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Properties

Label 7600.2.a.g.1.1
Level $7600$
Weight $2$
Character 7600.1
Self dual yes
Analytic conductor $60.686$
Analytic rank $1$
Dimension $1$
CM no
Inner twists $1$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7600,2,Mod(1,7600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7600, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7600.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 7600 = 2^{4} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 7600.a (trivial)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(60.6863055362\)
Analytic rank: \(1\)
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 \(\chi\) \(=\) 7600.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} -1.00000 q^{7} -2.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} -1.00000 q^{7} -2.00000 q^{9} +3.00000 q^{13} +7.00000 q^{17} +1.00000 q^{19} +1.00000 q^{21} -5.00000 q^{23} +5.00000 q^{27} -5.00000 q^{29} -10.0000 q^{31} -2.00000 q^{37} -3.00000 q^{39} +2.00000 q^{41} +6.00000 q^{43} -6.00000 q^{49} -7.00000 q^{51} -9.00000 q^{53} -1.00000 q^{57} +7.00000 q^{59} -4.00000 q^{61} +2.00000 q^{63} +7.00000 q^{67} +5.00000 q^{69} +9.00000 q^{73} +10.0000 q^{79} +1.00000 q^{81} -2.00000 q^{83} +5.00000 q^{87} -10.0000 q^{89} -3.00000 q^{91} +10.0000 q^{93} +18.0000 q^{97} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 −0.288675 − 0.957427i \(-0.593215\pi\)
−0.288675 + 0.957427i \(0.593215\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 −0.377964 −0.188982 − 0.981981i \(-0.560519\pi\)
−0.188982 + 0.981981i \(0.560519\pi\)
\(8\) 0 0
\(9\) −2.00000 −0.666667
\(10\) 0 0
\(11\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 3.00000 0.832050 0.416025 − 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 7.00000 1.69775 0.848875 − 0.528594i \(-0.177281\pi\)
0.848875 + 0.528594i \(0.177281\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 1.00000 0.218218
\(22\) 0 0
\(23\) −5.00000 −1.04257 −0.521286 − 0.853382i \(-0.674548\pi\)
−0.521286 + 0.853382i \(0.674548\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −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 \(-0.854999\pi\)
−0.898027 + 0.439941i \(0.854999\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 − 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 0 0
\(39\) −3.00000 −0.480384
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 − 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) 6.00000 0.914991 0.457496 − 0.889212i \(-0.348747\pi\)
0.457496 + 0.889212i \(0.348747\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 0 0
\(49\) −6.00000 −0.857143
\(50\) 0 0
\(51\) −7.00000 −0.980196
\(52\) 0 0
\(53\) −9.00000 −1.23625 −0.618123 − 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) 7.00000 0.911322 0.455661 − 0.890153i \(-0.349403\pi\)
0.455661 + 0.890153i \(0.349403\pi\)
\(60\) 0 0
\(61\) −4.00000 −0.512148 −0.256074 − 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(62\) 0 0
\(63\) 2.00000 0.251976
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 7.00000 0.855186 0.427593 − 0.903971i \(-0.359362\pi\)
0.427593 + 0.903971i \(0.359362\pi\)
\(68\) 0 0
\(69\) 5.00000 0.601929
\(70\) 0 0
\(71\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) 9.00000 1.05337 0.526685 − 0.850060i \(-0.323435\pi\)
0.526685 + 0.850060i \(0.323435\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 10.0000 1.12509 0.562544 − 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −2.00000 −0.219529 −0.109764 − 0.993958i \(-0.535010\pi\)
−0.109764 + 0.993958i \(0.535010\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 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
\(92\) 0 0
\(93\) 10.0000 1.03695
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 18.0000 1.82762 0.913812 − 0.406138i \(-0.133125\pi\)
0.913812 + 0.406138i \(0.133125\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.00000 −0.398015 −0.199007 − 0.979998i \(-0.563772\pi\)
−0.199007 + 0.979998i \(0.563772\pi\)
\(102\) 0 0
\(103\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.00000 0.870063 0.435031 − 0.900415i \(-0.356737\pi\)
0.435031 + 0.900415i \(0.356737\pi\)
\(108\) 0 0
\(109\) 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
\(112\) 0 0
\(113\) −8.00000 −0.752577 −0.376288 − 0.926503i \(-0.622800\pi\)
−0.376288 + 0.926503i \(0.622800\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −6.00000 −0.554700
\(118\) 0 0
\(119\) −7.00000 −0.641689
\(120\) 0 0
\(121\) −11.0000 −1.00000
\(122\) 0 0
\(123\) −2.00000 −0.180334
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −6.00000 −0.532414 −0.266207 − 0.963916i \(-0.585770\pi\)
−0.266207 + 0.963916i \(0.585770\pi\)
\(128\) 0 0
\(129\) −6.00000 −0.528271
\(130\) 0 0
\(131\) 20.0000 1.74741 0.873704 − 0.486458i \(-0.161711\pi\)
0.873704 + 0.486458i \(0.161711\pi\)
\(132\) 0 0
\(133\) −1.00000 −0.0867110
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 3.00000 0.256307 0.128154 − 0.991754i \(-0.459095\pi\)
0.128154 + 0.991754i \(0.459095\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 − 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 6.00000 0.494872
\(148\) 0 0
\(149\) 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 \(-0.421495\pi\)
0.244137 + 0.969741i \(0.421495\pi\)
\(152\) 0 0
\(153\) −14.0000 −1.13183
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −18.0000 −1.43656 −0.718278 − 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) 0 0
\(159\) 9.00000 0.713746
\(160\) 0 0
\(161\) 5.00000 0.394055
\(162\) 0 0
\(163\) −18.0000 −1.40987 −0.704934 − 0.709273i \(-0.749024\pi\)
−0.704934 + 0.709273i \(0.749024\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 14.0000 1.08335 0.541676 − 0.840587i \(-0.317790\pi\)
0.541676 + 0.840587i \(0.317790\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) −2.00000 −0.152944
\(172\) 0 0
\(173\) −6.00000 −0.456172 −0.228086 − 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −7.00000 −0.526152
\(178\) 0 0
\(179\) −24.0000 −1.79384 −0.896922 − 0.442189i \(-0.854202\pi\)
−0.896922 + 0.442189i \(0.854202\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 − 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 4.00000 0.295689
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −5.00000 −0.363696
\(190\) 0 0
\(191\) 7.00000 0.506502 0.253251 − 0.967401i \(-0.418500\pi\)
0.253251 + 0.967401i \(0.418500\pi\)
\(192\) 0 0
\(193\) 2.00000 0.143963 0.0719816 − 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 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 \(-0.705848\pi\)
−0.602549 + 0.798082i \(0.705848\pi\)
\(200\) 0 0
\(201\) −7.00000 −0.493742
\(202\) 0 0
\(203\) 5.00000 0.350931
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 10.0000 0.695048
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −5.00000 −0.344214 −0.172107 − 0.985078i \(-0.555058\pi\)
−0.172107 + 0.985078i \(0.555058\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 10.0000 0.678844
\(218\) 0 0
\(219\) −9.00000 −0.608164
\(220\) 0 0
\(221\) 21.0000 1.41261
\(222\) 0 0
\(223\) −22.0000 −1.47323 −0.736614 − 0.676313i \(-0.763577\pi\)
−0.736614 + 0.676313i \(0.763577\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −25.0000 −1.65931 −0.829654 − 0.558278i \(-0.811462\pi\)
−0.829654 + 0.558278i \(0.811462\pi\)
\(228\) 0 0
\(229\) −18.0000 −1.18947 −0.594737 − 0.803921i \(-0.702744\pi\)
−0.594737 + 0.803921i \(0.702744\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −26.0000 −1.70332 −0.851658 − 0.524097i \(-0.824403\pi\)
−0.851658 + 0.524097i \(0.824403\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −10.0000 −0.649570
\(238\) 0 0
\(239\) 27.0000 1.74648 0.873242 − 0.487286i \(-0.162013\pi\)
0.873242 + 0.487286i \(0.162013\pi\)
\(240\) 0 0
\(241\) −28.0000 −1.80364 −0.901819 − 0.432113i \(-0.857768\pi\)
−0.901819 + 0.432113i \(0.857768\pi\)
\(242\) 0 0
\(243\) −16.0000 −1.02640
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 3.00000 0.190885
\(248\) 0 0
\(249\) 2.00000 0.126745
\(250\) 0 0
\(251\) −4.00000 −0.252478 −0.126239 − 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6.00000 0.374270 0.187135 − 0.982334i \(-0.440080\pi\)
0.187135 + 0.982334i \(0.440080\pi\)
\(258\) 0 0
\(259\) 2.00000 0.124274
\(260\) 0 0
\(261\) 10.0000 0.618984
\(262\) 0 0
\(263\) −8.00000 −0.493301 −0.246651 − 0.969104i \(-0.579330\pi\)
−0.246651 + 0.969104i \(0.579330\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 10.0000 0.611990
\(268\) 0 0
\(269\) −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 \(-0.548528\pi\)
−0.151864 + 0.988401i \(0.548528\pi\)
\(272\) 0 0
\(273\) 3.00000 0.181568
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −28.0000 −1.68236 −0.841178 − 0.540758i \(-0.818138\pi\)
−0.841178 + 0.540758i \(0.818138\pi\)
\(278\) 0 0
\(279\) 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 \(-0.781129\pi\)
−0.772770 + 0.634686i \(0.781129\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −2.00000 −0.118056
\(288\) 0 0
\(289\) 32.0000 1.88235
\(290\) 0 0
\(291\) −18.0000 −1.05518
\(292\) 0 0
\(293\) −31.0000 −1.81104 −0.905520 − 0.424304i \(-0.860519\pi\)
−0.905520 + 0.424304i \(0.860519\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −15.0000 −0.867472
\(300\) 0 0
\(301\) −6.00000 −0.345834
\(302\) 0 0
\(303\) 4.00000 0.229794
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 − 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −33.0000 −1.87126 −0.935629 − 0.352985i \(-0.885167\pi\)
−0.935629 + 0.352985i \(0.885167\pi\)
\(312\) 0 0
\(313\) 29.0000 1.63918 0.819588 − 0.572953i \(-0.194202\pi\)
0.819588 + 0.572953i \(0.194202\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −3.00000 −0.168497 −0.0842484 − 0.996445i \(-0.526849\pi\)
−0.0842484 + 0.996445i \(0.526849\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) −9.00000 −0.502331
\(322\) 0 0
\(323\) 7.00000 0.389490
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −13.0000 −0.718902
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 17.0000 0.934405 0.467202 − 0.884150i \(-0.345262\pi\)
0.467202 + 0.884150i \(0.345262\pi\)
\(332\) 0 0
\(333\) 4.00000 0.219199
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 − 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 0 0
\(339\) 8.00000 0.434500
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 13.0000 0.701934
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −18.0000 −0.966291 −0.483145 − 0.875540i \(-0.660506\pi\)
−0.483145 + 0.875540i \(0.660506\pi\)
\(348\) 0 0
\(349\) 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 \(0.755186\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 7.00000 0.370479
\(358\) 0 0
\(359\) −27.0000 −1.42501 −0.712503 − 0.701669i \(-0.752438\pi\)
−0.712503 + 0.701669i \(0.752438\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 11.0000 0.577350
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 8.00000 0.417597 0.208798 − 0.977959i \(-0.433045\pi\)
0.208798 + 0.977959i \(0.433045\pi\)
\(368\) 0 0
\(369\) −4.00000 −0.208232
\(370\) 0 0
\(371\) 9.00000 0.467257
\(372\) 0 0
\(373\) −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
\(378\) 0 0
\(379\) 7.00000 0.359566 0.179783 − 0.983706i \(-0.442460\pi\)
0.179783 + 0.983706i \(0.442460\pi\)
\(380\) 0 0
\(381\) 6.00000 0.307389
\(382\) 0 0
\(383\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −12.0000 −0.609994
\(388\) 0 0
\(389\) 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
\(392\) 0 0
\(393\) −20.0000 −1.00887
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 20.0000 1.00377 0.501886 − 0.864934i \(-0.332640\pi\)
0.501886 + 0.864934i \(0.332640\pi\)
\(398\) 0 0
\(399\) 1.00000 0.0500626
\(400\) 0 0
\(401\) 18.0000 0.898877 0.449439 − 0.893311i \(-0.351624\pi\)
0.449439 + 0.893311i \(0.351624\pi\)
\(402\) 0 0
\(403\) −30.0000 −1.49441
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 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
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 12.0000 0.587643
\(418\) 0 0
\(419\) 26.0000 1.27018 0.635092 − 0.772437i \(-0.280962\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(420\) 0 0
\(421\) 31.0000 1.51085 0.755424 − 0.655237i \(-0.227431\pi\)
0.755424 + 0.655237i \(0.227431\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4.00000 0.193574
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 −0.578020 −0.289010 − 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 0 0
\(433\) −12.0000 −0.576683 −0.288342 − 0.957528i \(-0.593104\pi\)
−0.288342 + 0.957528i \(0.593104\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.00000 −0.239182
\(438\) 0 0
\(439\) −10.0000 −0.477274 −0.238637 − 0.971109i \(-0.576701\pi\)
−0.238637 + 0.971109i \(0.576701\pi\)
\(440\) 0 0
\(441\) 12.0000 0.571429
\(442\) 0 0
\(443\) 24.0000 1.14027 0.570137 − 0.821549i \(-0.306890\pi\)
0.570137 + 0.821549i \(0.306890\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −4.00000 −0.189194
\(448\) 0 0
\(449\) 14.0000 0.660701 0.330350 − 0.943858i \(-0.392833\pi\)
0.330350 + 0.943858i \(0.392833\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −6.00000 −0.281905
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 41.0000 1.91790 0.958950 − 0.283577i \(-0.0915211\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) 0 0
\(459\) 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 \(-0.378744\pi\)
0.371792 + 0.928316i \(0.378744\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −8.00000 −0.370196 −0.185098 − 0.982720i \(-0.559260\pi\)
−0.185098 + 0.982720i \(0.559260\pi\)
\(468\) 0 0
\(469\) −7.00000 −0.323230
\(470\) 0 0
\(471\) 18.0000 0.829396
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 18.0000 0.824163
\(478\) 0 0
\(479\) 24.0000 1.09659 0.548294 − 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) −6.00000 −0.273576
\(482\) 0 0
\(483\) −5.00000 −0.227508
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −2.00000 −0.0906287 −0.0453143 − 0.998973i \(-0.514429\pi\)
−0.0453143 + 0.998973i \(0.514429\pi\)
\(488\) 0 0
\(489\) 18.0000 0.813988
\(490\) 0 0
\(491\) −14.0000 −0.631811 −0.315906 − 0.948791i \(-0.602308\pi\)
−0.315906 + 0.948791i \(0.602308\pi\)
\(492\) 0 0
\(493\) −35.0000 −1.57632
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) −42.0000 −1.88018 −0.940089 − 0.340929i \(-0.889258\pi\)
−0.940089 + 0.340929i \(0.889258\pi\)
\(500\) 0 0
\(501\) −14.0000 −0.625474
\(502\) 0 0
\(503\) −17.0000 −0.757993 −0.378996 − 0.925398i \(-0.623731\pi\)
−0.378996 + 0.925398i \(0.623731\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 4.00000 0.177646
\(508\) 0 0
\(509\) −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
\(512\) 0 0
\(513\) 5.00000 0.220755
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 6.00000 0.263371
\(520\) 0 0
\(521\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(522\) 0 0
\(523\) −19.0000 −0.830812 −0.415406 − 0.909636i \(-0.636360\pi\)
−0.415406 + 0.909636i \(0.636360\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −70.0000 −3.04925
\(528\) 0 0
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) −14.0000 −0.607548
\(532\) 0 0
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 24.0000 1.03568
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −28.0000 −1.20381 −0.601907 − 0.798566i \(-0.705592\pi\)
−0.601907 + 0.798566i \(0.705592\pi\)
\(542\) 0 0
\(543\) 10.0000 0.429141
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −20.0000 −0.855138 −0.427569 − 0.903983i \(-0.640630\pi\)
−0.427569 + 0.903983i \(0.640630\pi\)
\(548\) 0 0
\(549\) 8.00000 0.341432
\(550\) 0 0
\(551\) −5.00000 −0.213007
\(552\) 0 0
\(553\) −10.0000 −0.425243
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.00000 −0.338971 −0.169485 − 0.985533i \(-0.554211\pi\)
−0.169485 + 0.985533i \(0.554211\pi\)
\(558\) 0 0
\(559\) 18.0000 0.761319
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −44.0000 −1.85438 −0.927189 − 0.374593i \(-0.877783\pi\)
−0.927189 + 0.374593i \(0.877783\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −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 \(-0.567100\pi\)
−0.209243 + 0.977864i \(0.567100\pi\)
\(572\) 0 0
\(573\) −7.00000 −0.292429
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 11.0000 0.457936 0.228968 − 0.973434i \(-0.426465\pi\)
0.228968 + 0.973434i \(0.426465\pi\)
\(578\) 0 0
\(579\) −2.00000 −0.0831172
\(580\) 0 0
\(581\) 2.00000 0.0829740
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 30.0000 1.23823 0.619116 − 0.785299i \(-0.287491\pi\)
0.619116 + 0.785299i \(0.287491\pi\)
\(588\) 0 0
\(589\) −10.0000 −0.412043
\(590\) 0 0
\(591\) −10.0000 −0.411345
\(592\) 0 0
\(593\) 34.0000 1.39621 0.698106 − 0.715994i \(-0.254026\pi\)
0.698106 + 0.715994i \(0.254026\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 17.0000 0.695764
\(598\) 0 0
\(599\) −30.0000 −1.22577 −0.612883 − 0.790173i \(-0.709990\pi\)
−0.612883 + 0.790173i \(0.709990\pi\)
\(600\) 0 0
\(601\) −10.0000 −0.407909 −0.203954 − 0.978980i \(-0.565379\pi\)
−0.203954 + 0.978980i \(0.565379\pi\)
\(602\) 0 0
\(603\) −14.0000 −0.570124
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 22.0000 0.892952 0.446476 − 0.894795i \(-0.352679\pi\)
0.446476 + 0.894795i \(0.352679\pi\)
\(608\) 0 0
\(609\) −5.00000 −0.202610
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 16.0000 0.646234 0.323117 − 0.946359i \(-0.395269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(614\) 0 0
\(615\) 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 \(-0.448601\pi\)
0.160774 + 0.986991i \(0.448601\pi\)
\(620\) 0 0
\(621\) −25.0000 −1.00322
\(622\) 0 0
\(623\) 10.0000 0.400642
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −14.0000 −0.558217
\(630\) 0 0
\(631\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) 0 0
\(633\) 5.00000 0.198732
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −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 \(0.576159\pi\)
\(642\) 0 0
\(643\) −2.00000 −0.0788723 −0.0394362 − 0.999222i \(-0.512556\pi\)
−0.0394362 + 0.999222i \(0.512556\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −9.00000 −0.353827 −0.176913 − 0.984226i \(-0.556611\pi\)
−0.176913 + 0.984226i \(0.556611\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −10.0000 −0.391931
\(652\) 0 0
\(653\) 12.0000 0.469596 0.234798 − 0.972044i \(-0.424557\pi\)
0.234798 + 0.972044i \(0.424557\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −18.0000 −0.702247
\(658\) 0 0
\(659\) −15.0000 −0.584317 −0.292159 − 0.956370i \(-0.594373\pi\)
−0.292159 + 0.956370i \(0.594373\pi\)
\(660\) 0 0
\(661\) 17.0000 0.661223 0.330612 − 0.943767i \(-0.392745\pi\)
0.330612 + 0.943767i \(0.392745\pi\)
\(662\) 0 0
\(663\) −21.0000 −0.815572
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 25.0000 0.968004
\(668\) 0 0
\(669\) 22.0000 0.850569
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 28.0000 1.07932 0.539660 − 0.841883i \(-0.318553\pi\)
0.539660 + 0.841883i \(0.318553\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −19.0000 −0.730229 −0.365115 − 0.930963i \(-0.618970\pi\)
−0.365115 + 0.930963i \(0.618970\pi\)
\(678\) 0 0
\(679\) −18.0000 −0.690777
\(680\) 0 0
\(681\) 25.0000 0.958002
\(682\) 0 0
\(683\) 36.0000 1.37750 0.688751 − 0.724998i \(-0.258159\pi\)
0.688751 + 0.724998i \(0.258159\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 18.0000 0.686743
\(688\) 0 0
\(689\) −27.0000 −1.02862
\(690\) 0 0
\(691\) −10.0000 −0.380418 −0.190209 − 0.981744i \(-0.560917\pi\)
−0.190209 + 0.981744i \(0.560917\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 14.0000 0.530288
\(698\) 0 0
\(699\) 26.0000 0.983410
\(700\) 0 0
\(701\) 24.0000 0.906467 0.453234 − 0.891392i \(-0.350270\pi\)
0.453234 + 0.891392i \(0.350270\pi\)
\(702\) 0 0
\(703\) −2.00000 −0.0754314
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 4.00000 0.150435
\(708\) 0 0
\(709\) −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
\(712\) 0 0
\(713\) 50.0000 1.87251
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −27.0000 −1.00833
\(718\) 0 0
\(719\) −29.0000 −1.08152 −0.540759 − 0.841178i \(-0.681863\pi\)
−0.540759 + 0.841178i \(0.681863\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 28.0000 1.04133
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 11.0000 0.407967 0.203984 − 0.978974i \(-0.434611\pi\)
0.203984 + 0.978974i \(0.434611\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) 42.0000 1.55343
\(732\) 0 0
\(733\) −24.0000 −0.886460 −0.443230 − 0.896408i \(-0.646168\pi\)
−0.443230 + 0.896408i \(0.646168\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −50.0000 −1.83928 −0.919640 − 0.392763i \(-0.871519\pi\)
−0.919640 + 0.392763i \(0.871519\pi\)
\(740\) 0 0
\(741\) −3.00000 −0.110208
\(742\) 0 0
\(743\) 34.0000 1.24734 0.623670 − 0.781688i \(-0.285641\pi\)
0.623670 + 0.781688i \(0.285641\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 4.00000 0.146352
\(748\) 0 0
\(749\) −9.00000 −0.328853
\(750\) 0 0
\(751\) −46.0000 −1.67856 −0.839282 − 0.543696i \(-0.817024\pi\)
−0.839282 + 0.543696i \(0.817024\pi\)
\(752\) 0 0
\(753\) 4.00000 0.145768
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −22.0000 −0.799604 −0.399802 − 0.916602i \(-0.630921\pi\)
−0.399802 + 0.916602i \(0.630921\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −45.0000 −1.63125 −0.815624 − 0.578582i \(-0.803606\pi\)
−0.815624 + 0.578582i \(0.803606\pi\)
\(762\) 0 0
\(763\) −13.0000 −0.470632
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 21.0000 0.758266
\(768\) 0 0
\(769\) 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
\(772\) 0 0
\(773\) −15.0000 −0.539513 −0.269756 − 0.962929i \(-0.586943\pi\)
−0.269756 + 0.962929i \(0.586943\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) −2.00000 −0.0717496
\(778\) 0 0
\(779\) 2.00000 0.0716574
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −25.0000 −0.893427
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 11.0000 0.392108 0.196054 − 0.980593i \(-0.437187\pi\)
0.196054 + 0.980593i \(0.437187\pi\)
\(788\) 0 0
\(789\) 8.00000 0.284808
\(790\) 0 0
\(791\) 8.00000 0.284447
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −5.00000 −0.177109 −0.0885545 − 0.996071i \(-0.528225\pi\)
−0.0885545 + 0.996071i \(0.528225\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 20.0000 0.706665
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 10.0000 0.352017
\(808\) 0 0
\(809\) −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 \(-0.561864\pi\)
−0.193131 + 0.981173i \(0.561864\pi\)
\(812\) 0 0
\(813\) 5.00000 0.175358
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 6.00000 0.209913
\(818\) 0 0
\(819\) 6.00000 0.209657
\(820\) 0 0
\(821\) −56.0000 −1.95441 −0.977207 − 0.212290i \(-0.931908\pi\)
−0.977207 + 0.212290i \(0.931908\pi\)
\(822\) 0 0
\(823\) −31.0000 −1.08059 −0.540296 − 0.841475i \(-0.681688\pi\)
−0.540296 + 0.841475i \(0.681688\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −9.00000 −0.312961 −0.156480 − 0.987681i \(-0.550015\pi\)
−0.156480 + 0.987681i \(0.550015\pi\)
\(828\) 0 0
\(829\) −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
\(832\) 0 0
\(833\) −42.0000 −1.45521
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −50.0000 −1.72825
\(838\) 0 0
\(839\) 48.0000 1.65714 0.828572 − 0.559883i \(-0.189154\pi\)
0.828572 + 0.559883i \(0.189154\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) 0 0
\(843\) 26.0000 0.895488
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 11.0000 0.377964
\(848\) 0 0
\(849\) 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 \(0.211372\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −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 \(-0.904519\pi\)
−0.955348 + 0.295484i \(0.904519\pi\)
\(860\) 0 0
\(861\) 2.00000 0.0681598
\(862\) 0 0
\(863\) 24.0000 0.816970 0.408485 − 0.912765i \(-0.366057\pi\)
0.408485 + 0.912765i \(0.366057\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −32.0000 −1.08678
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 21.0000 0.711558
\(872\) 0 0
\(873\) −36.0000 −1.21842
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 5.00000 0.168838 0.0844190 − 0.996430i \(-0.473097\pi\)
0.0844190 + 0.996430i \(0.473097\pi\)
\(878\) 0 0
\(879\) 31.0000 1.04560
\(880\) 0 0
\(881\) 2.00000 0.0673817 0.0336909 − 0.999432i \(-0.489274\pi\)
0.0336909 + 0.999432i \(0.489274\pi\)
\(882\) 0 0
\(883\) 26.0000 0.874970 0.437485 − 0.899226i \(-0.355869\pi\)
0.437485 + 0.899226i \(0.355869\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 52.0000 1.74599 0.872995 − 0.487730i \(-0.162175\pi\)
0.872995 + 0.487730i \(0.162175\pi\)
\(888\) 0 0
\(889\) 6.00000 0.201234
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 15.0000 0.500835
\(898\) 0 0
\(899\) 50.0000 1.66759
\(900\) 0 0
\(901\) −63.0000 −2.09883
\(902\) 0 0
\(903\) 6.00000 0.199667
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 5.00000 0.166022 0.0830111 − 0.996549i \(-0.473546\pi\)
0.0830111 + 0.996549i \(0.473546\pi\)
\(908\) 0 0
\(909\) 8.00000 0.265343
\(910\) 0 0
\(911\) 32.0000 1.06021 0.530104 − 0.847933i \(-0.322153\pi\)
0.530104 + 0.847933i \(0.322153\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −20.0000 −0.660458
\(918\) 0 0
\(919\) −11.0000 −0.362857 −0.181428 − 0.983404i \(-0.558072\pi\)
−0.181428 + 0.983404i \(0.558072\pi\)
\(920\) 0 0
\(921\) −4.00000 −0.131804
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 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
\(932\) 0 0
\(933\) 33.0000 1.08037
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 13.0000 0.424691 0.212346 − 0.977195i \(-0.431890\pi\)
0.212346 + 0.977195i \(0.431890\pi\)
\(938\) 0 0
\(939\) −29.0000 −0.946379
\(940\) 0 0
\(941\) −37.0000 −1.20617 −0.603083 − 0.797679i \(-0.706061\pi\)
−0.603083 + 0.797679i \(0.706061\pi\)
\(942\) 0 0
\(943\) −10.0000 −0.325645
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −28.0000 −0.909878 −0.454939 − 0.890523i \(-0.650339\pi\)
−0.454939 + 0.890523i \(0.650339\pi\)
\(948\) 0 0
\(949\) 27.0000 0.876457
\(950\) 0 0
\(951\) 3.00000 0.0972817
\(952\) 0 0
\(953\) −44.0000 −1.42530 −0.712650 − 0.701520i \(-0.752505\pi\)
−0.712650 + 0.701520i \(0.752505\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −3.00000 −0.0968751
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) 0 0
\(963\) −18.0000 −0.580042
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 12.0000 0.385894 0.192947 − 0.981209i \(-0.438195\pi\)
0.192947 + 0.981209i \(0.438195\pi\)
\(968\) 0 0
\(969\) −7.00000 −0.224872
\(970\) 0 0
\(971\) −36.0000 −1.15529 −0.577647 − 0.816286i \(-0.696029\pi\)
−0.577647 + 0.816286i \(0.696029\pi\)
\(972\) 0 0
\(973\) 12.0000 0.384702
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 18.0000 0.575871 0.287936 − 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −26.0000 −0.830116
\(982\) 0 0
\(983\) −18.0000 −0.574111 −0.287055 − 0.957914i \(-0.592676\pi\)
−0.287055 + 0.957914i \(0.592676\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −30.0000 −0.953945
\(990\) 0 0
\(991\) 46.0000 1.46124 0.730619 − 0.682785i \(-0.239232\pi\)
0.730619 + 0.682785i \(0.239232\pi\)
\(992\) 0 0
\(993\) −17.0000 −0.539479
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −14.0000 −0.443384 −0.221692 − 0.975117i \(-0.571158\pi\)
−0.221692 + 0.975117i \(0.571158\pi\)
\(998\) 0 0
\(999\) −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 7600.2.a.g.1.1 1
4.3 odd 2 950.2.a.e.1.1 1
5.4 even 2 1520.2.a.g.1.1 1
12.11 even 2 8550.2.a.l.1.1 1
20.3 even 4 950.2.b.d.799.1 2
20.7 even 4 950.2.b.d.799.2 2
20.19 odd 2 190.2.a.a.1.1 ✓ 1
40.19 odd 2 6080.2.a.r.1.1 1
40.29 even 2 6080.2.a.i.1.1 1
60.59 even 2 1710.2.a.r.1.1 1
140.139 even 2 9310.2.a.i.1.1 1
380.379 even 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 20.19 odd 2
950.2.a.e.1.1 1 4.3 odd 2
950.2.b.d.799.1 2 20.3 even 4
950.2.b.d.799.2 2 20.7 even 4
1520.2.a.g.1.1 1 5.4 even 2
1710.2.a.r.1.1 1 60.59 even 2
3610.2.a.h.1.1 1 380.379 even 2
6080.2.a.i.1.1 1 40.29 even 2
6080.2.a.r.1.1 1 40.19 odd 2
7600.2.a.g.1.1 1 1.1 even 1 trivial
8550.2.a.l.1.1 1 12.11 even 2
9310.2.a.i.1.1 1 140.139 even 2