Properties

Label 950.2.a.e.1.1
Level $950$
Weight $2$
Character 950.1
Self dual yes
Analytic conductor $7.586$
Analytic rank $0$
Dimension $1$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 950.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(7.58578819202\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 190)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 950.1

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.00000 q^{9} +1.00000 q^{12} +3.00000 q^{13} +1.00000 q^{14} +1.00000 q^{16} +7.00000 q^{17} -2.00000 q^{18} -1.00000 q^{19} +1.00000 q^{21} +5.00000 q^{23} +1.00000 q^{24} +3.00000 q^{26} -5.00000 q^{27} +1.00000 q^{28} -5.00000 q^{29} +10.0000 q^{31} +1.00000 q^{32} +7.00000 q^{34} -2.00000 q^{36} -2.00000 q^{37} -1.00000 q^{38} +3.00000 q^{39} +2.00000 q^{41} +1.00000 q^{42} -6.00000 q^{43} +5.00000 q^{46} +1.00000 q^{48} -6.00000 q^{49} +7.00000 q^{51} +3.00000 q^{52} -9.00000 q^{53} -5.00000 q^{54} +1.00000 q^{56} -1.00000 q^{57} -5.00000 q^{58} -7.00000 q^{59} -4.00000 q^{61} +10.0000 q^{62} -2.00000 q^{63} +1.00000 q^{64} -7.00000 q^{67} +7.00000 q^{68} +5.00000 q^{69} -2.00000 q^{72} +9.00000 q^{73} -2.00000 q^{74} -1.00000 q^{76} +3.00000 q^{78} -10.0000 q^{79} +1.00000 q^{81} +2.00000 q^{82} +2.00000 q^{83} +1.00000 q^{84} -6.00000 q^{86} -5.00000 q^{87} -10.0000 q^{89} +3.00000 q^{91} +5.00000 q^{92} +10.0000 q^{93} +1.00000 q^{96} +18.0000 q^{97} -6.00000 q^{98} +O(q^{100})\)

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
\(3\) 1.00000 0.577350 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 1.00000 0.408248
\(7\) 1.00000 0.377964 0.188982 0.981981i \(-0.439481\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 1.00000 0.353553
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 7.00000 1.69775 0.848875 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) −2.00000 −0.471405
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) 5.00000 1.04257 0.521286 0.853382i \(-0.325452\pi\)
0.521286 + 0.853382i \(0.325452\pi\)
\(24\) 1.00000 0.204124
\(25\) 0 0
\(26\) 3.00000 0.588348
\(27\) −5.00000 −0.962250
\(28\) 1.00000 0.188982
\(29\) −5.00000 −0.928477 −0.464238 0.885710i \(-0.653672\pi\)
−0.464238 + 0.885710i \(0.653672\pi\)
\(30\) 0 0
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 7.00000 1.20049
\(35\) 0 0
\(36\) −2.00000 −0.333333
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −1.00000 −0.162221
\(39\) 3.00000 0.480384
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 1.00000 0.154303
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 5.00000 0.737210
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000 0.144338
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) 7.00000 0.980196
\(52\) 3.00000 0.416025
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) −5.00000 −0.680414
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) −1.00000 −0.132453
\(58\) −5.00000 −0.656532
\(59\) −7.00000 −0.911322 −0.455661 0.890153i \(-0.650597\pi\)
−0.455661 + 0.890153i \(0.650597\pi\)
\(60\) 0 0
\(61\) −4.00000 −0.512148 −0.256074 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(62\) 10.0000 1.27000
\(63\) −2.00000 −0.251976
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) −7.00000 −0.855186 −0.427593 0.903971i \(-0.640638\pi\)
−0.427593 + 0.903971i \(0.640638\pi\)
\(68\) 7.00000 0.848875
\(69\) 5.00000 0.601929
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −2.00000 −0.235702
\(73\) 9.00000 1.05337 0.526685 0.850060i \(-0.323435\pi\)
0.526685 + 0.850060i \(0.323435\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) −1.00000 −0.114708
\(77\) 0 0
\(78\) 3.00000 0.339683
\(79\) −10.0000 −1.12509 −0.562544 0.826767i \(-0.690177\pi\)
−0.562544 + 0.826767i \(0.690177\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 2.00000 0.220863
\(83\) 2.00000 0.219529 0.109764 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 1.00000 0.109109
\(85\) 0 0
\(86\) −6.00000 −0.646997
\(87\) −5.00000 −0.536056
\(88\) 0 0
\(89\) −10.0000 −1.06000 −0.529999 0.847998i \(-0.677808\pi\)
−0.529999 + 0.847998i \(0.677808\pi\)
\(90\) 0 0
\(91\) 3.00000 0.314485
\(92\) 5.00000 0.521286
\(93\) 10.0000 1.03695
\(94\) 0 0
\(95\) 0 0
\(96\) 1.00000 0.102062
\(97\) 18.0000 1.82762 0.913812 0.406138i \(-0.133125\pi\)
0.913812 + 0.406138i \(0.133125\pi\)
\(98\) −6.00000 −0.606092
\(99\) 0 0
\(100\) 0 0
\(101\) −4.00000 −0.398015 −0.199007 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(102\) 7.00000 0.693103
\(103\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 3.00000 0.294174
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) −9.00000 −0.870063 −0.435031 0.900415i \(-0.643263\pi\)
−0.435031 + 0.900415i \(0.643263\pi\)
\(108\) −5.00000 −0.481125
\(109\) 13.0000 1.24517 0.622587 0.782551i \(-0.286082\pi\)
0.622587 + 0.782551i \(0.286082\pi\)
\(110\) 0 0
\(111\) −2.00000 −0.189832
\(112\) 1.00000 0.0944911
\(113\) −8.00000 −0.752577 −0.376288 0.926503i \(-0.622800\pi\)
−0.376288 + 0.926503i \(0.622800\pi\)
\(114\) −1.00000 −0.0936586
\(115\) 0 0
\(116\) −5.00000 −0.464238
\(117\) −6.00000 −0.554700
\(118\) −7.00000 −0.644402
\(119\) 7.00000 0.641689
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) −4.00000 −0.362143
\(123\) 2.00000 0.180334
\(124\) 10.0000 0.898027
\(125\) 0 0
\(126\) −2.00000 −0.178174
\(127\) 6.00000 0.532414 0.266207 0.963916i \(-0.414230\pi\)
0.266207 + 0.963916i \(0.414230\pi\)
\(128\) 1.00000 0.0883883
\(129\) −6.00000 −0.528271
\(130\) 0 0
\(131\) −20.0000 −1.74741 −0.873704 0.486458i \(-0.838289\pi\)
−0.873704 + 0.486458i \(0.838289\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) −7.00000 −0.604708
\(135\) 0 0
\(136\) 7.00000 0.600245
\(137\) 3.00000 0.256307 0.128154 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 5.00000 0.425628
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −2.00000 −0.166667
\(145\) 0 0
\(146\) 9.00000 0.744845
\(147\) −6.00000 −0.494872
\(148\) −2.00000 −0.164399
\(149\) 4.00000 0.327693 0.163846 0.986486i \(-0.447610\pi\)
0.163846 + 0.986486i \(0.447610\pi\)
\(150\) 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
\(153\) −14.0000 −1.13183
\(154\) 0 0
\(155\) 0 0
\(156\) 3.00000 0.240192
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) −10.0000 −0.795557
\(159\) −9.00000 −0.713746
\(160\) 0 0
\(161\) 5.00000 0.394055
\(162\) 1.00000 0.0785674
\(163\) 18.0000 1.40987 0.704934 0.709273i \(-0.250976\pi\)
0.704934 + 0.709273i \(0.250976\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) 2.00000 0.155230
\(167\) −14.0000 −1.08335 −0.541676 0.840587i \(-0.682210\pi\)
−0.541676 + 0.840587i \(0.682210\pi\)
\(168\) 1.00000 0.0771517
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 2.00000 0.152944
\(172\) −6.00000 −0.457496
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) −5.00000 −0.379049
\(175\) 0 0
\(176\) 0 0
\(177\) −7.00000 −0.526152
\(178\) −10.0000 −0.749532
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 3.00000 0.222375
\(183\) −4.00000 −0.295689
\(184\) 5.00000 0.368605
\(185\) 0 0
\(186\) 10.0000 0.733236
\(187\) 0 0
\(188\) 0 0
\(189\) −5.00000 −0.363696
\(190\) 0 0
\(191\) −7.00000 −0.506502 −0.253251 0.967401i \(-0.581500\pi\)
−0.253251 + 0.967401i \(0.581500\pi\)
\(192\) 1.00000 0.0721688
\(193\) 2.00000 0.143963 0.0719816 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 18.0000 1.29232
\(195\) 0 0
\(196\) −6.00000 −0.428571
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) 0 0
\(199\) 17.0000 1.20510 0.602549 0.798082i \(-0.294152\pi\)
0.602549 + 0.798082i \(0.294152\pi\)
\(200\) 0 0
\(201\) −7.00000 −0.493742
\(202\) −4.00000 −0.281439
\(203\) −5.00000 −0.350931
\(204\) 7.00000 0.490098
\(205\) 0 0
\(206\) 0 0
\(207\) −10.0000 −0.695048
\(208\) 3.00000 0.208013
\(209\) 0 0
\(210\) 0 0
\(211\) 5.00000 0.344214 0.172107 0.985078i \(-0.444942\pi\)
0.172107 + 0.985078i \(0.444942\pi\)
\(212\) −9.00000 −0.618123
\(213\) 0 0
\(214\) −9.00000 −0.615227
\(215\) 0 0
\(216\) −5.00000 −0.340207
\(217\) 10.0000 0.678844
\(218\) 13.0000 0.880471
\(219\) 9.00000 0.608164
\(220\) 0 0
\(221\) 21.0000 1.41261
\(222\) −2.00000 −0.134231
\(223\) 22.0000 1.47323 0.736614 0.676313i \(-0.236423\pi\)
0.736614 + 0.676313i \(0.236423\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −8.00000 −0.532152
\(227\) 25.0000 1.65931 0.829654 0.558278i \(-0.188538\pi\)
0.829654 + 0.558278i \(0.188538\pi\)
\(228\) −1.00000 −0.0662266
\(229\) −18.0000 −1.18947 −0.594737 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −5.00000 −0.328266
\(233\) −26.0000 −1.70332 −0.851658 0.524097i \(-0.824403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) −6.00000 −0.392232
\(235\) 0 0
\(236\) −7.00000 −0.455661
\(237\) −10.0000 −0.649570
\(238\) 7.00000 0.453743
\(239\) −27.0000 −1.74648 −0.873242 0.487286i \(-0.837987\pi\)
−0.873242 + 0.487286i \(0.837987\pi\)
\(240\) 0 0
\(241\) −28.0000 −1.80364 −0.901819 0.432113i \(-0.857768\pi\)
−0.901819 + 0.432113i \(0.857768\pi\)
\(242\) −11.0000 −0.707107
\(243\) 16.0000 1.02640
\(244\) −4.00000 −0.256074
\(245\) 0 0
\(246\) 2.00000 0.127515
\(247\) −3.00000 −0.190885
\(248\) 10.0000 0.635001
\(249\) 2.00000 0.126745
\(250\) 0 0
\(251\) 4.00000 0.252478 0.126239 0.992000i \(-0.459709\pi\)
0.126239 + 0.992000i \(0.459709\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) 6.00000 0.376473
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 6.00000 0.374270 0.187135 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) −6.00000 −0.373544
\(259\) −2.00000 −0.124274
\(260\) 0 0
\(261\) 10.0000 0.618984
\(262\) −20.0000 −1.23560
\(263\) 8.00000 0.493301 0.246651 0.969104i \(-0.420670\pi\)
0.246651 + 0.969104i \(0.420670\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −1.00000 −0.0613139
\(267\) −10.0000 −0.611990
\(268\) −7.00000 −0.427593
\(269\) −10.0000 −0.609711 −0.304855 0.952399i \(-0.598608\pi\)
−0.304855 + 0.952399i \(0.598608\pi\)
\(270\) 0 0
\(271\) 5.00000 0.303728 0.151864 0.988401i \(-0.451472\pi\)
0.151864 + 0.988401i \(0.451472\pi\)
\(272\) 7.00000 0.424437
\(273\) 3.00000 0.181568
\(274\) 3.00000 0.181237
\(275\) 0 0
\(276\) 5.00000 0.300965
\(277\) −28.0000 −1.68236 −0.841178 0.540758i \(-0.818138\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 12.0000 0.719712
\(279\) −20.0000 −1.19737
\(280\) 0 0
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 0 0
\(283\) 26.0000 1.54554 0.772770 0.634686i \(-0.218871\pi\)
0.772770 + 0.634686i \(0.218871\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.00000 0.118056
\(288\) −2.00000 −0.117851
\(289\) 32.0000 1.88235
\(290\) 0 0
\(291\) 18.0000 1.05518
\(292\) 9.00000 0.526685
\(293\) −31.0000 −1.81104 −0.905520 0.424304i \(-0.860519\pi\)
−0.905520 + 0.424304i \(0.860519\pi\)
\(294\) −6.00000 −0.349927
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 4.00000 0.231714
\(299\) 15.0000 0.867472
\(300\) 0 0
\(301\) −6.00000 −0.345834
\(302\) −6.00000 −0.345261
\(303\) −4.00000 −0.229794
\(304\) −1.00000 −0.0573539
\(305\) 0 0
\(306\) −14.0000 −0.800327
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 33.0000 1.87126 0.935629 0.352985i \(-0.114833\pi\)
0.935629 + 0.352985i \(0.114833\pi\)
\(312\) 3.00000 0.169842
\(313\) 29.0000 1.63918 0.819588 0.572953i \(-0.194202\pi\)
0.819588 + 0.572953i \(0.194202\pi\)
\(314\) −18.0000 −1.01580
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −3.00000 −0.168497 −0.0842484 0.996445i \(-0.526849\pi\)
−0.0842484 + 0.996445i \(0.526849\pi\)
\(318\) −9.00000 −0.504695
\(319\) 0 0
\(320\) 0 0
\(321\) −9.00000 −0.502331
\(322\) 5.00000 0.278639
\(323\) −7.00000 −0.389490
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 18.0000 0.996928
\(327\) 13.0000 0.718902
\(328\) 2.00000 0.110432
\(329\) 0 0
\(330\) 0 0
\(331\) −17.0000 −0.934405 −0.467202 0.884150i \(-0.654738\pi\)
−0.467202 + 0.884150i \(0.654738\pi\)
\(332\) 2.00000 0.109764
\(333\) 4.00000 0.219199
\(334\) −14.0000 −0.766046
\(335\) 0 0
\(336\) 1.00000 0.0545545
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) −4.00000 −0.217571
\(339\) −8.00000 −0.434500
\(340\) 0 0
\(341\) 0 0
\(342\) 2.00000 0.108148
\(343\) −13.0000 −0.701934
\(344\) −6.00000 −0.323498
\(345\) 0 0
\(346\) −6.00000 −0.322562
\(347\) 18.0000 0.966291 0.483145 0.875540i \(-0.339494\pi\)
0.483145 + 0.875540i \(0.339494\pi\)
\(348\) −5.00000 −0.268028
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) −15.0000 −0.800641
\(352\) 0 0
\(353\) −27.0000 −1.43706 −0.718532 0.695493i \(-0.755186\pi\)
−0.718532 + 0.695493i \(0.755186\pi\)
\(354\) −7.00000 −0.372046
\(355\) 0 0
\(356\) −10.0000 −0.529999
\(357\) 7.00000 0.370479
\(358\) 24.0000 1.26844
\(359\) 27.0000 1.42501 0.712503 0.701669i \(-0.247562\pi\)
0.712503 + 0.701669i \(0.247562\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) −10.0000 −0.525588
\(363\) −11.0000 −0.577350
\(364\) 3.00000 0.157243
\(365\) 0 0
\(366\) −4.00000 −0.209083
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 5.00000 0.260643
\(369\) −4.00000 −0.208232
\(370\) 0 0
\(371\) −9.00000 −0.467257
\(372\) 10.0000 0.518476
\(373\) −3.00000 −0.155334 −0.0776671 0.996979i \(-0.524747\pi\)
−0.0776671 + 0.996979i \(0.524747\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −15.0000 −0.772539
\(378\) −5.00000 −0.257172
\(379\) −7.00000 −0.359566 −0.179783 0.983706i \(-0.557540\pi\)
−0.179783 + 0.983706i \(0.557540\pi\)
\(380\) 0 0
\(381\) 6.00000 0.307389
\(382\) −7.00000 −0.358151
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) 2.00000 0.101797
\(387\) 12.0000 0.609994
\(388\) 18.0000 0.913812
\(389\) 24.0000 1.21685 0.608424 0.793612i \(-0.291802\pi\)
0.608424 + 0.793612i \(0.291802\pi\)
\(390\) 0 0
\(391\) 35.0000 1.77003
\(392\) −6.00000 −0.303046
\(393\) −20.0000 −1.00887
\(394\) 10.0000 0.503793
\(395\) 0 0
\(396\) 0 0
\(397\) 20.0000 1.00377 0.501886 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) 17.0000 0.852133
\(399\) −1.00000 −0.0500626
\(400\) 0 0
\(401\) 18.0000 0.898877 0.449439 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) −7.00000 −0.349128
\(403\) 30.0000 1.49441
\(404\) −4.00000 −0.199007
\(405\) 0 0
\(406\) −5.00000 −0.248146
\(407\) 0 0
\(408\) 7.00000 0.346552
\(409\) 26.0000 1.28562 0.642809 0.766027i \(-0.277769\pi\)
0.642809 + 0.766027i \(0.277769\pi\)
\(410\) 0 0
\(411\) 3.00000 0.147979
\(412\) 0 0
\(413\) −7.00000 −0.344447
\(414\) −10.0000 −0.491473
\(415\) 0 0
\(416\) 3.00000 0.147087
\(417\) 12.0000 0.587643
\(418\) 0 0
\(419\) −26.0000 −1.27018 −0.635092 0.772437i \(-0.719038\pi\)
−0.635092 + 0.772437i \(0.719038\pi\)
\(420\) 0 0
\(421\) 31.0000 1.51085 0.755424 0.655237i \(-0.227431\pi\)
0.755424 + 0.655237i \(0.227431\pi\)
\(422\) 5.00000 0.243396
\(423\) 0 0
\(424\) −9.00000 −0.437079
\(425\) 0 0
\(426\) 0 0
\(427\) −4.00000 −0.193574
\(428\) −9.00000 −0.435031
\(429\) 0 0
\(430\) 0 0
\(431\) 12.0000 0.578020 0.289010 0.957326i \(-0.406674\pi\)
0.289010 + 0.957326i \(0.406674\pi\)
\(432\) −5.00000 −0.240563
\(433\) −12.0000 −0.576683 −0.288342 0.957528i \(-0.593104\pi\)
−0.288342 + 0.957528i \(0.593104\pi\)
\(434\) 10.0000 0.480015
\(435\) 0 0
\(436\) 13.0000 0.622587
\(437\) −5.00000 −0.239182
\(438\) 9.00000 0.430037
\(439\) 10.0000 0.477274 0.238637 0.971109i \(-0.423299\pi\)
0.238637 + 0.971109i \(0.423299\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 21.0000 0.998868
\(443\) −24.0000 −1.14027 −0.570137 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) −2.00000 −0.0949158
\(445\) 0 0
\(446\) 22.0000 1.04173
\(447\) 4.00000 0.189194
\(448\) 1.00000 0.0472456
\(449\) 14.0000 0.660701 0.330350 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −8.00000 −0.376288
\(453\) −6.00000 −0.281905
\(454\) 25.0000 1.17331
\(455\) 0 0
\(456\) −1.00000 −0.0468293
\(457\) 41.0000 1.91790 0.958950 0.283577i \(-0.0915211\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) −18.0000 −0.841085
\(459\) −35.0000 −1.63366
\(460\) 0 0
\(461\) −10.0000 −0.465746 −0.232873 0.972507i \(-0.574813\pi\)
−0.232873 + 0.972507i \(0.574813\pi\)
\(462\) 0 0
\(463\) −16.0000 −0.743583 −0.371792 0.928316i \(-0.621256\pi\)
−0.371792 + 0.928316i \(0.621256\pi\)
\(464\) −5.00000 −0.232119
\(465\) 0 0
\(466\) −26.0000 −1.20443
\(467\) 8.00000 0.370196 0.185098 0.982720i \(-0.440740\pi\)
0.185098 + 0.982720i \(0.440740\pi\)
\(468\) −6.00000 −0.277350
\(469\) −7.00000 −0.323230
\(470\) 0 0
\(471\) −18.0000 −0.829396
\(472\) −7.00000 −0.322201
\(473\) 0 0
\(474\) −10.0000 −0.459315
\(475\) 0 0
\(476\) 7.00000 0.320844
\(477\) 18.0000 0.824163
\(478\) −27.0000 −1.23495
\(479\) −24.0000 −1.09659 −0.548294 0.836286i \(-0.684723\pi\)
−0.548294 + 0.836286i \(0.684723\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) −28.0000 −1.27537
\(483\) 5.00000 0.227508
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 16.0000 0.725775
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) −4.00000 −0.181071
\(489\) 18.0000 0.813988
\(490\) 0 0
\(491\) 14.0000 0.631811 0.315906 0.948791i \(-0.397692\pi\)
0.315906 + 0.948791i \(0.397692\pi\)
\(492\) 2.00000 0.0901670
\(493\) −35.0000 −1.57632
\(494\) −3.00000 −0.134976
\(495\) 0 0
\(496\) 10.0000 0.449013
\(497\) 0 0
\(498\) 2.00000 0.0896221
\(499\) 42.0000 1.88018 0.940089 0.340929i \(-0.110742\pi\)
0.940089 + 0.340929i \(0.110742\pi\)
\(500\) 0 0
\(501\) −14.0000 −0.625474
\(502\) 4.00000 0.178529
\(503\) 17.0000 0.757993 0.378996 0.925398i \(-0.376269\pi\)
0.378996 + 0.925398i \(0.376269\pi\)
\(504\) −2.00000 −0.0890871
\(505\) 0 0
\(506\) 0 0
\(507\) −4.00000 −0.177646
\(508\) 6.00000 0.266207
\(509\) −42.0000 −1.86162 −0.930809 0.365507i \(-0.880896\pi\)
−0.930809 + 0.365507i \(0.880896\pi\)
\(510\) 0 0
\(511\) 9.00000 0.398137
\(512\) 1.00000 0.0441942
\(513\) 5.00000 0.220755
\(514\) 6.00000 0.264649
\(515\) 0 0
\(516\) −6.00000 −0.264135
\(517\) 0 0
\(518\) −2.00000 −0.0878750
\(519\) −6.00000 −0.263371
\(520\) 0 0
\(521\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 10.0000 0.437688
\(523\) 19.0000 0.830812 0.415406 0.909636i \(-0.363640\pi\)
0.415406 + 0.909636i \(0.363640\pi\)
\(524\) −20.0000 −0.873704
\(525\) 0 0
\(526\) 8.00000 0.348817
\(527\) 70.0000 3.04925
\(528\) 0 0
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) 14.0000 0.607548
\(532\) −1.00000 −0.0433555
\(533\) 6.00000 0.259889
\(534\) −10.0000 −0.432742
\(535\) 0 0
\(536\) −7.00000 −0.302354
\(537\) 24.0000 1.03568
\(538\) −10.0000 −0.431131
\(539\) 0 0
\(540\) 0 0
\(541\) −28.0000 −1.20381 −0.601907 0.798566i \(-0.705592\pi\)
−0.601907 + 0.798566i \(0.705592\pi\)
\(542\) 5.00000 0.214768
\(543\) −10.0000 −0.429141
\(544\) 7.00000 0.300123
\(545\) 0 0
\(546\) 3.00000 0.128388
\(547\) 20.0000 0.855138 0.427569 0.903983i \(-0.359370\pi\)
0.427569 + 0.903983i \(0.359370\pi\)
\(548\) 3.00000 0.128154
\(549\) 8.00000 0.341432
\(550\) 0 0
\(551\) 5.00000 0.213007
\(552\) 5.00000 0.212814
\(553\) −10.0000 −0.425243
\(554\) −28.0000 −1.18961
\(555\) 0 0
\(556\) 12.0000 0.508913
\(557\) −8.00000 −0.338971 −0.169485 0.985533i \(-0.554211\pi\)
−0.169485 + 0.985533i \(0.554211\pi\)
\(558\) −20.0000 −0.846668
\(559\) −18.0000 −0.761319
\(560\) 0 0
\(561\) 0 0
\(562\) −26.0000 −1.09674
\(563\) 44.0000 1.85438 0.927189 0.374593i \(-0.122217\pi\)
0.927189 + 0.374593i \(0.122217\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 26.0000 1.09286
\(567\) 1.00000 0.0419961
\(568\) 0 0
\(569\) −8.00000 −0.335377 −0.167689 0.985840i \(-0.553630\pi\)
−0.167689 + 0.985840i \(0.553630\pi\)
\(570\) 0 0
\(571\) 10.0000 0.418487 0.209243 0.977864i \(-0.432900\pi\)
0.209243 + 0.977864i \(0.432900\pi\)
\(572\) 0 0
\(573\) −7.00000 −0.292429
\(574\) 2.00000 0.0834784
\(575\) 0 0
\(576\) −2.00000 −0.0833333
\(577\) 11.0000 0.457936 0.228968 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 32.0000 1.33102
\(579\) 2.00000 0.0831172
\(580\) 0 0
\(581\) 2.00000 0.0829740
\(582\) 18.0000 0.746124
\(583\) 0 0
\(584\) 9.00000 0.372423
\(585\) 0 0
\(586\) −31.0000 −1.28060
\(587\) −30.0000 −1.23823 −0.619116 0.785299i \(-0.712509\pi\)
−0.619116 + 0.785299i \(0.712509\pi\)
\(588\) −6.00000 −0.247436
\(589\) −10.0000 −0.412043
\(590\) 0 0
\(591\) 10.0000 0.411345
\(592\) −2.00000 −0.0821995
\(593\) 34.0000 1.39621 0.698106 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.00000 0.163846
\(597\) 17.0000 0.695764
\(598\) 15.0000 0.613396
\(599\) 30.0000 1.22577 0.612883 0.790173i \(-0.290010\pi\)
0.612883 + 0.790173i \(0.290010\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) −6.00000 −0.244542
\(603\) 14.0000 0.570124
\(604\) −6.00000 −0.244137
\(605\) 0 0
\(606\) −4.00000 −0.162489
\(607\) −22.0000 −0.892952 −0.446476 0.894795i \(-0.647321\pi\)
−0.446476 + 0.894795i \(0.647321\pi\)
\(608\) −1.00000 −0.0405554
\(609\) −5.00000 −0.202610
\(610\) 0 0
\(611\) 0 0
\(612\) −14.0000 −0.565916
\(613\) 16.0000 0.646234 0.323117 0.946359i \(-0.395269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(614\) −4.00000 −0.161427
\(615\) 0 0
\(616\) 0 0
\(617\) 2.00000 0.0805170 0.0402585 0.999189i \(-0.487182\pi\)
0.0402585 + 0.999189i \(0.487182\pi\)
\(618\) 0 0
\(619\) −8.00000 −0.321547 −0.160774 0.986991i \(-0.551399\pi\)
−0.160774 + 0.986991i \(0.551399\pi\)
\(620\) 0 0
\(621\) −25.0000 −1.00322
\(622\) 33.0000 1.32318
\(623\) −10.0000 −0.400642
\(624\) 3.00000 0.120096
\(625\) 0 0
\(626\) 29.0000 1.15907
\(627\) 0 0
\(628\) −18.0000 −0.718278
\(629\) −14.0000 −0.558217
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) −10.0000 −0.397779
\(633\) 5.00000 0.198732
\(634\) −3.00000 −0.119145
\(635\) 0 0
\(636\) −9.00000 −0.356873
\(637\) −18.0000 −0.713186
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −12.0000 −0.473972 −0.236986 0.971513i \(-0.576159\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(642\) −9.00000 −0.355202
\(643\) 2.00000 0.0788723 0.0394362 0.999222i \(-0.487444\pi\)
0.0394362 + 0.999222i \(0.487444\pi\)
\(644\) 5.00000 0.197028
\(645\) 0 0
\(646\) −7.00000 −0.275411
\(647\) 9.00000 0.353827 0.176913 0.984226i \(-0.443389\pi\)
0.176913 + 0.984226i \(0.443389\pi\)
\(648\) 1.00000 0.0392837
\(649\) 0 0
\(650\) 0 0
\(651\) 10.0000 0.391931
\(652\) 18.0000 0.704934
\(653\) 12.0000 0.469596 0.234798 0.972044i \(-0.424557\pi\)
0.234798 + 0.972044i \(0.424557\pi\)
\(654\) 13.0000 0.508340
\(655\) 0 0
\(656\) 2.00000 0.0780869
\(657\) −18.0000 −0.702247
\(658\) 0 0
\(659\) 15.0000 0.584317 0.292159 0.956370i \(-0.405627\pi\)
0.292159 + 0.956370i \(0.405627\pi\)
\(660\) 0 0
\(661\) 17.0000 0.661223 0.330612 0.943767i \(-0.392745\pi\)
0.330612 + 0.943767i \(0.392745\pi\)
\(662\) −17.0000 −0.660724
\(663\) 21.0000 0.815572
\(664\) 2.00000 0.0776151
\(665\) 0 0
\(666\) 4.00000 0.154997
\(667\) −25.0000 −0.968004
\(668\) −14.0000 −0.541676
\(669\) 22.0000 0.850569
\(670\) 0 0
\(671\) 0 0
\(672\) 1.00000 0.0385758
\(673\) 28.0000 1.07932 0.539660 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) 14.0000 0.539260
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) −19.0000 −0.730229 −0.365115 0.930963i \(-0.618970\pi\)
−0.365115 + 0.930963i \(0.618970\pi\)
\(678\) −8.00000 −0.307238
\(679\) 18.0000 0.690777
\(680\) 0 0
\(681\) 25.0000 0.958002
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 2.00000 0.0764719
\(685\) 0 0
\(686\) −13.0000 −0.496342
\(687\) −18.0000 −0.686743
\(688\) −6.00000 −0.228748
\(689\) −27.0000 −1.02862
\(690\) 0 0
\(691\) 10.0000 0.380418 0.190209 0.981744i \(-0.439083\pi\)
0.190209 + 0.981744i \(0.439083\pi\)
\(692\) −6.00000 −0.228086
\(693\) 0 0
\(694\) 18.0000 0.683271
\(695\) 0 0
\(696\) −5.00000 −0.189525
\(697\) 14.0000 0.530288
\(698\) 10.0000 0.378506
\(699\) −26.0000 −0.983410
\(700\) 0 0
\(701\) 24.0000 0.906467 0.453234 0.891392i \(-0.350270\pi\)
0.453234 + 0.891392i \(0.350270\pi\)
\(702\) −15.0000 −0.566139
\(703\) 2.00000 0.0754314
\(704\) 0 0
\(705\) 0 0
\(706\) −27.0000 −1.01616
\(707\) −4.00000 −0.150435
\(708\) −7.00000 −0.263076
\(709\) −34.0000 −1.27690 −0.638448 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) 0 0
\(711\) 20.0000 0.750059
\(712\) −10.0000 −0.374766
\(713\) 50.0000 1.87251
\(714\) 7.00000 0.261968
\(715\) 0 0
\(716\) 24.0000 0.896922
\(717\) −27.0000 −1.00833
\(718\) 27.0000 1.00763
\(719\) 29.0000 1.08152 0.540759 0.841178i \(-0.318137\pi\)
0.540759 + 0.841178i \(0.318137\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000 0.0372161
\(723\) −28.0000 −1.04133
\(724\) −10.0000 −0.371647
\(725\) 0 0
\(726\) −11.0000 −0.408248
\(727\) −11.0000 −0.407967 −0.203984 0.978974i \(-0.565389\pi\)
−0.203984 + 0.978974i \(0.565389\pi\)
\(728\) 3.00000 0.111187
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −42.0000 −1.55343
\(732\) −4.00000 −0.147844
\(733\) −24.0000 −0.886460 −0.443230 0.896408i \(-0.646168\pi\)
−0.443230 + 0.896408i \(0.646168\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) 5.00000 0.184302
\(737\) 0 0
\(738\) −4.00000 −0.147242
\(739\) 50.0000 1.83928 0.919640 0.392763i \(-0.128481\pi\)
0.919640 + 0.392763i \(0.128481\pi\)
\(740\) 0 0
\(741\) −3.00000 −0.110208
\(742\) −9.00000 −0.330400
\(743\) −34.0000 −1.24734 −0.623670 0.781688i \(-0.714359\pi\)
−0.623670 + 0.781688i \(0.714359\pi\)
\(744\) 10.0000 0.366618
\(745\) 0 0
\(746\) −3.00000 −0.109838
\(747\) −4.00000 −0.146352
\(748\) 0 0
\(749\) −9.00000 −0.328853
\(750\) 0 0
\(751\) 46.0000 1.67856 0.839282 0.543696i \(-0.182976\pi\)
0.839282 + 0.543696i \(0.182976\pi\)
\(752\) 0 0
\(753\) 4.00000 0.145768
\(754\) −15.0000 −0.546268
\(755\) 0 0
\(756\) −5.00000 −0.181848
\(757\) −22.0000 −0.799604 −0.399802 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) −7.00000 −0.254251
\(759\) 0 0
\(760\) 0 0
\(761\) −45.0000 −1.63125 −0.815624 0.578582i \(-0.803606\pi\)
−0.815624 + 0.578582i \(0.803606\pi\)
\(762\) 6.00000 0.217357
\(763\) 13.0000 0.470632
\(764\) −7.00000 −0.253251
\(765\) 0 0
\(766\) 0 0
\(767\) −21.0000 −0.758266
\(768\) 1.00000 0.0360844
\(769\) 49.0000 1.76699 0.883493 0.468445i \(-0.155186\pi\)
0.883493 + 0.468445i \(0.155186\pi\)
\(770\) 0 0
\(771\) 6.00000 0.216085
\(772\) 2.00000 0.0719816
\(773\) −15.0000 −0.539513 −0.269756 0.962929i \(-0.586943\pi\)
−0.269756 + 0.962929i \(0.586943\pi\)
\(774\) 12.0000 0.431331
\(775\) 0 0
\(776\) 18.0000 0.646162
\(777\) −2.00000 −0.0717496
\(778\) 24.0000 0.860442
\(779\) −2.00000 −0.0716574
\(780\) 0 0
\(781\) 0 0
\(782\) 35.0000 1.25160
\(783\) 25.0000 0.893427
\(784\) −6.00000 −0.214286
\(785\) 0 0
\(786\) −20.0000 −0.713376
\(787\) −11.0000 −0.392108 −0.196054 0.980593i \(-0.562813\pi\)
−0.196054 + 0.980593i \(0.562813\pi\)
\(788\) 10.0000 0.356235
\(789\) 8.00000 0.284808
\(790\) 0 0
\(791\) −8.00000 −0.284447
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) 20.0000 0.709773
\(795\) 0 0
\(796\) 17.0000 0.602549
\(797\) −5.00000 −0.177109 −0.0885545 0.996071i \(-0.528225\pi\)
−0.0885545 + 0.996071i \(0.528225\pi\)
\(798\) −1.00000 −0.0353996
\(799\) 0 0
\(800\) 0 0
\(801\) 20.0000 0.706665
\(802\) 18.0000 0.635602
\(803\) 0 0
\(804\) −7.00000 −0.246871
\(805\) 0 0
\(806\) 30.0000 1.05670
\(807\) −10.0000 −0.352017
\(808\) −4.00000 −0.140720
\(809\) −39.0000 −1.37117 −0.685583 0.727994i \(-0.740453\pi\)
−0.685583 + 0.727994i \(0.740453\pi\)
\(810\) 0 0
\(811\) 11.0000 0.386262 0.193131 0.981173i \(-0.438136\pi\)
0.193131 + 0.981173i \(0.438136\pi\)
\(812\) −5.00000 −0.175466
\(813\) 5.00000 0.175358
\(814\) 0 0
\(815\) 0 0
\(816\) 7.00000 0.245049
\(817\) 6.00000 0.209913
\(818\) 26.0000 0.909069
\(819\) −6.00000 −0.209657
\(820\) 0 0
\(821\) −56.0000 −1.95441 −0.977207 0.212290i \(-0.931908\pi\)
−0.977207 + 0.212290i \(0.931908\pi\)
\(822\) 3.00000 0.104637
\(823\) 31.0000 1.08059 0.540296 0.841475i \(-0.318312\pi\)
0.540296 + 0.841475i \(0.318312\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −7.00000 −0.243561
\(827\) 9.00000 0.312961 0.156480 0.987681i \(-0.449985\pi\)
0.156480 + 0.987681i \(0.449985\pi\)
\(828\) −10.0000 −0.347524
\(829\) −51.0000 −1.77130 −0.885652 0.464350i \(-0.846288\pi\)
−0.885652 + 0.464350i \(0.846288\pi\)
\(830\) 0 0
\(831\) −28.0000 −0.971309
\(832\) 3.00000 0.104006
\(833\) −42.0000 −1.45521
\(834\) 12.0000 0.415526
\(835\) 0 0
\(836\) 0 0
\(837\) −50.0000 −1.72825
\(838\) −26.0000 −0.898155
\(839\) −48.0000 −1.65714 −0.828572 0.559883i \(-0.810846\pi\)
−0.828572 + 0.559883i \(0.810846\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) 31.0000 1.06833
\(843\) −26.0000 −0.895488
\(844\) 5.00000 0.172107
\(845\) 0 0
\(846\) 0 0
\(847\) −11.0000 −0.377964
\(848\) −9.00000 −0.309061
\(849\) 26.0000 0.892318
\(850\) 0 0
\(851\) −10.0000 −0.342796
\(852\) 0 0
\(853\) 46.0000 1.57501 0.787505 0.616308i \(-0.211372\pi\)
0.787505 + 0.616308i \(0.211372\pi\)
\(854\) −4.00000 −0.136877
\(855\) 0 0
\(856\) −9.00000 −0.307614
\(857\) −24.0000 −0.819824 −0.409912 0.912125i \(-0.634441\pi\)
−0.409912 + 0.912125i \(0.634441\pi\)
\(858\) 0 0
\(859\) 56.0000 1.91070 0.955348 0.295484i \(-0.0954809\pi\)
0.955348 + 0.295484i \(0.0954809\pi\)
\(860\) 0 0
\(861\) 2.00000 0.0681598
\(862\) 12.0000 0.408722
\(863\) −24.0000 −0.816970 −0.408485 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) −5.00000 −0.170103
\(865\) 0 0
\(866\) −12.0000 −0.407777
\(867\) 32.0000 1.08678
\(868\) 10.0000 0.339422
\(869\) 0 0
\(870\) 0 0
\(871\) −21.0000 −0.711558
\(872\) 13.0000 0.440236
\(873\) −36.0000 −1.21842
\(874\) −5.00000 −0.169128
\(875\) 0 0
\(876\) 9.00000 0.304082
\(877\) 5.00000 0.168838 0.0844190 0.996430i \(-0.473097\pi\)
0.0844190 + 0.996430i \(0.473097\pi\)
\(878\) 10.0000 0.337484
\(879\) −31.0000 −1.04560
\(880\) 0 0
\(881\) 2.00000 0.0673817 0.0336909 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) 12.0000 0.404061
\(883\) −26.0000 −0.874970 −0.437485 0.899226i \(-0.644131\pi\)
−0.437485 + 0.899226i \(0.644131\pi\)
\(884\) 21.0000 0.706306
\(885\) 0 0
\(886\) −24.0000 −0.806296
\(887\) −52.0000 −1.74599 −0.872995 0.487730i \(-0.837825\pi\)
−0.872995 + 0.487730i \(0.837825\pi\)
\(888\) −2.00000 −0.0671156
\(889\) 6.00000 0.201234
\(890\) 0 0
\(891\) 0 0
\(892\) 22.0000 0.736614
\(893\) 0 0
\(894\) 4.00000 0.133780
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 15.0000 0.500835
\(898\) 14.0000 0.467186
\(899\) −50.0000 −1.66759
\(900\) 0 0
\(901\) −63.0000 −2.09883
\(902\) 0 0
\(903\) −6.00000 −0.199667
\(904\) −8.00000 −0.266076
\(905\) 0 0
\(906\) −6.00000 −0.199337
\(907\) −5.00000 −0.166022 −0.0830111 0.996549i \(-0.526454\pi\)
−0.0830111 + 0.996549i \(0.526454\pi\)
\(908\) 25.0000 0.829654
\(909\) 8.00000 0.265343
\(910\) 0 0
\(911\) −32.0000 −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(912\) −1.00000 −0.0331133
\(913\) 0 0
\(914\) 41.0000 1.35616
\(915\) 0 0
\(916\) −18.0000 −0.594737
\(917\) −20.0000 −0.660458
\(918\) −35.0000 −1.15517
\(919\) 11.0000 0.362857 0.181428 0.983404i \(-0.441928\pi\)
0.181428 + 0.983404i \(0.441928\pi\)
\(920\) 0 0
\(921\) −4.00000 −0.131804
\(922\) −10.0000 −0.329332
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) −16.0000 −0.525793
\(927\) 0 0
\(928\) −5.00000 −0.164133
\(929\) 21.0000 0.688988 0.344494 0.938789i \(-0.388051\pi\)
0.344494 + 0.938789i \(0.388051\pi\)
\(930\) 0 0
\(931\) 6.00000 0.196642
\(932\) −26.0000 −0.851658
\(933\) 33.0000 1.08037
\(934\) 8.00000 0.261768
\(935\) 0 0
\(936\) −6.00000 −0.196116
\(937\) 13.0000 0.424691 0.212346 0.977195i \(-0.431890\pi\)
0.212346 + 0.977195i \(0.431890\pi\)
\(938\) −7.00000 −0.228558
\(939\) 29.0000 0.946379
\(940\) 0 0
\(941\) −37.0000 −1.20617 −0.603083 0.797679i \(-0.706061\pi\)
−0.603083 + 0.797679i \(0.706061\pi\)
\(942\) −18.0000 −0.586472
\(943\) 10.0000 0.325645
\(944\) −7.00000 −0.227831
\(945\) 0 0
\(946\) 0 0
\(947\) 28.0000 0.909878 0.454939 0.890523i \(-0.349661\pi\)
0.454939 + 0.890523i \(0.349661\pi\)
\(948\) −10.0000 −0.324785
\(949\) 27.0000 0.876457
\(950\) 0 0
\(951\) −3.00000 −0.0972817
\(952\) 7.00000 0.226871
\(953\) −44.0000 −1.42530 −0.712650 0.701520i \(-0.752505\pi\)
−0.712650 + 0.701520i \(0.752505\pi\)
\(954\) 18.0000 0.582772
\(955\) 0 0
\(956\) −27.0000 −0.873242
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) 3.00000 0.0968751
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) −6.00000 −0.193448
\(963\) 18.0000 0.580042
\(964\) −28.0000 −0.901819
\(965\) 0 0
\(966\) 5.00000 0.160872
\(967\) −12.0000 −0.385894 −0.192947 0.981209i \(-0.561805\pi\)
−0.192947 + 0.981209i \(0.561805\pi\)
\(968\) −11.0000 −0.353553
\(969\) −7.00000 −0.224872
\(970\) 0 0
\(971\) 36.0000 1.15529 0.577647 0.816286i \(-0.303971\pi\)
0.577647 + 0.816286i \(0.303971\pi\)
\(972\) 16.0000 0.513200
\(973\) 12.0000 0.384702
\(974\) 2.00000 0.0640841
\(975\) 0 0
\(976\) −4.00000 −0.128037
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 18.0000 0.575577
\(979\) 0 0
\(980\) 0 0
\(981\) −26.0000 −0.830116
\(982\) 14.0000 0.446758
\(983\) 18.0000 0.574111 0.287055 0.957914i \(-0.407324\pi\)
0.287055 + 0.957914i \(0.407324\pi\)
\(984\) 2.00000 0.0637577
\(985\) 0 0
\(986\) −35.0000 −1.11463
\(987\) 0 0
\(988\) −3.00000 −0.0954427
\(989\) −30.0000 −0.953945
\(990\) 0 0
\(991\) −46.0000 −1.46124 −0.730619 0.682785i \(-0.760768\pi\)
−0.730619 + 0.682785i \(0.760768\pi\)
\(992\) 10.0000 0.317500
\(993\) −17.0000 −0.539479
\(994\) 0 0
\(995\) 0 0
\(996\) 2.00000 0.0633724
\(997\) −14.0000 −0.443384 −0.221692 0.975117i \(-0.571158\pi\)
−0.221692 + 0.975117i \(0.571158\pi\)
\(998\) 42.0000 1.32949
\(999\) 10.0000 0.316386
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 950.2.a.e.1.1 1
3.2 odd 2 8550.2.a.l.1.1 1
4.3 odd 2 7600.2.a.g.1.1 1
5.2 odd 4 950.2.b.d.799.2 2
5.3 odd 4 950.2.b.d.799.1 2
5.4 even 2 190.2.a.a.1.1 1
15.14 odd 2 1710.2.a.r.1.1 1
20.19 odd 2 1520.2.a.g.1.1 1
35.34 odd 2 9310.2.a.i.1.1 1
40.19 odd 2 6080.2.a.i.1.1 1
40.29 even 2 6080.2.a.r.1.1 1
95.94 odd 2 3610.2.a.h.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
190.2.a.a.1.1 1 5.4 even 2
950.2.a.e.1.1 1 1.1 even 1 trivial
950.2.b.d.799.1 2 5.3 odd 4
950.2.b.d.799.2 2 5.2 odd 4
1520.2.a.g.1.1 1 20.19 odd 2
1710.2.a.r.1.1 1 15.14 odd 2
3610.2.a.h.1.1 1 95.94 odd 2
6080.2.a.i.1.1 1 40.19 odd 2
6080.2.a.r.1.1 1 40.29 even 2
7600.2.a.g.1.1 1 4.3 odd 2
8550.2.a.l.1.1 1 3.2 odd 2
9310.2.a.i.1.1 1 35.34 odd 2