i \(-0.200662\pi\)
0.807792 + 0.589467i \(0.200662\pi\)
\(614\) 7.00000 0.282497
\(615\) 0 0
\(616\) 0 0
\(617\) −27.0000 −1.08698 −0.543490 0.839416i \(-0.682897\pi\)
−0.543490 + 0.839416i \(0.682897\pi\)
\(618\) 0 0
\(619\) 8.00000 0.321547 0.160774 0.986991i \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 17.0000 0.681638
\(623\) −18.0000 −0.721155
\(624\) 0 0
\(625\) 25.0000 1.00000
\(626\) −1.00000 −0.0399680
\(627\) 0 0
\(628\) 12.0000 0.478852
\(629\) 15.0000 0.598089
\(630\) 0 0
\(631\) −25.0000 −0.995234 −0.497617 0.867397i \(-0.665792\pi\)
−0.497617 + 0.867397i \(0.665792\pi\)
\(632\) 10.0000 0.397779
\(633\) 0 0
\(634\) 11.0000 0.436866
\(635\) 0 0
\(636\) 0 0
\(637\) −2.00000 −0.0792429
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 0 0
\(641\) −22.0000 −0.868948 −0.434474 0.900684i \(-0.643066\pi\)
−0.434474 + 0.900684i \(0.643066\pi\)
\(642\) 0 0
\(643\) 28.0000 1.10421 0.552106 0.833774i \(-0.313824\pi\)
0.552106 + 0.833774i \(0.313824\pi\)
\(644\) −15.0000 −0.591083
\(645\) 0 0
\(646\) −5.00000 −0.196722
\(647\) 24.0000 0.943537 0.471769 0.881722i \(-0.343616\pi\)
0.471769 + 0.881722i \(0.343616\pi\)
\(648\) −9.00000 −0.353553
\(649\) 0 0
\(650\) −5.00000 −0.196116
\(651\) 0 0
\(652\) 4.00000 0.156652
\(653\) 8.00000 0.313064 0.156532 0.987673i \(-0.449969\pi\)
0.156532 + 0.987673i \(0.449969\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 2.00000 0.0780869
\(657\) 45.0000 1.75562
\(658\) −9.00000 −0.350857
\(659\) −31.0000 −1.20759 −0.603794 0.797140i \(-0.706345\pi\)
−0.603794 + 0.797140i \(0.706345\pi\)
\(660\) 0 0
\(661\) −26.0000 −1.01128 −0.505641 0.862744i \(-0.668744\pi\)
−0.505641 + 0.862744i \(0.668744\pi\)
\(662\) −7.00000 −0.272063
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −9.00000 −0.348743
\(667\) −30.0000 −1.16160
\(668\) −8.00000 −0.309529
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 6.00000 0.231283 0.115642 0.993291i \(-0.463108\pi\)
0.115642 + 0.993291i \(0.463108\pi\)
\(674\) −4.00000 −0.154074
\(675\) 0 0
\(676\) −12.0000 −0.461538
\(677\) −7.00000 −0.269032 −0.134516 0.990911i \(-0.542948\pi\)
−0.134516 + 0.990911i \(0.542948\pi\)
\(678\) 0 0
\(679\) −6.00000 −0.230259
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 3.00000 0.114708
\(685\) 0 0
\(686\) −15.0000 −0.572703
\(687\) 0 0
\(688\) 4.00000 0.152499
\(689\) −2.00000 −0.0761939
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 15.0000 0.570214
\(693\) 0 0
\(694\) −16.0000 −0.607352
\(695\) 0 0
\(696\) 0 0
\(697\) −10.0000 −0.378777
\(698\) −10.0000 −0.378506
\(699\) 0 0
\(700\) 15.0000 0.566947
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 3.00000 0.113147
\(704\) 0 0
\(705\) 0 0
\(706\) 30.0000 1.12906
\(707\) 30.0000 1.12827
\(708\) 0 0
\(709\) −32.0000 −1.20179 −0.600893 0.799330i \(-0.705188\pi\)
−0.600893 + 0.799330i \(0.705188\pi\)
\(710\) 0 0
\(711\) 30.0000 1.12509
\(712\) −6.00000 −0.224860
\(713\) 10.0000 0.374503
\(714\) 0 0
\(715\) 0 0
\(716\) −21.0000 −0.784807
\(717\) 0 0
\(718\) −1.00000 −0.0373197
\(719\) −5.00000 −0.186469 −0.0932343 0.995644i \(-0.529721\pi\)
−0.0932343 + 0.995644i \(0.529721\pi\)
\(720\) 0 0
\(721\) −42.0000 −1.56416
\(722\) −1.00000 −0.0372161
\(723\) 0 0
\(724\) −2.00000 −0.0743294
\(725\) 30.0000 1.11417
\(726\) 0 0
\(727\) 52.0000 1.92857 0.964287 0.264861i \(-0.0853260\pi\)
0.964287 + 0.264861i \(0.0853260\pi\)
\(728\) −3.00000 −0.111187
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −20.0000 −0.739727
\(732\) 0 0
\(733\) 24.0000 0.886460 0.443230 0.896408i \(-0.353832\pi\)
0.443230 + 0.896408i \(0.353832\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) −5.00000 −0.184302
\(737\) 0 0
\(738\) 6.00000 0.220863
\(739\) −2.00000 −0.0735712 −0.0367856 0.999323i \(-0.511712\pi\)
−0.0367856 + 0.999323i \(0.511712\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 6.00000 0.220267
\(743\) 22.0000 0.807102 0.403551 0.914957i \(-0.367776\pi\)
0.403551 + 0.914957i \(0.367776\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −10.0000 −0.366126
\(747\) 0 0
\(748\) 0 0
\(749\) −9.00000 −0.328853
\(750\) 0 0
\(751\) 50.0000 1.82453 0.912263 0.409605i \(-0.134333\pi\)
0.912263 + 0.409605i \(0.134333\pi\)
\(752\) −3.00000 −0.109399
\(753\) 0 0
\(754\) −6.00000 −0.218507
\(755\) 0 0
\(756\) 0 0
\(757\) −4.00000 −0.145382 −0.0726912 0.997354i \(-0.523159\pi\)
−0.0726912 + 0.997354i \(0.523159\pi\)
\(758\) −25.0000 −0.908041
\(759\) 0 0
\(760\) 0 0
\(761\) 43.0000 1.55875 0.779374 0.626559i \(-0.215537\pi\)
0.779374 + 0.626559i \(0.215537\pi\)
\(762\) 0 0
\(763\) −51.0000 −1.84632
\(764\) 9.00000 0.325609
\(765\) 0 0
\(766\) −6.00000 −0.216789
\(767\) −1.00000 −0.0361079
\(768\) 0 0
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 20.0000 0.719816
\(773\) −51.0000 −1.83434 −0.917171 0.398493i \(-0.869533\pi\)
−0.917171 + 0.398493i \(0.869533\pi\)
\(774\) 12.0000 0.431331
\(775\) −10.0000 −0.359211
\(776\) −2.00000 −0.0717958
\(777\) 0 0
\(778\) −10.0000 −0.358517
\(779\) −2.00000 −0.0716574
\(780\) 0 0
\(781\) 0 0
\(782\) 25.0000 0.893998
\(783\) 0 0
\(784\) 2.00000 0.0714286
\(785\) 0 0
\(786\) 0 0
\(787\) −8.00000 −0.285169 −0.142585 0.989783i \(-0.545541\pi\)
−0.142585 + 0.989783i \(0.545541\pi\)
\(788\) 2.00000 0.0712470
\(789\) 0 0
\(790\) 0 0
\(791\) −48.0000 −1.70668
\(792\) 0 0
\(793\) 0 0
\(794\) −12.0000 −0.425864
\(795\) 0 0
\(796\) 7.00000 0.248108
\(797\) −53.0000 −1.87736 −0.938678 0.344795i \(-0.887949\pi\)
−0.938678 + 0.344795i \(0.887949\pi\)
\(798\) 0 0
\(799\) 15.0000 0.530662
\(800\) 5.00000 0.176777
\(801\) −18.0000 −0.635999
\(802\) −12.0000 −0.423735
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 2.00000 0.0704470
\(807\) 0 0
\(808\) 10.0000 0.351799
\(809\) −42.0000 −1.47664 −0.738321 0.674450i \(-0.764381\pi\)
−0.738321 + 0.674450i \(0.764381\pi\)
\(810\) 0 0
\(811\) −44.0000 −1.54505 −0.772524 0.634985i \(-0.781006\pi\)
−0.772524 + 0.634985i \(0.781006\pi\)
\(812\) 18.0000 0.631676
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −4.00000 −0.139942
\(818\) −28.0000 −0.978997
\(819\) −9.00000 −0.314485
\(820\) 0 0
\(821\) 36.0000 1.25641 0.628204 0.778048i \(-0.283790\pi\)
0.628204 + 0.778048i \(0.283790\pi\)
\(822\) 0 0
\(823\) −28.0000 −0.976019 −0.488009 0.872838i \(-0.662277\pi\)
−0.488009 + 0.872838i \(0.662277\pi\)
\(824\) −14.0000 −0.487713
\(825\) 0 0
\(826\) 3.00000 0.104383
\(827\) 3.00000 0.104320 0.0521601 0.998639i \(-0.483389\pi\)
0.0521601 + 0.998639i \(0.483389\pi\)
\(828\) −15.0000 −0.521286
\(829\) −23.0000 −0.798823 −0.399412 0.916772i \(-0.630786\pi\)
−0.399412 + 0.916772i \(0.630786\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −1.00000 −0.0346688
\(833\) −10.0000 −0.346479
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 4.00000 0.138178
\(839\) 24.0000 0.828572 0.414286 0.910147i \(-0.364031\pi\)
0.414286 + 0.910147i \(0.364031\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −35.0000 −1.20618
\(843\) 0 0
\(844\) −28.0000 −0.963800
\(845\) 0 0
\(846\) −9.00000 −0.309426
\(847\) 0 0
\(848\) 2.00000 0.0686803
\(849\) 0 0
\(850\) −25.0000 −0.857493
\(851\) −15.0000 −0.514193
\(852\) 0 0
\(853\) 36.0000 1.23262 0.616308 0.787505i \(-0.288628\pi\)
0.616308 + 0.787505i \(0.288628\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −3.00000 −0.102538
\(857\) −24.0000 −0.819824 −0.409912 0.912125i \(-0.634441\pi\)
−0.409912 + 0.912125i \(0.634441\pi\)
\(858\) 0 0
\(859\) −18.0000 −0.614152 −0.307076 0.951685i \(-0.599351\pi\)
−0.307076 + 0.951685i \(0.599351\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −10.0000 −0.340404 −0.170202 0.985409i \(-0.554442\pi\)
−0.170202 + 0.985409i \(0.554442\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −2.00000 −0.0679628
\(867\) 0 0
\(868\) −6.00000 −0.203653
\(869\) 0 0
\(870\) 0 0
\(871\) −3.00000 −0.101651
\(872\) −17.0000 −0.575693
\(873\) −6.00000 −0.203069
\(874\) 5.00000 0.169128
\(875\) 0 0
\(876\) 0 0
\(877\) −27.0000 −0.911725 −0.455863 0.890050i \(-0.650669\pi\)
−0.455863 + 0.890050i \(0.650669\pi\)
\(878\) 26.0000 0.877457
\(879\) 0 0
\(880\) 0 0
\(881\) −19.0000 −0.640126 −0.320063 0.947396i \(-0.603704\pi\)
−0.320063 + 0.947396i \(0.603704\pi\)
\(882\) 6.00000 0.202031
\(883\) −4.00000 −0.134611 −0.0673054 0.997732i \(-0.521440\pi\)
−0.0673054 + 0.997732i \(0.521440\pi\)
\(884\) 5.00000 0.168168
\(885\) 0 0
\(886\) 38.0000 1.27663
\(887\) −36.0000 −1.20876 −0.604381 0.796696i \(-0.706579\pi\)
−0.604381 + 0.796696i \(0.706579\pi\)
\(888\) 0 0
\(889\) −30.0000 −1.00617
\(890\) 0 0
\(891\) 0 0
\(892\) −8.00000 −0.267860
\(893\) 3.00000 0.100391
\(894\) 0 0
\(895\) 0 0
\(896\) 3.00000 0.100223
\(897\) 0 0
\(898\) −14.0000 −0.467186
\(899\) −12.0000 −0.400222
\(900\) 15.0000 0.500000
\(901\) −10.0000 −0.333148
\(902\) 0 0
\(903\) 0 0
\(904\) −16.0000 −0.532152
\(905\) 0 0
\(906\) 0 0
\(907\) 43.0000 1.42779 0.713896 0.700252i \(-0.246929\pi\)
0.713896 + 0.700252i \(0.246929\pi\)
\(908\) −13.0000 −0.431420
\(909\) 30.0000 0.995037
\(910\) 0 0
\(911\) −12.0000 −0.397578 −0.198789 0.980042i \(-0.563701\pi\)
−0.198789 + 0.980042i \(0.563701\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −13.0000 −0.430002
\(915\) 0 0
\(916\) 22.0000 0.726900
\(917\) −36.0000 −1.18882
\(918\) 0 0
\(919\) 9.00000 0.296883 0.148441 0.988921i \(-0.452574\pi\)
0.148441 + 0.988921i \(0.452574\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 12.0000 0.395199
\(923\) 4.00000 0.131662
\(924\) 0 0
\(925\) 15.0000 0.493197
\(926\) −8.00000 −0.262896
\(927\) −42.0000 −1.37946
\(928\) 6.00000 0.196960
\(929\) 14.0000 0.459325 0.229663 0.973270i \(-0.426238\pi\)
0.229663 + 0.973270i \(0.426238\pi\)
\(930\) 0 0
\(931\) −2.00000 −0.0655474
\(932\) 19.0000 0.622366
\(933\) 0 0
\(934\) 14.0000 0.458094
\(935\) 0 0
\(936\) −3.00000 −0.0980581
\(937\) 26.0000 0.849383 0.424691 0.905338i \(-0.360383\pi\)
0.424691 + 0.905338i \(0.360383\pi\)
\(938\) 9.00000 0.293860
\(939\) 0 0
\(940\) 0 0
\(941\) 15.0000 0.488986 0.244493 0.969651i \(-0.421378\pi\)
0.244493 + 0.969651i \(0.421378\pi\)
\(942\) 0 0
\(943\) 10.0000 0.325645
\(944\) 1.00000 0.0325472
\(945\) 0 0
\(946\) 0 0
\(947\) 40.0000 1.29983 0.649913 0.760009i \(-0.274805\pi\)
0.649913 + 0.760009i \(0.274805\pi\)
\(948\) 0 0
\(949\) 15.0000 0.486921
\(950\) −5.00000 −0.162221
\(951\) 0 0
\(952\) −15.0000 −0.486153
\(953\) −26.0000 −0.842223 −0.421111 0.907009i \(-0.638360\pi\)
−0.421111 + 0.907009i \(0.638360\pi\)
\(954\) 6.00000 0.194257
\(955\) 0 0
\(956\) 24.0000 0.776215
\(957\) 0 0
\(958\) 5.00000 0.161543
\(959\) −9.00000 −0.290625
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) −3.00000 −0.0967239
\(963\) −9.00000 −0.290021
\(964\) 10.0000 0.322078
\(965\) 0 0
\(966\) 0 0
\(967\) −37.0000 −1.18984 −0.594920 0.803785i \(-0.702816\pi\)
−0.594920 + 0.803785i \(0.702816\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −45.0000 −1.44412 −0.722059 0.691831i \(-0.756804\pi\)
−0.722059 + 0.691831i \(0.756804\pi\)
\(972\) 0 0
\(973\) −42.0000 −1.34646
\(974\) 12.0000 0.384505
\(975\) 0 0
\(976\) 0 0
\(977\) 24.0000 0.767828 0.383914 0.923369i \(-0.374576\pi\)
0.383914 + 0.923369i \(0.374576\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −51.0000 −1.62830
\(982\) −2.00000 −0.0638226
\(983\) −42.0000 −1.33959 −0.669796 0.742545i \(-0.733618\pi\)
−0.669796 + 0.742545i \(0.733618\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −30.0000 −0.955395
\(987\) 0 0
\(988\) 1.00000 0.0318142
\(989\) 20.0000 0.635963
\(990\) 0 0
\(991\) −10.0000 −0.317660 −0.158830 0.987306i \(-0.550772\pi\)
−0.158830 + 0.987306i \(0.550772\pi\)
\(992\) −2.00000 −0.0635001
\(993\) 0 0
\(994\) −12.0000 −0.380617
\(995\) 0 0
\(996\) 0 0
\(997\) −8.00000 −0.253363 −0.126681 0.991943i \(-0.540433\pi\)
−0.126681 + 0.991943i \(0.540433\pi\)
\(998\) 4.00000 0.126618
\(999\) 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 4598.2.a.e.1.1 1
11.10 odd 2 4598.2.a.n.1.1 yes 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4598.2.a.e.1.1 1 1.1 even 1 trivial
4598.2.a.n.1.1 yes 1 11.10 odd 2