Properties

Label 5610.2.a.bj.1.1
Level $5610$
Weight $2$
Character 5610.1
Self dual yes
Analytic conductor $44.796$
Analytic rank $0$
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] = [5610,2,Mod(1,5610)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5610, 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("5610.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5610.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: \(44.7960755339\)
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 \(\chi\) \(=\) 5610.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +5.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +5.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -4.00000 q^{13} +5.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -4.00000 q^{19} -1.00000 q^{20} +5.00000 q^{21} +1.00000 q^{22} -3.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -4.00000 q^{26} +1.00000 q^{27} +5.00000 q^{28} +9.00000 q^{29} -1.00000 q^{30} +5.00000 q^{31} +1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} -5.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -4.00000 q^{38} -4.00000 q^{39} -1.00000 q^{40} +5.00000 q^{42} +11.0000 q^{43} +1.00000 q^{44} -1.00000 q^{45} -3.00000 q^{46} +1.00000 q^{48} +18.0000 q^{49} +1.00000 q^{50} -1.00000 q^{51} -4.00000 q^{52} +12.0000 q^{53} +1.00000 q^{54} -1.00000 q^{55} +5.00000 q^{56} -4.00000 q^{57} +9.00000 q^{58} -6.00000 q^{59} -1.00000 q^{60} +2.00000 q^{61} +5.00000 q^{62} +5.00000 q^{63} +1.00000 q^{64} +4.00000 q^{65} +1.00000 q^{66} -4.00000 q^{67} -1.00000 q^{68} -3.00000 q^{69} -5.00000 q^{70} -6.00000 q^{71} +1.00000 q^{72} +2.00000 q^{73} +2.00000 q^{74} +1.00000 q^{75} -4.00000 q^{76} +5.00000 q^{77} -4.00000 q^{78} +8.00000 q^{79} -1.00000 q^{80} +1.00000 q^{81} +12.0000 q^{83} +5.00000 q^{84} +1.00000 q^{85} +11.0000 q^{86} +9.00000 q^{87} +1.00000 q^{88} -1.00000 q^{90} -20.0000 q^{91} -3.00000 q^{92} +5.00000 q^{93} +4.00000 q^{95} +1.00000 q^{96} -7.00000 q^{97} +18.0000 q^{98} +1.00000 q^{99} +O(q^{100})\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.00000 0.577350
\(4\) 1.00000 0.500000
\(5\) −1.00000 −0.447214
\(6\) 1.00000 0.408248
\(7\) 5.00000 1.88982 0.944911 0.327327i \(-0.106148\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 1.00000 0.353553
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 5.00000 1.33631
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) −1.00000 −0.242536
\(18\) 1.00000 0.235702
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) −1.00000 −0.223607
\(21\) 5.00000 1.09109
\(22\) 1.00000 0.213201
\(23\) −3.00000 −0.625543 −0.312772 0.949828i \(-0.601257\pi\)
−0.312772 + 0.949828i \(0.601257\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) −4.00000 −0.784465
\(27\) 1.00000 0.192450
\(28\) 5.00000 0.944911
\(29\) 9.00000 1.67126 0.835629 0.549294i \(-0.185103\pi\)
0.835629 + 0.549294i \(0.185103\pi\)
\(30\) −1.00000 −0.182574
\(31\) 5.00000 0.898027 0.449013 0.893525i \(-0.351776\pi\)
0.449013 + 0.893525i \(0.351776\pi\)
\(32\) 1.00000 0.176777
\(33\) 1.00000 0.174078
\(34\) −1.00000 −0.171499
\(35\) −5.00000 −0.845154
\(36\) 1.00000 0.166667
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −4.00000 −0.648886
\(39\) −4.00000 −0.640513
\(40\) −1.00000 −0.158114
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 5.00000 0.771517
\(43\) 11.0000 1.67748 0.838742 0.544529i \(-0.183292\pi\)
0.838742 + 0.544529i \(0.183292\pi\)
\(44\) 1.00000 0.150756
\(45\) −1.00000 −0.149071
\(46\) −3.00000 −0.442326
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000 0.144338
\(49\) 18.0000 2.57143
\(50\) 1.00000 0.141421
\(51\) −1.00000 −0.140028
\(52\) −4.00000 −0.554700
\(53\) 12.0000 1.64833 0.824163 0.566352i \(-0.191646\pi\)
0.824163 + 0.566352i \(0.191646\pi\)
\(54\) 1.00000 0.136083
\(55\) −1.00000 −0.134840
\(56\) 5.00000 0.668153
\(57\) −4.00000 −0.529813
\(58\) 9.00000 1.18176
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) −1.00000 −0.129099
\(61\) 2.00000 0.256074 0.128037 0.991769i \(-0.459132\pi\)
0.128037 + 0.991769i \(0.459132\pi\)
\(62\) 5.00000 0.635001
\(63\) 5.00000 0.629941
\(64\) 1.00000 0.125000
\(65\) 4.00000 0.496139
\(66\) 1.00000 0.123091
\(67\) −4.00000 −0.488678 −0.244339 0.969690i \(-0.578571\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) −1.00000 −0.121268
\(69\) −3.00000 −0.361158
\(70\) −5.00000 −0.597614
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 1.00000 0.117851
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 2.00000 0.232495
\(75\) 1.00000 0.115470
\(76\) −4.00000 −0.458831
\(77\) 5.00000 0.569803
\(78\) −4.00000 −0.452911
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 12.0000 1.31717 0.658586 0.752506i \(-0.271155\pi\)
0.658586 + 0.752506i \(0.271155\pi\)
\(84\) 5.00000 0.545545
\(85\) 1.00000 0.108465
\(86\) 11.0000 1.18616
\(87\) 9.00000 0.964901
\(88\) 1.00000 0.106600
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) −1.00000 −0.105409
\(91\) −20.0000 −2.09657
\(92\) −3.00000 −0.312772
\(93\) 5.00000 0.518476
\(94\) 0 0
\(95\) 4.00000 0.410391
\(96\) 1.00000 0.102062
\(97\) −7.00000 −0.710742 −0.355371 0.934725i \(-0.615646\pi\)
−0.355371 + 0.934725i \(0.615646\pi\)
\(98\) 18.0000 1.81827
\(99\) 1.00000 0.100504
\(100\) 1.00000 0.100000
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) −1.00000 −0.0990148
\(103\) 5.00000 0.492665 0.246332 0.969185i \(-0.420775\pi\)
0.246332 + 0.969185i \(0.420775\pi\)
\(104\) −4.00000 −0.392232
\(105\) −5.00000 −0.487950
\(106\) 12.0000 1.16554
\(107\) −15.0000 −1.45010 −0.725052 0.688694i \(-0.758184\pi\)
−0.725052 + 0.688694i \(0.758184\pi\)
\(108\) 1.00000 0.0962250
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 2.00000 0.189832
\(112\) 5.00000 0.472456
\(113\) 18.0000 1.69330 0.846649 0.532152i \(-0.178617\pi\)
0.846649 + 0.532152i \(0.178617\pi\)
\(114\) −4.00000 −0.374634
\(115\) 3.00000 0.279751
\(116\) 9.00000 0.835629
\(117\) −4.00000 −0.369800
\(118\) −6.00000 −0.552345
\(119\) −5.00000 −0.458349
\(120\) −1.00000 −0.0912871
\(121\) 1.00000 0.0909091
\(122\) 2.00000 0.181071
\(123\) 0 0
\(124\) 5.00000 0.449013
\(125\) −1.00000 −0.0894427
\(126\) 5.00000 0.445435
\(127\) 2.00000 0.177471 0.0887357 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) 1.00000 0.0883883
\(129\) 11.0000 0.968496
\(130\) 4.00000 0.350823
\(131\) −12.0000 −1.04844 −0.524222 0.851581i \(-0.675644\pi\)
−0.524222 + 0.851581i \(0.675644\pi\)
\(132\) 1.00000 0.0870388
\(133\) −20.0000 −1.73422
\(134\) −4.00000 −0.345547
\(135\) −1.00000 −0.0860663
\(136\) −1.00000 −0.0857493
\(137\) −3.00000 −0.256307 −0.128154 0.991754i \(-0.540905\pi\)
−0.128154 + 0.991754i \(0.540905\pi\)
\(138\) −3.00000 −0.255377
\(139\) 17.0000 1.44192 0.720961 0.692976i \(-0.243701\pi\)
0.720961 + 0.692976i \(0.243701\pi\)
\(140\) −5.00000 −0.422577
\(141\) 0 0
\(142\) −6.00000 −0.503509
\(143\) −4.00000 −0.334497
\(144\) 1.00000 0.0833333
\(145\) −9.00000 −0.747409
\(146\) 2.00000 0.165521
\(147\) 18.0000 1.48461
\(148\) 2.00000 0.164399
\(149\) −12.0000 −0.983078 −0.491539 0.870855i \(-0.663566\pi\)
−0.491539 + 0.870855i \(0.663566\pi\)
\(150\) 1.00000 0.0816497
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) −4.00000 −0.324443
\(153\) −1.00000 −0.0808452
\(154\) 5.00000 0.402911
\(155\) −5.00000 −0.401610
\(156\) −4.00000 −0.320256
\(157\) −10.0000 −0.798087 −0.399043 0.916932i \(-0.630658\pi\)
−0.399043 + 0.916932i \(0.630658\pi\)
\(158\) 8.00000 0.636446
\(159\) 12.0000 0.951662
\(160\) −1.00000 −0.0790569
\(161\) −15.0000 −1.18217
\(162\) 1.00000 0.0785674
\(163\) 11.0000 0.861586 0.430793 0.902451i \(-0.358234\pi\)
0.430793 + 0.902451i \(0.358234\pi\)
\(164\) 0 0
\(165\) −1.00000 −0.0778499
\(166\) 12.0000 0.931381
\(167\) −6.00000 −0.464294 −0.232147 0.972681i \(-0.574575\pi\)
−0.232147 + 0.972681i \(0.574575\pi\)
\(168\) 5.00000 0.385758
\(169\) 3.00000 0.230769
\(170\) 1.00000 0.0766965
\(171\) −4.00000 −0.305888
\(172\) 11.0000 0.838742
\(173\) −18.0000 −1.36851 −0.684257 0.729241i \(-0.739873\pi\)
−0.684257 + 0.729241i \(0.739873\pi\)
\(174\) 9.00000 0.682288
\(175\) 5.00000 0.377964
\(176\) 1.00000 0.0753778
\(177\) −6.00000 −0.450988
\(178\) 0 0
\(179\) 18.0000 1.34538 0.672692 0.739923i \(-0.265138\pi\)
0.672692 + 0.739923i \(0.265138\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 5.00000 0.371647 0.185824 0.982583i \(-0.440505\pi\)
0.185824 + 0.982583i \(0.440505\pi\)
\(182\) −20.0000 −1.48250
\(183\) 2.00000 0.147844
\(184\) −3.00000 −0.221163
\(185\) −2.00000 −0.147043
\(186\) 5.00000 0.366618
\(187\) −1.00000 −0.0731272
\(188\) 0 0
\(189\) 5.00000 0.363696
\(190\) 4.00000 0.290191
\(191\) −21.0000 −1.51951 −0.759753 0.650211i \(-0.774680\pi\)
−0.759753 + 0.650211i \(0.774680\pi\)
\(192\) 1.00000 0.0721688
\(193\) 2.00000 0.143963 0.0719816 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) −7.00000 −0.502571
\(195\) 4.00000 0.286446
\(196\) 18.0000 1.28571
\(197\) −24.0000 −1.70993 −0.854965 0.518686i \(-0.826421\pi\)
−0.854965 + 0.518686i \(0.826421\pi\)
\(198\) 1.00000 0.0710669
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 1.00000 0.0707107
\(201\) −4.00000 −0.282138
\(202\) −6.00000 −0.422159
\(203\) 45.0000 3.15838
\(204\) −1.00000 −0.0700140
\(205\) 0 0
\(206\) 5.00000 0.348367
\(207\) −3.00000 −0.208514
\(208\) −4.00000 −0.277350
\(209\) −4.00000 −0.276686
\(210\) −5.00000 −0.345033
\(211\) −1.00000 −0.0688428 −0.0344214 0.999407i \(-0.510959\pi\)
−0.0344214 + 0.999407i \(0.510959\pi\)
\(212\) 12.0000 0.824163
\(213\) −6.00000 −0.411113
\(214\) −15.0000 −1.02538
\(215\) −11.0000 −0.750194
\(216\) 1.00000 0.0680414
\(217\) 25.0000 1.69711
\(218\) −16.0000 −1.08366
\(219\) 2.00000 0.135147
\(220\) −1.00000 −0.0674200
\(221\) 4.00000 0.269069
\(222\) 2.00000 0.134231
\(223\) −19.0000 −1.27233 −0.636167 0.771551i \(-0.719481\pi\)
−0.636167 + 0.771551i \(0.719481\pi\)
\(224\) 5.00000 0.334077
\(225\) 1.00000 0.0666667
\(226\) 18.0000 1.19734
\(227\) −15.0000 −0.995585 −0.497792 0.867296i \(-0.665856\pi\)
−0.497792 + 0.867296i \(0.665856\pi\)
\(228\) −4.00000 −0.264906
\(229\) −4.00000 −0.264327 −0.132164 0.991228i \(-0.542192\pi\)
−0.132164 + 0.991228i \(0.542192\pi\)
\(230\) 3.00000 0.197814
\(231\) 5.00000 0.328976
\(232\) 9.00000 0.590879
\(233\) −21.0000 −1.37576 −0.687878 0.725826i \(-0.741458\pi\)
−0.687878 + 0.725826i \(0.741458\pi\)
\(234\) −4.00000 −0.261488
\(235\) 0 0
\(236\) −6.00000 −0.390567
\(237\) 8.00000 0.519656
\(238\) −5.00000 −0.324102
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −1.00000 −0.0644157 −0.0322078 0.999481i \(-0.510254\pi\)
−0.0322078 + 0.999481i \(0.510254\pi\)
\(242\) 1.00000 0.0642824
\(243\) 1.00000 0.0641500
\(244\) 2.00000 0.128037
\(245\) −18.0000 −1.14998
\(246\) 0 0
\(247\) 16.0000 1.01806
\(248\) 5.00000 0.317500
\(249\) 12.0000 0.760469
\(250\) −1.00000 −0.0632456
\(251\) −24.0000 −1.51487 −0.757433 0.652913i \(-0.773547\pi\)
−0.757433 + 0.652913i \(0.773547\pi\)
\(252\) 5.00000 0.314970
\(253\) −3.00000 −0.188608
\(254\) 2.00000 0.125491
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) 3.00000 0.187135 0.0935674 0.995613i \(-0.470173\pi\)
0.0935674 + 0.995613i \(0.470173\pi\)
\(258\) 11.0000 0.684830
\(259\) 10.0000 0.621370
\(260\) 4.00000 0.248069
\(261\) 9.00000 0.557086
\(262\) −12.0000 −0.741362
\(263\) 9.00000 0.554964 0.277482 0.960731i \(-0.410500\pi\)
0.277482 + 0.960731i \(0.410500\pi\)
\(264\) 1.00000 0.0615457
\(265\) −12.0000 −0.737154
\(266\) −20.0000 −1.22628
\(267\) 0 0
\(268\) −4.00000 −0.244339
\(269\) 18.0000 1.09748 0.548740 0.835993i \(-0.315108\pi\)
0.548740 + 0.835993i \(0.315108\pi\)
\(270\) −1.00000 −0.0608581
\(271\) 17.0000 1.03268 0.516338 0.856385i \(-0.327295\pi\)
0.516338 + 0.856385i \(0.327295\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −20.0000 −1.21046
\(274\) −3.00000 −0.181237
\(275\) 1.00000 0.0603023
\(276\) −3.00000 −0.180579
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) 17.0000 1.01959
\(279\) 5.00000 0.299342
\(280\) −5.00000 −0.298807
\(281\) 9.00000 0.536895 0.268447 0.963294i \(-0.413489\pi\)
0.268447 + 0.963294i \(0.413489\pi\)
\(282\) 0 0
\(283\) 14.0000 0.832214 0.416107 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) −6.00000 −0.356034
\(285\) 4.00000 0.236940
\(286\) −4.00000 −0.236525
\(287\) 0 0
\(288\) 1.00000 0.0589256
\(289\) 1.00000 0.0588235
\(290\) −9.00000 −0.528498
\(291\) −7.00000 −0.410347
\(292\) 2.00000 0.117041
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 18.0000 1.04978
\(295\) 6.00000 0.349334
\(296\) 2.00000 0.116248
\(297\) 1.00000 0.0580259
\(298\) −12.0000 −0.695141
\(299\) 12.0000 0.693978
\(300\) 1.00000 0.0577350
\(301\) 55.0000 3.17015
\(302\) 20.0000 1.15087
\(303\) −6.00000 −0.344691
\(304\) −4.00000 −0.229416
\(305\) −2.00000 −0.114520
\(306\) −1.00000 −0.0571662
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 5.00000 0.284901
\(309\) 5.00000 0.284440
\(310\) −5.00000 −0.283981
\(311\) −24.0000 −1.36092 −0.680458 0.732787i \(-0.738219\pi\)
−0.680458 + 0.732787i \(0.738219\pi\)
\(312\) −4.00000 −0.226455
\(313\) 23.0000 1.30004 0.650018 0.759918i \(-0.274761\pi\)
0.650018 + 0.759918i \(0.274761\pi\)
\(314\) −10.0000 −0.564333
\(315\) −5.00000 −0.281718
\(316\) 8.00000 0.450035
\(317\) 3.00000 0.168497 0.0842484 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) 12.0000 0.672927
\(319\) 9.00000 0.503903
\(320\) −1.00000 −0.0559017
\(321\) −15.0000 −0.837218
\(322\) −15.0000 −0.835917
\(323\) 4.00000 0.222566
\(324\) 1.00000 0.0555556
\(325\) −4.00000 −0.221880
\(326\) 11.0000 0.609234
\(327\) −16.0000 −0.884802
\(328\) 0 0
\(329\) 0 0
\(330\) −1.00000 −0.0550482
\(331\) 5.00000 0.274825 0.137412 0.990514i \(-0.456121\pi\)
0.137412 + 0.990514i \(0.456121\pi\)
\(332\) 12.0000 0.658586
\(333\) 2.00000 0.109599
\(334\) −6.00000 −0.328305
\(335\) 4.00000 0.218543
\(336\) 5.00000 0.272772
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 3.00000 0.163178
\(339\) 18.0000 0.977626
\(340\) 1.00000 0.0542326
\(341\) 5.00000 0.270765
\(342\) −4.00000 −0.216295
\(343\) 55.0000 2.96972
\(344\) 11.0000 0.593080
\(345\) 3.00000 0.161515
\(346\) −18.0000 −0.967686
\(347\) −12.0000 −0.644194 −0.322097 0.946707i \(-0.604388\pi\)
−0.322097 + 0.946707i \(0.604388\pi\)
\(348\) 9.00000 0.482451
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 5.00000 0.267261
\(351\) −4.00000 −0.213504
\(352\) 1.00000 0.0533002
\(353\) −3.00000 −0.159674 −0.0798369 0.996808i \(-0.525440\pi\)
−0.0798369 + 0.996808i \(0.525440\pi\)
\(354\) −6.00000 −0.318896
\(355\) 6.00000 0.318447
\(356\) 0 0
\(357\) −5.00000 −0.264628
\(358\) 18.0000 0.951330
\(359\) 6.00000 0.316668 0.158334 0.987386i \(-0.449388\pi\)
0.158334 + 0.987386i \(0.449388\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −3.00000 −0.157895
\(362\) 5.00000 0.262794
\(363\) 1.00000 0.0524864
\(364\) −20.0000 −1.04828
\(365\) −2.00000 −0.104685
\(366\) 2.00000 0.104542
\(367\) 2.00000 0.104399 0.0521996 0.998637i \(-0.483377\pi\)
0.0521996 + 0.998637i \(0.483377\pi\)
\(368\) −3.00000 −0.156386
\(369\) 0 0
\(370\) −2.00000 −0.103975
\(371\) 60.0000 3.11504
\(372\) 5.00000 0.259238
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) −1.00000 −0.0517088
\(375\) −1.00000 −0.0516398
\(376\) 0 0
\(377\) −36.0000 −1.85409
\(378\) 5.00000 0.257172
\(379\) 8.00000 0.410932 0.205466 0.978664i \(-0.434129\pi\)
0.205466 + 0.978664i \(0.434129\pi\)
\(380\) 4.00000 0.205196
\(381\) 2.00000 0.102463
\(382\) −21.0000 −1.07445
\(383\) −12.0000 −0.613171 −0.306586 0.951843i \(-0.599187\pi\)
−0.306586 + 0.951843i \(0.599187\pi\)
\(384\) 1.00000 0.0510310
\(385\) −5.00000 −0.254824
\(386\) 2.00000 0.101797
\(387\) 11.0000 0.559161
\(388\) −7.00000 −0.355371
\(389\) 6.00000 0.304212 0.152106 0.988364i \(-0.451394\pi\)
0.152106 + 0.988364i \(0.451394\pi\)
\(390\) 4.00000 0.202548
\(391\) 3.00000 0.151717
\(392\) 18.0000 0.909137
\(393\) −12.0000 −0.605320
\(394\) −24.0000 −1.20910
\(395\) −8.00000 −0.402524
\(396\) 1.00000 0.0502519
\(397\) −34.0000 −1.70641 −0.853206 0.521575i \(-0.825345\pi\)
−0.853206 + 0.521575i \(0.825345\pi\)
\(398\) −16.0000 −0.802008
\(399\) −20.0000 −1.00125
\(400\) 1.00000 0.0500000
\(401\) −15.0000 −0.749064 −0.374532 0.927214i \(-0.622197\pi\)
−0.374532 + 0.927214i \(0.622197\pi\)
\(402\) −4.00000 −0.199502
\(403\) −20.0000 −0.996271
\(404\) −6.00000 −0.298511
\(405\) −1.00000 −0.0496904
\(406\) 45.0000 2.23331
\(407\) 2.00000 0.0991363
\(408\) −1.00000 −0.0495074
\(409\) 32.0000 1.58230 0.791149 0.611623i \(-0.209483\pi\)
0.791149 + 0.611623i \(0.209483\pi\)
\(410\) 0 0
\(411\) −3.00000 −0.147979
\(412\) 5.00000 0.246332
\(413\) −30.0000 −1.47620
\(414\) −3.00000 −0.147442
\(415\) −12.0000 −0.589057
\(416\) −4.00000 −0.196116
\(417\) 17.0000 0.832494
\(418\) −4.00000 −0.195646
\(419\) −21.0000 −1.02592 −0.512959 0.858413i \(-0.671451\pi\)
−0.512959 + 0.858413i \(0.671451\pi\)
\(420\) −5.00000 −0.243975
\(421\) 32.0000 1.55958 0.779792 0.626038i \(-0.215325\pi\)
0.779792 + 0.626038i \(0.215325\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 0 0
\(424\) 12.0000 0.582772
\(425\) −1.00000 −0.0485071
\(426\) −6.00000 −0.290701
\(427\) 10.0000 0.483934
\(428\) −15.0000 −0.725052
\(429\) −4.00000 −0.193122
\(430\) −11.0000 −0.530467
\(431\) 15.0000 0.722525 0.361262 0.932464i \(-0.382346\pi\)
0.361262 + 0.932464i \(0.382346\pi\)
\(432\) 1.00000 0.0481125
\(433\) −40.0000 −1.92228 −0.961139 0.276066i \(-0.910969\pi\)
−0.961139 + 0.276066i \(0.910969\pi\)
\(434\) 25.0000 1.20004
\(435\) −9.00000 −0.431517
\(436\) −16.0000 −0.766261
\(437\) 12.0000 0.574038
\(438\) 2.00000 0.0955637
\(439\) −34.0000 −1.62273 −0.811366 0.584539i \(-0.801275\pi\)
−0.811366 + 0.584539i \(0.801275\pi\)
\(440\) −1.00000 −0.0476731
\(441\) 18.0000 0.857143
\(442\) 4.00000 0.190261
\(443\) −15.0000 −0.712672 −0.356336 0.934358i \(-0.615974\pi\)
−0.356336 + 0.934358i \(0.615974\pi\)
\(444\) 2.00000 0.0949158
\(445\) 0 0
\(446\) −19.0000 −0.899676
\(447\) −12.0000 −0.567581
\(448\) 5.00000 0.236228
\(449\) −21.0000 −0.991051 −0.495526 0.868593i \(-0.665025\pi\)
−0.495526 + 0.868593i \(0.665025\pi\)
\(450\) 1.00000 0.0471405
\(451\) 0 0
\(452\) 18.0000 0.846649
\(453\) 20.0000 0.939682
\(454\) −15.0000 −0.703985
\(455\) 20.0000 0.937614
\(456\) −4.00000 −0.187317
\(457\) −10.0000 −0.467780 −0.233890 0.972263i \(-0.575146\pi\)
−0.233890 + 0.972263i \(0.575146\pi\)
\(458\) −4.00000 −0.186908
\(459\) −1.00000 −0.0466760
\(460\) 3.00000 0.139876
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 5.00000 0.232621
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 9.00000 0.417815
\(465\) −5.00000 −0.231869
\(466\) −21.0000 −0.972806
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) −4.00000 −0.184900
\(469\) −20.0000 −0.923514
\(470\) 0 0
\(471\) −10.0000 −0.460776
\(472\) −6.00000 −0.276172
\(473\) 11.0000 0.505781
\(474\) 8.00000 0.367452
\(475\) −4.00000 −0.183533
\(476\) −5.00000 −0.229175
\(477\) 12.0000 0.549442
\(478\) 6.00000 0.274434
\(479\) 33.0000 1.50781 0.753904 0.656984i \(-0.228168\pi\)
0.753904 + 0.656984i \(0.228168\pi\)
\(480\) −1.00000 −0.0456435
\(481\) −8.00000 −0.364769
\(482\) −1.00000 −0.0455488
\(483\) −15.0000 −0.682524
\(484\) 1.00000 0.0454545
\(485\) 7.00000 0.317854
\(486\) 1.00000 0.0453609
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) 2.00000 0.0905357
\(489\) 11.0000 0.497437
\(490\) −18.0000 −0.813157
\(491\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 0 0
\(493\) −9.00000 −0.405340
\(494\) 16.0000 0.719874
\(495\) −1.00000 −0.0449467
\(496\) 5.00000 0.224507
\(497\) −30.0000 −1.34568
\(498\) 12.0000 0.537733
\(499\) 8.00000 0.358129 0.179065 0.983837i \(-0.442693\pi\)
0.179065 + 0.983837i \(0.442693\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −6.00000 −0.268060
\(502\) −24.0000 −1.07117
\(503\) 36.0000 1.60516 0.802580 0.596544i \(-0.203460\pi\)
0.802580 + 0.596544i \(0.203460\pi\)
\(504\) 5.00000 0.222718
\(505\) 6.00000 0.266996
\(506\) −3.00000 −0.133366
\(507\) 3.00000 0.133235
\(508\) 2.00000 0.0887357
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) 1.00000 0.0442807
\(511\) 10.0000 0.442374
\(512\) 1.00000 0.0441942
\(513\) −4.00000 −0.176604
\(514\) 3.00000 0.132324
\(515\) −5.00000 −0.220326
\(516\) 11.0000 0.484248
\(517\) 0 0
\(518\) 10.0000 0.439375
\(519\) −18.0000 −0.790112
\(520\) 4.00000 0.175412
\(521\) −30.0000 −1.31432 −0.657162 0.753749i \(-0.728243\pi\)
−0.657162 + 0.753749i \(0.728243\pi\)
\(522\) 9.00000 0.393919
\(523\) 11.0000 0.480996 0.240498 0.970650i \(-0.422689\pi\)
0.240498 + 0.970650i \(0.422689\pi\)
\(524\) −12.0000 −0.524222
\(525\) 5.00000 0.218218
\(526\) 9.00000 0.392419
\(527\) −5.00000 −0.217803
\(528\) 1.00000 0.0435194
\(529\) −14.0000 −0.608696
\(530\) −12.0000 −0.521247
\(531\) −6.00000 −0.260378
\(532\) −20.0000 −0.867110
\(533\) 0 0
\(534\) 0 0
\(535\) 15.0000 0.648507
\(536\) −4.00000 −0.172774
\(537\) 18.0000 0.776757
\(538\) 18.0000 0.776035
\(539\) 18.0000 0.775315
\(540\) −1.00000 −0.0430331
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 17.0000 0.730213
\(543\) 5.00000 0.214571
\(544\) −1.00000 −0.0428746
\(545\) 16.0000 0.685365
\(546\) −20.0000 −0.855921
\(547\) −34.0000 −1.45374 −0.726868 0.686778i \(-0.759025\pi\)
−0.726868 + 0.686778i \(0.759025\pi\)
\(548\) −3.00000 −0.128154
\(549\) 2.00000 0.0853579
\(550\) 1.00000 0.0426401
\(551\) −36.0000 −1.53365
\(552\) −3.00000 −0.127688
\(553\) 40.0000 1.70097
\(554\) −10.0000 −0.424859
\(555\) −2.00000 −0.0848953
\(556\) 17.0000 0.720961
\(557\) 9.00000 0.381342 0.190671 0.981654i \(-0.438934\pi\)
0.190671 + 0.981654i \(0.438934\pi\)
\(558\) 5.00000 0.211667
\(559\) −44.0000 −1.86100
\(560\) −5.00000 −0.211289
\(561\) −1.00000 −0.0422200
\(562\) 9.00000 0.379642
\(563\) −24.0000 −1.01148 −0.505740 0.862686i \(-0.668780\pi\)
−0.505740 + 0.862686i \(0.668780\pi\)
\(564\) 0 0
\(565\) −18.0000 −0.757266
\(566\) 14.0000 0.588464
\(567\) 5.00000 0.209980
\(568\) −6.00000 −0.251754
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 4.00000 0.167542
\(571\) −28.0000 −1.17176 −0.585882 0.810397i \(-0.699252\pi\)
−0.585882 + 0.810397i \(0.699252\pi\)
\(572\) −4.00000 −0.167248
\(573\) −21.0000 −0.877288
\(574\) 0 0
\(575\) −3.00000 −0.125109
\(576\) 1.00000 0.0416667
\(577\) −10.0000 −0.416305 −0.208153 0.978096i \(-0.566745\pi\)
−0.208153 + 0.978096i \(0.566745\pi\)
\(578\) 1.00000 0.0415945
\(579\) 2.00000 0.0831172
\(580\) −9.00000 −0.373705
\(581\) 60.0000 2.48922
\(582\) −7.00000 −0.290159
\(583\) 12.0000 0.496989
\(584\) 2.00000 0.0827606
\(585\) 4.00000 0.165380
\(586\) −9.00000 −0.371787
\(587\) −9.00000 −0.371470 −0.185735 0.982600i \(-0.559467\pi\)
−0.185735 + 0.982600i \(0.559467\pi\)
\(588\) 18.0000 0.742307
\(589\) −20.0000 −0.824086
\(590\) 6.00000 0.247016
\(591\) −24.0000 −0.987228
\(592\) 2.00000 0.0821995
\(593\) −18.0000 −0.739171 −0.369586 0.929197i \(-0.620500\pi\)
−0.369586 + 0.929197i \(0.620500\pi\)
\(594\) 1.00000 0.0410305
\(595\) 5.00000 0.204980
\(596\) −12.0000 −0.491539
\(597\) −16.0000 −0.654836
\(598\) 12.0000 0.490716
\(599\) −3.00000 −0.122577 −0.0612883 0.998120i \(-0.519521\pi\)
−0.0612883 + 0.998120i \(0.519521\pi\)
\(600\) 1.00000 0.0408248
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 55.0000 2.24163
\(603\) −4.00000 −0.162893
\(604\) 20.0000 0.813788
\(605\) −1.00000 −0.0406558
\(606\) −6.00000 −0.243733
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) −4.00000 −0.162221
\(609\) 45.0000 1.82349
\(610\) −2.00000 −0.0809776
\(611\) 0 0
\(612\) −1.00000 −0.0404226
\(613\) −34.0000 −1.37325 −0.686624 0.727013i \(-0.740908\pi\)
−0.686624 + 0.727013i \(0.740908\pi\)
\(614\) 20.0000 0.807134
\(615\) 0 0
\(616\) 5.00000 0.201456
\(617\) 42.0000 1.69086 0.845428 0.534089i \(-0.179345\pi\)
0.845428 + 0.534089i \(0.179345\pi\)
\(618\) 5.00000 0.201129
\(619\) −10.0000 −0.401934 −0.200967 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) −5.00000 −0.200805
\(621\) −3.00000 −0.120386
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) −4.00000 −0.160128
\(625\) 1.00000 0.0400000
\(626\) 23.0000 0.919265
\(627\) −4.00000 −0.159745
\(628\) −10.0000 −0.399043
\(629\) −2.00000 −0.0797452
\(630\) −5.00000 −0.199205
\(631\) 14.0000 0.557331 0.278666 0.960388i \(-0.410108\pi\)
0.278666 + 0.960388i \(0.410108\pi\)
\(632\) 8.00000 0.318223
\(633\) −1.00000 −0.0397464
\(634\) 3.00000 0.119145
\(635\) −2.00000 −0.0793676
\(636\) 12.0000 0.475831
\(637\) −72.0000 −2.85274
\(638\) 9.00000 0.356313
\(639\) −6.00000 −0.237356
\(640\) −1.00000 −0.0395285
\(641\) −9.00000 −0.355479 −0.177739 0.984078i \(-0.556878\pi\)
−0.177739 + 0.984078i \(0.556878\pi\)
\(642\) −15.0000 −0.592003
\(643\) 29.0000 1.14365 0.571824 0.820376i \(-0.306236\pi\)
0.571824 + 0.820376i \(0.306236\pi\)
\(644\) −15.0000 −0.591083
\(645\) −11.0000 −0.433125
\(646\) 4.00000 0.157378
\(647\) −42.0000 −1.65119 −0.825595 0.564263i \(-0.809160\pi\)
−0.825595 + 0.564263i \(0.809160\pi\)
\(648\) 1.00000 0.0392837
\(649\) −6.00000 −0.235521
\(650\) −4.00000 −0.156893
\(651\) 25.0000 0.979827
\(652\) 11.0000 0.430793
\(653\) 27.0000 1.05659 0.528296 0.849060i \(-0.322831\pi\)
0.528296 + 0.849060i \(0.322831\pi\)
\(654\) −16.0000 −0.625650
\(655\) 12.0000 0.468879
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) −45.0000 −1.75295 −0.876476 0.481446i \(-0.840112\pi\)
−0.876476 + 0.481446i \(0.840112\pi\)
\(660\) −1.00000 −0.0389249
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) 5.00000 0.194331
\(663\) 4.00000 0.155347
\(664\) 12.0000 0.465690
\(665\) 20.0000 0.775567
\(666\) 2.00000 0.0774984
\(667\) −27.0000 −1.04544
\(668\) −6.00000 −0.232147
\(669\) −19.0000 −0.734582
\(670\) 4.00000 0.154533
\(671\) 2.00000 0.0772091
\(672\) 5.00000 0.192879
\(673\) −4.00000 −0.154189 −0.0770943 0.997024i \(-0.524564\pi\)
−0.0770943 + 0.997024i \(0.524564\pi\)
\(674\) 14.0000 0.539260
\(675\) 1.00000 0.0384900
\(676\) 3.00000 0.115385
\(677\) 6.00000 0.230599 0.115299 0.993331i \(-0.463217\pi\)
0.115299 + 0.993331i \(0.463217\pi\)
\(678\) 18.0000 0.691286
\(679\) −35.0000 −1.34318
\(680\) 1.00000 0.0383482
\(681\) −15.0000 −0.574801
\(682\) 5.00000 0.191460
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) −4.00000 −0.152944
\(685\) 3.00000 0.114624
\(686\) 55.0000 2.09991
\(687\) −4.00000 −0.152610
\(688\) 11.0000 0.419371
\(689\) −48.0000 −1.82865
\(690\) 3.00000 0.114208
\(691\) −28.0000 −1.06517 −0.532585 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) −18.0000 −0.684257
\(693\) 5.00000 0.189934
\(694\) −12.0000 −0.455514
\(695\) −17.0000 −0.644847
\(696\) 9.00000 0.341144
\(697\) 0 0
\(698\) −10.0000 −0.378506
\(699\) −21.0000 −0.794293
\(700\) 5.00000 0.188982
\(701\) 6.00000 0.226617 0.113308 0.993560i \(-0.463855\pi\)
0.113308 + 0.993560i \(0.463855\pi\)
\(702\) −4.00000 −0.150970
\(703\) −8.00000 −0.301726
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) −3.00000 −0.112906
\(707\) −30.0000 −1.12827
\(708\) −6.00000 −0.225494
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) 6.00000 0.225176
\(711\) 8.00000 0.300023
\(712\) 0 0
\(713\) −15.0000 −0.561754
\(714\) −5.00000 −0.187120
\(715\) 4.00000 0.149592
\(716\) 18.0000 0.672692
\(717\) 6.00000 0.224074
\(718\) 6.00000 0.223918
\(719\) −18.0000 −0.671287 −0.335643 0.941989i \(-0.608954\pi\)
−0.335643 + 0.941989i \(0.608954\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 25.0000 0.931049
\(722\) −3.00000 −0.111648
\(723\) −1.00000 −0.0371904
\(724\) 5.00000 0.185824
\(725\) 9.00000 0.334252
\(726\) 1.00000 0.0371135
\(727\) 53.0000 1.96566 0.982831 0.184510i \(-0.0590699\pi\)
0.982831 + 0.184510i \(0.0590699\pi\)
\(728\) −20.0000 −0.741249
\(729\) 1.00000 0.0370370
\(730\) −2.00000 −0.0740233
\(731\) −11.0000 −0.406850
\(732\) 2.00000 0.0739221
\(733\) 20.0000 0.738717 0.369358 0.929287i \(-0.379577\pi\)
0.369358 + 0.929287i \(0.379577\pi\)
\(734\) 2.00000 0.0738213
\(735\) −18.0000 −0.663940
\(736\) −3.00000 −0.110581
\(737\) −4.00000 −0.147342
\(738\) 0 0
\(739\) −22.0000 −0.809283 −0.404642 0.914475i \(-0.632604\pi\)
−0.404642 + 0.914475i \(0.632604\pi\)
\(740\) −2.00000 −0.0735215
\(741\) 16.0000 0.587775
\(742\) 60.0000 2.20267
\(743\) −36.0000 −1.32071 −0.660356 0.750953i \(-0.729595\pi\)
−0.660356 + 0.750953i \(0.729595\pi\)
\(744\) 5.00000 0.183309
\(745\) 12.0000 0.439646
\(746\) −22.0000 −0.805477
\(747\) 12.0000 0.439057
\(748\) −1.00000 −0.0365636
\(749\) −75.0000 −2.74044
\(750\) −1.00000 −0.0365148
\(751\) −37.0000 −1.35015 −0.675075 0.737749i \(-0.735889\pi\)
−0.675075 + 0.737749i \(0.735889\pi\)
\(752\) 0 0
\(753\) −24.0000 −0.874609
\(754\) −36.0000 −1.31104
\(755\) −20.0000 −0.727875
\(756\) 5.00000 0.181848
\(757\) −7.00000 −0.254419 −0.127210 0.991876i \(-0.540602\pi\)
−0.127210 + 0.991876i \(0.540602\pi\)
\(758\) 8.00000 0.290573
\(759\) −3.00000 −0.108893
\(760\) 4.00000 0.145095
\(761\) 15.0000 0.543750 0.271875 0.962333i \(-0.412356\pi\)
0.271875 + 0.962333i \(0.412356\pi\)
\(762\) 2.00000 0.0724524
\(763\) −80.0000 −2.89619
\(764\) −21.0000 −0.759753
\(765\) 1.00000 0.0361551
\(766\) −12.0000 −0.433578
\(767\) 24.0000 0.866590
\(768\) 1.00000 0.0360844
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) −5.00000 −0.180187
\(771\) 3.00000 0.108042
\(772\) 2.00000 0.0719816
\(773\) −48.0000 −1.72644 −0.863220 0.504828i \(-0.831556\pi\)
−0.863220 + 0.504828i \(0.831556\pi\)
\(774\) 11.0000 0.395387
\(775\) 5.00000 0.179605
\(776\) −7.00000 −0.251285
\(777\) 10.0000 0.358748
\(778\) 6.00000 0.215110
\(779\) 0 0
\(780\) 4.00000 0.143223
\(781\) −6.00000 −0.214697
\(782\) 3.00000 0.107280
\(783\) 9.00000 0.321634
\(784\) 18.0000 0.642857
\(785\) 10.0000 0.356915
\(786\) −12.0000 −0.428026
\(787\) 8.00000 0.285169 0.142585 0.989783i \(-0.454459\pi\)
0.142585 + 0.989783i \(0.454459\pi\)
\(788\) −24.0000 −0.854965
\(789\) 9.00000 0.320408
\(790\) −8.00000 −0.284627
\(791\) 90.0000 3.20003
\(792\) 1.00000 0.0355335
\(793\) −8.00000 −0.284088
\(794\) −34.0000 −1.20661
\(795\) −12.0000 −0.425596
\(796\) −16.0000 −0.567105
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) −20.0000 −0.707992
\(799\) 0 0
\(800\) 1.00000 0.0353553
\(801\) 0 0
\(802\) −15.0000 −0.529668
\(803\) 2.00000 0.0705785
\(804\) −4.00000 −0.141069
\(805\) 15.0000 0.528681
\(806\) −20.0000 −0.704470
\(807\) 18.0000 0.633630
\(808\) −6.00000 −0.211079
\(809\) −6.00000 −0.210949 −0.105474 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) −1.00000 −0.0351364
\(811\) −40.0000 −1.40459 −0.702295 0.711886i \(-0.747841\pi\)
−0.702295 + 0.711886i \(0.747841\pi\)
\(812\) 45.0000 1.57919
\(813\) 17.0000 0.596216
\(814\) 2.00000 0.0701000
\(815\) −11.0000 −0.385313
\(816\) −1.00000 −0.0350070
\(817\) −44.0000 −1.53937
\(818\) 32.0000 1.11885
\(819\) −20.0000 −0.698857
\(820\) 0 0
\(821\) 3.00000 0.104701 0.0523504 0.998629i \(-0.483329\pi\)
0.0523504 + 0.998629i \(0.483329\pi\)
\(822\) −3.00000 −0.104637
\(823\) −34.0000 −1.18517 −0.592583 0.805510i \(-0.701892\pi\)
−0.592583 + 0.805510i \(0.701892\pi\)
\(824\) 5.00000 0.174183
\(825\) 1.00000 0.0348155
\(826\) −30.0000 −1.04383
\(827\) −9.00000 −0.312961 −0.156480 0.987681i \(-0.550015\pi\)
−0.156480 + 0.987681i \(0.550015\pi\)
\(828\) −3.00000 −0.104257
\(829\) −46.0000 −1.59765 −0.798823 0.601566i \(-0.794544\pi\)
−0.798823 + 0.601566i \(0.794544\pi\)
\(830\) −12.0000 −0.416526
\(831\) −10.0000 −0.346896
\(832\) −4.00000 −0.138675
\(833\) −18.0000 −0.623663
\(834\) 17.0000 0.588662
\(835\) 6.00000 0.207639
\(836\) −4.00000 −0.138343
\(837\) 5.00000 0.172825
\(838\) −21.0000 −0.725433
\(839\) 54.0000 1.86429 0.932144 0.362089i \(-0.117936\pi\)
0.932144 + 0.362089i \(0.117936\pi\)
\(840\) −5.00000 −0.172516
\(841\) 52.0000 1.79310
\(842\) 32.0000 1.10279
\(843\) 9.00000 0.309976
\(844\) −1.00000 −0.0344214
\(845\) −3.00000 −0.103203
\(846\) 0 0
\(847\) 5.00000 0.171802
\(848\) 12.0000 0.412082
\(849\) 14.0000 0.480479
\(850\) −1.00000 −0.0342997
\(851\) −6.00000 −0.205677
\(852\) −6.00000 −0.205557
\(853\) 53.0000 1.81469 0.907343 0.420392i \(-0.138107\pi\)
0.907343 + 0.420392i \(0.138107\pi\)
\(854\) 10.0000 0.342193
\(855\) 4.00000 0.136797
\(856\) −15.0000 −0.512689
\(857\) −27.0000 −0.922302 −0.461151 0.887322i \(-0.652563\pi\)
−0.461151 + 0.887322i \(0.652563\pi\)
\(858\) −4.00000 −0.136558
\(859\) −13.0000 −0.443554 −0.221777 0.975097i \(-0.571186\pi\)
−0.221777 + 0.975097i \(0.571186\pi\)
\(860\) −11.0000 −0.375097
\(861\) 0 0
\(862\) 15.0000 0.510902
\(863\) −24.0000 −0.816970 −0.408485 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) 1.00000 0.0340207
\(865\) 18.0000 0.612018
\(866\) −40.0000 −1.35926
\(867\) 1.00000 0.0339618
\(868\) 25.0000 0.848555
\(869\) 8.00000 0.271381
\(870\) −9.00000 −0.305129
\(871\) 16.0000 0.542139
\(872\) −16.0000 −0.541828
\(873\) −7.00000 −0.236914
\(874\) 12.0000 0.405906
\(875\) −5.00000 −0.169031
\(876\) 2.00000 0.0675737
\(877\) 5.00000 0.168838 0.0844190 0.996430i \(-0.473097\pi\)
0.0844190 + 0.996430i \(0.473097\pi\)
\(878\) −34.0000 −1.14744
\(879\) −9.00000 −0.303562
\(880\) −1.00000 −0.0337100
\(881\) 57.0000 1.92038 0.960189 0.279350i \(-0.0901189\pi\)
0.960189 + 0.279350i \(0.0901189\pi\)
\(882\) 18.0000 0.606092
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 4.00000 0.134535
\(885\) 6.00000 0.201688
\(886\) −15.0000 −0.503935
\(887\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(888\) 2.00000 0.0671156
\(889\) 10.0000 0.335389
\(890\) 0 0
\(891\) 1.00000 0.0335013
\(892\) −19.0000 −0.636167
\(893\) 0 0
\(894\) −12.0000 −0.401340
\(895\) −18.0000 −0.601674
\(896\) 5.00000 0.167038
\(897\) 12.0000 0.400668
\(898\) −21.0000 −0.700779
\(899\) 45.0000 1.50083
\(900\) 1.00000 0.0333333
\(901\) −12.0000 −0.399778
\(902\) 0 0
\(903\) 55.0000 1.83029
\(904\) 18.0000 0.598671
\(905\) −5.00000 −0.166206
\(906\) 20.0000 0.664455
\(907\) 5.00000 0.166022 0.0830111 0.996549i \(-0.473546\pi\)
0.0830111 + 0.996549i \(0.473546\pi\)
\(908\) −15.0000 −0.497792
\(909\) −6.00000 −0.199007
\(910\) 20.0000 0.662994
\(911\) 36.0000 1.19273 0.596367 0.802712i \(-0.296610\pi\)
0.596367 + 0.802712i \(0.296610\pi\)
\(912\) −4.00000 −0.132453
\(913\) 12.0000 0.397142
\(914\) −10.0000 −0.330771
\(915\) −2.00000 −0.0661180
\(916\) −4.00000 −0.132164
\(917\) −60.0000 −1.98137
\(918\) −1.00000 −0.0330049
\(919\) −25.0000 −0.824674 −0.412337 0.911031i \(-0.635287\pi\)
−0.412337 + 0.911031i \(0.635287\pi\)
\(920\) 3.00000 0.0989071
\(921\) 20.0000 0.659022
\(922\) 18.0000 0.592798
\(923\) 24.0000 0.789970
\(924\) 5.00000 0.164488
\(925\) 2.00000 0.0657596
\(926\) 32.0000 1.05159
\(927\) 5.00000 0.164222
\(928\) 9.00000 0.295439
\(929\) −21.0000 −0.688988 −0.344494 0.938789i \(-0.611949\pi\)
−0.344494 + 0.938789i \(0.611949\pi\)
\(930\) −5.00000 −0.163956
\(931\) −72.0000 −2.35970
\(932\) −21.0000 −0.687878
\(933\) −24.0000 −0.785725
\(934\) −12.0000 −0.392652
\(935\) 1.00000 0.0327035
\(936\) −4.00000 −0.130744
\(937\) 14.0000 0.457360 0.228680 0.973502i \(-0.426559\pi\)
0.228680 + 0.973502i \(0.426559\pi\)
\(938\) −20.0000 −0.653023
\(939\) 23.0000 0.750577
\(940\) 0 0
\(941\) −18.0000 −0.586783 −0.293392 0.955992i \(-0.594784\pi\)
−0.293392 + 0.955992i \(0.594784\pi\)
\(942\) −10.0000 −0.325818
\(943\) 0 0
\(944\) −6.00000 −0.195283
\(945\) −5.00000 −0.162650
\(946\) 11.0000 0.357641
\(947\) 18.0000 0.584921 0.292461 0.956278i \(-0.405526\pi\)
0.292461 + 0.956278i \(0.405526\pi\)
\(948\) 8.00000 0.259828
\(949\) −8.00000 −0.259691
\(950\) −4.00000 −0.129777
\(951\) 3.00000 0.0972817
\(952\) −5.00000 −0.162051
\(953\) 30.0000 0.971795 0.485898 0.874016i \(-0.338493\pi\)
0.485898 + 0.874016i \(0.338493\pi\)
\(954\) 12.0000 0.388514
\(955\) 21.0000 0.679544
\(956\) 6.00000 0.194054
\(957\) 9.00000 0.290929
\(958\) 33.0000 1.06618
\(959\) −15.0000 −0.484375
\(960\) −1.00000 −0.0322749
\(961\) −6.00000 −0.193548
\(962\) −8.00000 −0.257930
\(963\) −15.0000 −0.483368
\(964\) −1.00000 −0.0322078
\(965\) −2.00000 −0.0643823
\(966\) −15.0000 −0.482617
\(967\) 50.0000 1.60789 0.803946 0.594703i \(-0.202730\pi\)
0.803946 + 0.594703i \(0.202730\pi\)
\(968\) 1.00000 0.0321412
\(969\) 4.00000 0.128499
\(970\) 7.00000 0.224756
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 1.00000 0.0320750
\(973\) 85.0000 2.72497
\(974\) 38.0000 1.21760
\(975\) −4.00000 −0.128103
\(976\) 2.00000 0.0640184
\(977\) 18.0000 0.575871 0.287936 0.957650i \(-0.407031\pi\)
0.287936 + 0.957650i \(0.407031\pi\)
\(978\) 11.0000 0.351741
\(979\) 0 0
\(980\) −18.0000 −0.574989
\(981\) −16.0000 −0.510841
\(982\) 0 0
\(983\) 21.0000 0.669796 0.334898 0.942254i \(-0.391298\pi\)
0.334898 + 0.942254i \(0.391298\pi\)
\(984\) 0 0
\(985\) 24.0000 0.764704
\(986\) −9.00000 −0.286618
\(987\) 0 0
\(988\) 16.0000 0.509028
\(989\) −33.0000 −1.04934
\(990\) −1.00000 −0.0317821
\(991\) −25.0000 −0.794151 −0.397076 0.917786i \(-0.629975\pi\)
−0.397076 + 0.917786i \(0.629975\pi\)
\(992\) 5.00000 0.158750
\(993\) 5.00000 0.158670
\(994\) −30.0000 −0.951542
\(995\) 16.0000 0.507234
\(996\) 12.0000 0.380235
\(997\) −25.0000 −0.791758 −0.395879 0.918303i \(-0.629560\pi\)
−0.395879 + 0.918303i \(0.629560\pi\)
\(998\) 8.00000 0.253236
\(999\) 2.00000 0.0632772
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 5610.2.a.bj.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.bj.1.1 1 1.1 even 1 trivial