Properties

Label 5610.2.a.f.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

Downloads

Learn more

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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} -1.00000 q^{12} -4.00000 q^{13} +3.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} +3.00000 q^{21} +1.00000 q^{22} -1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.00000 q^{26} -1.00000 q^{27} -3.00000 q^{28} -3.00000 q^{29} +1.00000 q^{30} -5.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} +1.00000 q^{34} -3.00000 q^{35} +1.00000 q^{36} -6.00000 q^{37} -4.00000 q^{38} +4.00000 q^{39} -1.00000 q^{40} +8.00000 q^{41} -3.00000 q^{42} +13.0000 q^{43} -1.00000 q^{44} +1.00000 q^{45} +1.00000 q^{46} -12.0000 q^{47} -1.00000 q^{48} +2.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} -4.00000 q^{52} -4.00000 q^{53} +1.00000 q^{54} -1.00000 q^{55} +3.00000 q^{56} -4.00000 q^{57} +3.00000 q^{58} -6.00000 q^{59} -1.00000 q^{60} -10.0000 q^{61} +5.00000 q^{62} -3.00000 q^{63} +1.00000 q^{64} -4.00000 q^{65} -1.00000 q^{66} +8.00000 q^{67} -1.00000 q^{68} +1.00000 q^{69} +3.00000 q^{70} +14.0000 q^{71} -1.00000 q^{72} -6.00000 q^{73} +6.00000 q^{74} -1.00000 q^{75} +4.00000 q^{76} +3.00000 q^{77} -4.00000 q^{78} +4.00000 q^{79} +1.00000 q^{80} +1.00000 q^{81} -8.00000 q^{82} -8.00000 q^{83} +3.00000 q^{84} -1.00000 q^{85} -13.0000 q^{86} +3.00000 q^{87} +1.00000 q^{88} -4.00000 q^{89} -1.00000 q^{90} +12.0000 q^{91} -1.00000 q^{92} +5.00000 q^{93} +12.0000 q^{94} +4.00000 q^{95} +1.00000 q^{96} -1.00000 q^{97} -2.00000 q^{98} -1.00000 q^{99} +O(q^{100})\)

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
\(7\) −3.00000 −1.13389 −0.566947 0.823754i \(-0.691875\pi\)
−0.566947 + 0.823754i \(0.691875\pi\)
\(8\) −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 \(0.687167\pi\)
\(14\) 3.00000 0.801784
\(15\) −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 \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 1.00000 0.223607
\(21\) 3.00000 0.654654
\(22\) 1.00000 0.213201
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) 1.00000 0.204124
\(25\) 1.00000 0.200000
\(26\) 4.00000 0.784465
\(27\) −1.00000 −0.192450
\(28\) −3.00000 −0.566947
\(29\) −3.00000 −0.557086 −0.278543 0.960424i \(-0.589851\pi\)
−0.278543 + 0.960424i \(0.589851\pi\)
\(30\) 1.00000 0.182574
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) −1.00000 −0.176777
\(33\) 1.00000 0.174078
\(34\) 1.00000 0.171499
\(35\) −3.00000 −0.507093
\(36\) 1.00000 0.166667
\(37\) −6.00000 −0.986394 −0.493197 0.869918i \(-0.664172\pi\)
−0.493197 + 0.869918i \(0.664172\pi\)
\(38\) −4.00000 −0.648886
\(39\) 4.00000 0.640513
\(40\) −1.00000 −0.158114
\(41\) 8.00000 1.24939 0.624695 0.780869i \(-0.285223\pi\)
0.624695 + 0.780869i \(0.285223\pi\)
\(42\) −3.00000 −0.462910
\(43\) 13.0000 1.98248 0.991241 0.132068i \(-0.0421616\pi\)
0.991241 + 0.132068i \(0.0421616\pi\)
\(44\) −1.00000 −0.150756
\(45\) 1.00000 0.149071
\(46\) 1.00000 0.147442
\(47\) −12.0000 −1.75038 −0.875190 0.483779i \(-0.839264\pi\)
−0.875190 + 0.483779i \(0.839264\pi\)
\(48\) −1.00000 −0.144338
\(49\) 2.00000 0.285714
\(50\) −1.00000 −0.141421
\(51\) 1.00000 0.140028
\(52\) −4.00000 −0.554700
\(53\) −4.00000 −0.549442 −0.274721 0.961524i \(-0.588586\pi\)
−0.274721 + 0.961524i \(0.588586\pi\)
\(54\) 1.00000 0.136083
\(55\) −1.00000 −0.134840
\(56\) 3.00000 0.400892
\(57\) −4.00000 −0.529813
\(58\) 3.00000 0.393919
\(59\) −6.00000 −0.781133 −0.390567 0.920575i \(-0.627721\pi\)
−0.390567 + 0.920575i \(0.627721\pi\)
\(60\) −1.00000 −0.129099
\(61\) −10.0000 −1.28037 −0.640184 0.768221i \(-0.721142\pi\)
−0.640184 + 0.768221i \(0.721142\pi\)
\(62\) 5.00000 0.635001
\(63\) −3.00000 −0.377964
\(64\) 1.00000 0.125000
\(65\) −4.00000 −0.496139
\(66\) −1.00000 −0.123091
\(67\) 8.00000 0.977356 0.488678 0.872464i \(-0.337479\pi\)
0.488678 + 0.872464i \(0.337479\pi\)
\(68\) −1.00000 −0.121268
\(69\) 1.00000 0.120386
\(70\) 3.00000 0.358569
\(71\) 14.0000 1.66149 0.830747 0.556650i \(-0.187914\pi\)
0.830747 + 0.556650i \(0.187914\pi\)
\(72\) −1.00000 −0.117851
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) 6.00000 0.697486
\(75\) −1.00000 −0.115470
\(76\) 4.00000 0.458831
\(77\) 3.00000 0.341882
\(78\) −4.00000 −0.452911
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 1.00000 0.111803
\(81\) 1.00000 0.111111
\(82\) −8.00000 −0.883452
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 3.00000 0.327327
\(85\) −1.00000 −0.108465
\(86\) −13.0000 −1.40183
\(87\) 3.00000 0.321634
\(88\) 1.00000 0.106600
\(89\) −4.00000 −0.423999 −0.212000 0.977270i \(-0.567998\pi\)
−0.212000 + 0.977270i \(0.567998\pi\)
\(90\) −1.00000 −0.105409
\(91\) 12.0000 1.25794
\(92\) −1.00000 −0.104257
\(93\) 5.00000 0.518476
\(94\) 12.0000 1.23771
\(95\) 4.00000 0.410391
\(96\) 1.00000 0.102062
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) −2.00000 −0.202031
\(99\) −1.00000 −0.100504
\(100\) 1.00000 0.100000
\(101\) −2.00000 −0.199007 −0.0995037 0.995037i \(-0.531726\pi\)
−0.0995037 + 0.995037i \(0.531726\pi\)
\(102\) −1.00000 −0.0990148
\(103\) −11.0000 −1.08386 −0.541931 0.840423i \(-0.682307\pi\)
−0.541931 + 0.840423i \(0.682307\pi\)
\(104\) 4.00000 0.392232
\(105\) 3.00000 0.292770
\(106\) 4.00000 0.388514
\(107\) 5.00000 0.483368 0.241684 0.970355i \(-0.422300\pi\)
0.241684 + 0.970355i \(0.422300\pi\)
\(108\) −1.00000 −0.0962250
\(109\) 8.00000 0.766261 0.383131 0.923694i \(-0.374846\pi\)
0.383131 + 0.923694i \(0.374846\pi\)
\(110\) 1.00000 0.0953463
\(111\) 6.00000 0.569495
\(112\) −3.00000 −0.283473
\(113\) 10.0000 0.940721 0.470360 0.882474i \(-0.344124\pi\)
0.470360 + 0.882474i \(0.344124\pi\)
\(114\) 4.00000 0.374634
\(115\) −1.00000 −0.0932505
\(116\) −3.00000 −0.278543
\(117\) −4.00000 −0.369800
\(118\) 6.00000 0.552345
\(119\) 3.00000 0.275010
\(120\) 1.00000 0.0912871
\(121\) 1.00000 0.0909091
\(122\) 10.0000 0.905357
\(123\) −8.00000 −0.721336
\(124\) −5.00000 −0.449013
\(125\) 1.00000 0.0894427
\(126\) 3.00000 0.267261
\(127\) −6.00000 −0.532414 −0.266207 0.963916i \(-0.585770\pi\)
−0.266207 + 0.963916i \(0.585770\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −13.0000 −1.14459
\(130\) 4.00000 0.350823
\(131\) 12.0000 1.04844 0.524222 0.851581i \(-0.324356\pi\)
0.524222 + 0.851581i \(0.324356\pi\)
\(132\) 1.00000 0.0870388
\(133\) −12.0000 −1.04053
\(134\) −8.00000 −0.691095
\(135\) −1.00000 −0.0860663
\(136\) 1.00000 0.0857493
\(137\) 17.0000 1.45241 0.726204 0.687479i \(-0.241283\pi\)
0.726204 + 0.687479i \(0.241283\pi\)
\(138\) −1.00000 −0.0851257
\(139\) 1.00000 0.0848189 0.0424094 0.999100i \(-0.486497\pi\)
0.0424094 + 0.999100i \(0.486497\pi\)
\(140\) −3.00000 −0.253546
\(141\) 12.0000 1.01058
\(142\) −14.0000 −1.17485
\(143\) 4.00000 0.334497
\(144\) 1.00000 0.0833333
\(145\) −3.00000 −0.249136
\(146\) 6.00000 0.496564
\(147\) −2.00000 −0.164957
\(148\) −6.00000 −0.493197
\(149\) 16.0000 1.31077 0.655386 0.755295i \(-0.272506\pi\)
0.655386 + 0.755295i \(0.272506\pi\)
\(150\) 1.00000 0.0816497
\(151\) 12.0000 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(152\) −4.00000 −0.324443
\(153\) −1.00000 −0.0808452
\(154\) −3.00000 −0.241747
\(155\) −5.00000 −0.401610
\(156\) 4.00000 0.320256
\(157\) −18.0000 −1.43656 −0.718278 0.695756i \(-0.755069\pi\)
−0.718278 + 0.695756i \(0.755069\pi\)
\(158\) −4.00000 −0.318223
\(159\) 4.00000 0.317221
\(160\) −1.00000 −0.0790569
\(161\) 3.00000 0.236433
\(162\) −1.00000 −0.0785674
\(163\) 21.0000 1.64485 0.822423 0.568876i \(-0.192621\pi\)
0.822423 + 0.568876i \(0.192621\pi\)
\(164\) 8.00000 0.624695
\(165\) 1.00000 0.0778499
\(166\) 8.00000 0.620920
\(167\) 18.0000 1.39288 0.696441 0.717614i \(-0.254766\pi\)
0.696441 + 0.717614i \(0.254766\pi\)
\(168\) −3.00000 −0.231455
\(169\) 3.00000 0.230769
\(170\) 1.00000 0.0766965
\(171\) 4.00000 0.305888
\(172\) 13.0000 0.991241
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) −3.00000 −0.227429
\(175\) −3.00000 −0.226779
\(176\) −1.00000 −0.0753778
\(177\) 6.00000 0.450988
\(178\) 4.00000 0.299813
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 1.00000 0.0745356
\(181\) −5.00000 −0.371647 −0.185824 0.982583i \(-0.559495\pi\)
−0.185824 + 0.982583i \(0.559495\pi\)
\(182\) −12.0000 −0.889499
\(183\) 10.0000 0.739221
\(184\) 1.00000 0.0737210
\(185\) −6.00000 −0.441129
\(186\) −5.00000 −0.366618
\(187\) 1.00000 0.0731272
\(188\) −12.0000 −0.875190
\(189\) 3.00000 0.218218
\(190\) −4.00000 −0.290191
\(191\) −9.00000 −0.651217 −0.325609 0.945505i \(-0.605569\pi\)
−0.325609 + 0.945505i \(0.605569\pi\)
\(192\) −1.00000 −0.0721688
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) 1.00000 0.0717958
\(195\) 4.00000 0.286446
\(196\) 2.00000 0.142857
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 1.00000 0.0710669
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −8.00000 −0.564276
\(202\) 2.00000 0.140720
\(203\) 9.00000 0.631676
\(204\) 1.00000 0.0700140
\(205\) 8.00000 0.558744
\(206\) 11.0000 0.766406
\(207\) −1.00000 −0.0695048
\(208\) −4.00000 −0.277350
\(209\) −4.00000 −0.276686
\(210\) −3.00000 −0.207020
\(211\) 15.0000 1.03264 0.516321 0.856395i \(-0.327301\pi\)
0.516321 + 0.856395i \(0.327301\pi\)
\(212\) −4.00000 −0.274721
\(213\) −14.0000 −0.959264
\(214\) −5.00000 −0.341793
\(215\) 13.0000 0.886593
\(216\) 1.00000 0.0680414
\(217\) 15.0000 1.01827
\(218\) −8.00000 −0.541828
\(219\) 6.00000 0.405442
\(220\) −1.00000 −0.0674200
\(221\) 4.00000 0.269069
\(222\) −6.00000 −0.402694
\(223\) −19.0000 −1.27233 −0.636167 0.771551i \(-0.719481\pi\)
−0.636167 + 0.771551i \(0.719481\pi\)
\(224\) 3.00000 0.200446
\(225\) 1.00000 0.0666667
\(226\) −10.0000 −0.665190
\(227\) 21.0000 1.39382 0.696909 0.717159i \(-0.254558\pi\)
0.696909 + 0.717159i \(0.254558\pi\)
\(228\) −4.00000 −0.264906
\(229\) −24.0000 −1.58596 −0.792982 0.609245i \(-0.791473\pi\)
−0.792982 + 0.609245i \(0.791473\pi\)
\(230\) 1.00000 0.0659380
\(231\) −3.00000 −0.197386
\(232\) 3.00000 0.196960
\(233\) 23.0000 1.50678 0.753390 0.657574i \(-0.228417\pi\)
0.753390 + 0.657574i \(0.228417\pi\)
\(234\) 4.00000 0.261488
\(235\) −12.0000 −0.782794
\(236\) −6.00000 −0.390567
\(237\) −4.00000 −0.259828
\(238\) −3.00000 −0.194461
\(239\) 6.00000 0.388108 0.194054 0.980991i \(-0.437836\pi\)
0.194054 + 0.980991i \(0.437836\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −9.00000 −0.579741 −0.289870 0.957066i \(-0.593612\pi\)
−0.289870 + 0.957066i \(0.593612\pi\)
\(242\) −1.00000 −0.0642824
\(243\) −1.00000 −0.0641500
\(244\) −10.0000 −0.640184
\(245\) 2.00000 0.127775
\(246\) 8.00000 0.510061
\(247\) −16.0000 −1.01806
\(248\) 5.00000 0.317500
\(249\) 8.00000 0.506979
\(250\) −1.00000 −0.0632456
\(251\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(252\) −3.00000 −0.188982
\(253\) 1.00000 0.0628695
\(254\) 6.00000 0.376473
\(255\) 1.00000 0.0626224
\(256\) 1.00000 0.0625000
\(257\) −17.0000 −1.06043 −0.530215 0.847863i \(-0.677889\pi\)
−0.530215 + 0.847863i \(0.677889\pi\)
\(258\) 13.0000 0.809345
\(259\) 18.0000 1.11847
\(260\) −4.00000 −0.248069
\(261\) −3.00000 −0.185695
\(262\) −12.0000 −0.741362
\(263\) 11.0000 0.678289 0.339145 0.940734i \(-0.389862\pi\)
0.339145 + 0.940734i \(0.389862\pi\)
\(264\) −1.00000 −0.0615457
\(265\) −4.00000 −0.245718
\(266\) 12.0000 0.735767
\(267\) 4.00000 0.244796
\(268\) 8.00000 0.488678
\(269\) 26.0000 1.58525 0.792624 0.609711i \(-0.208714\pi\)
0.792624 + 0.609711i \(0.208714\pi\)
\(270\) 1.00000 0.0608581
\(271\) −25.0000 −1.51864 −0.759321 0.650716i \(-0.774469\pi\)
−0.759321 + 0.650716i \(0.774469\pi\)
\(272\) −1.00000 −0.0606339
\(273\) −12.0000 −0.726273
\(274\) −17.0000 −1.02701
\(275\) −1.00000 −0.0603023
\(276\) 1.00000 0.0601929
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −1.00000 −0.0599760
\(279\) −5.00000 −0.299342
\(280\) 3.00000 0.179284
\(281\) 3.00000 0.178965 0.0894825 0.995988i \(-0.471479\pi\)
0.0894825 + 0.995988i \(0.471479\pi\)
\(282\) −12.0000 −0.714590
\(283\) −2.00000 −0.118888 −0.0594438 0.998232i \(-0.518933\pi\)
−0.0594438 + 0.998232i \(0.518933\pi\)
\(284\) 14.0000 0.830747
\(285\) −4.00000 −0.236940
\(286\) −4.00000 −0.236525
\(287\) −24.0000 −1.41668
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) 3.00000 0.176166
\(291\) 1.00000 0.0586210
\(292\) −6.00000 −0.351123
\(293\) −3.00000 −0.175262 −0.0876309 0.996153i \(-0.527930\pi\)
−0.0876309 + 0.996153i \(0.527930\pi\)
\(294\) 2.00000 0.116642
\(295\) −6.00000 −0.349334
\(296\) 6.00000 0.348743
\(297\) 1.00000 0.0580259
\(298\) −16.0000 −0.926855
\(299\) 4.00000 0.231326
\(300\) −1.00000 −0.0577350
\(301\) −39.0000 −2.24792
\(302\) −12.0000 −0.690522
\(303\) 2.00000 0.114897
\(304\) 4.00000 0.229416
\(305\) −10.0000 −0.572598
\(306\) 1.00000 0.0571662
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 3.00000 0.170941
\(309\) 11.0000 0.625768
\(310\) 5.00000 0.283981
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) −4.00000 −0.226455
\(313\) 17.0000 0.960897 0.480448 0.877023i \(-0.340474\pi\)
0.480448 + 0.877023i \(0.340474\pi\)
\(314\) 18.0000 1.01580
\(315\) −3.00000 −0.169031
\(316\) 4.00000 0.225018
\(317\) −31.0000 −1.74113 −0.870567 0.492050i \(-0.836248\pi\)
−0.870567 + 0.492050i \(0.836248\pi\)
\(318\) −4.00000 −0.224309
\(319\) 3.00000 0.167968
\(320\) 1.00000 0.0559017
\(321\) −5.00000 −0.279073
\(322\) −3.00000 −0.167183
\(323\) −4.00000 −0.222566
\(324\) 1.00000 0.0555556
\(325\) −4.00000 −0.221880
\(326\) −21.0000 −1.16308
\(327\) −8.00000 −0.442401
\(328\) −8.00000 −0.441726
\(329\) 36.0000 1.98474
\(330\) −1.00000 −0.0550482
\(331\) −11.0000 −0.604615 −0.302307 0.953211i \(-0.597757\pi\)
−0.302307 + 0.953211i \(0.597757\pi\)
\(332\) −8.00000 −0.439057
\(333\) −6.00000 −0.328798
\(334\) −18.0000 −0.984916
\(335\) 8.00000 0.437087
\(336\) 3.00000 0.163663
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) −3.00000 −0.163178
\(339\) −10.0000 −0.543125
\(340\) −1.00000 −0.0542326
\(341\) 5.00000 0.270765
\(342\) −4.00000 −0.216295
\(343\) 15.0000 0.809924
\(344\) −13.0000 −0.700913
\(345\) 1.00000 0.0538382
\(346\) 6.00000 0.322562
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 3.00000 0.160817
\(349\) 26.0000 1.39175 0.695874 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 3.00000 0.160357
\(351\) 4.00000 0.213504
\(352\) 1.00000 0.0533002
\(353\) 25.0000 1.33062 0.665308 0.746569i \(-0.268300\pi\)
0.665308 + 0.746569i \(0.268300\pi\)
\(354\) −6.00000 −0.318896
\(355\) 14.0000 0.743043
\(356\) −4.00000 −0.212000
\(357\) −3.00000 −0.158777
\(358\) 6.00000 0.317110
\(359\) 14.0000 0.738892 0.369446 0.929252i \(-0.379548\pi\)
0.369446 + 0.929252i \(0.379548\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −3.00000 −0.157895
\(362\) 5.00000 0.262794
\(363\) −1.00000 −0.0524864
\(364\) 12.0000 0.628971
\(365\) −6.00000 −0.314054
\(366\) −10.0000 −0.522708
\(367\) 22.0000 1.14839 0.574195 0.818718i \(-0.305315\pi\)
0.574195 + 0.818718i \(0.305315\pi\)
\(368\) −1.00000 −0.0521286
\(369\) 8.00000 0.416463
\(370\) 6.00000 0.311925
\(371\) 12.0000 0.623009
\(372\) 5.00000 0.259238
\(373\) 22.0000 1.13912 0.569558 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) −1.00000 −0.0517088
\(375\) −1.00000 −0.0516398
\(376\) 12.0000 0.618853
\(377\) 12.0000 0.618031
\(378\) −3.00000 −0.154303
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 4.00000 0.205196
\(381\) 6.00000 0.307389
\(382\) 9.00000 0.460480
\(383\) 8.00000 0.408781 0.204390 0.978889i \(-0.434479\pi\)
0.204390 + 0.978889i \(0.434479\pi\)
\(384\) 1.00000 0.0510310
\(385\) 3.00000 0.152894
\(386\) 6.00000 0.305392
\(387\) 13.0000 0.660827
\(388\) −1.00000 −0.0507673
\(389\) 22.0000 1.11544 0.557722 0.830028i \(-0.311675\pi\)
0.557722 + 0.830028i \(0.311675\pi\)
\(390\) −4.00000 −0.202548
\(391\) 1.00000 0.0505722
\(392\) −2.00000 −0.101015
\(393\) −12.0000 −0.605320
\(394\) 12.0000 0.604551
\(395\) 4.00000 0.201262
\(396\) −1.00000 −0.0502519
\(397\) −18.0000 −0.903394 −0.451697 0.892171i \(-0.649181\pi\)
−0.451697 + 0.892171i \(0.649181\pi\)
\(398\) −8.00000 −0.401004
\(399\) 12.0000 0.600751
\(400\) 1.00000 0.0500000
\(401\) 3.00000 0.149813 0.0749064 0.997191i \(-0.476134\pi\)
0.0749064 + 0.997191i \(0.476134\pi\)
\(402\) 8.00000 0.399004
\(403\) 20.0000 0.996271
\(404\) −2.00000 −0.0995037
\(405\) 1.00000 0.0496904
\(406\) −9.00000 −0.446663
\(407\) 6.00000 0.297409
\(408\) −1.00000 −0.0495074
\(409\) 8.00000 0.395575 0.197787 0.980245i \(-0.436624\pi\)
0.197787 + 0.980245i \(0.436624\pi\)
\(410\) −8.00000 −0.395092
\(411\) −17.0000 −0.838548
\(412\) −11.0000 −0.541931
\(413\) 18.0000 0.885722
\(414\) 1.00000 0.0491473
\(415\) −8.00000 −0.392705
\(416\) 4.00000 0.196116
\(417\) −1.00000 −0.0489702
\(418\) 4.00000 0.195646
\(419\) 25.0000 1.22133 0.610665 0.791889i \(-0.290902\pi\)
0.610665 + 0.791889i \(0.290902\pi\)
\(420\) 3.00000 0.146385
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) −15.0000 −0.730189
\(423\) −12.0000 −0.583460
\(424\) 4.00000 0.194257
\(425\) −1.00000 −0.0485071
\(426\) 14.0000 0.678302
\(427\) 30.0000 1.45180
\(428\) 5.00000 0.241684
\(429\) −4.00000 −0.193122
\(430\) −13.0000 −0.626916
\(431\) 35.0000 1.68589 0.842945 0.537999i \(-0.180820\pi\)
0.842945 + 0.537999i \(0.180820\pi\)
\(432\) −1.00000 −0.0481125
\(433\) 12.0000 0.576683 0.288342 0.957528i \(-0.406896\pi\)
0.288342 + 0.957528i \(0.406896\pi\)
\(434\) −15.0000 −0.720023
\(435\) 3.00000 0.143839
\(436\) 8.00000 0.383131
\(437\) −4.00000 −0.191346
\(438\) −6.00000 −0.286691
\(439\) −34.0000 −1.62273 −0.811366 0.584539i \(-0.801275\pi\)
−0.811366 + 0.584539i \(0.801275\pi\)
\(440\) 1.00000 0.0476731
\(441\) 2.00000 0.0952381
\(442\) −4.00000 −0.190261
\(443\) 13.0000 0.617649 0.308824 0.951119i \(-0.400064\pi\)
0.308824 + 0.951119i \(0.400064\pi\)
\(444\) 6.00000 0.284747
\(445\) −4.00000 −0.189618
\(446\) 19.0000 0.899676
\(447\) −16.0000 −0.756774
\(448\) −3.00000 −0.141737
\(449\) 41.0000 1.93491 0.967455 0.253044i \(-0.0814317\pi\)
0.967455 + 0.253044i \(0.0814317\pi\)
\(450\) −1.00000 −0.0471405
\(451\) −8.00000 −0.376705
\(452\) 10.0000 0.470360
\(453\) −12.0000 −0.563809
\(454\) −21.0000 −0.985579
\(455\) 12.0000 0.562569
\(456\) 4.00000 0.187317
\(457\) −22.0000 −1.02912 −0.514558 0.857455i \(-0.672044\pi\)
−0.514558 + 0.857455i \(0.672044\pi\)
\(458\) 24.0000 1.12145
\(459\) 1.00000 0.0466760
\(460\) −1.00000 −0.0466252
\(461\) −26.0000 −1.21094 −0.605470 0.795868i \(-0.707015\pi\)
−0.605470 + 0.795868i \(0.707015\pi\)
\(462\) 3.00000 0.139573
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) −3.00000 −0.139272
\(465\) 5.00000 0.231869
\(466\) −23.0000 −1.06545
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) −4.00000 −0.184900
\(469\) −24.0000 −1.10822
\(470\) 12.0000 0.553519
\(471\) 18.0000 0.829396
\(472\) 6.00000 0.276172
\(473\) −13.0000 −0.597741
\(474\) 4.00000 0.183726
\(475\) 4.00000 0.183533
\(476\) 3.00000 0.137505
\(477\) −4.00000 −0.183147
\(478\) −6.00000 −0.274434
\(479\) 29.0000 1.32504 0.662522 0.749043i \(-0.269486\pi\)
0.662522 + 0.749043i \(0.269486\pi\)
\(480\) 1.00000 0.0456435
\(481\) 24.0000 1.09431
\(482\) 9.00000 0.409939
\(483\) −3.00000 −0.136505
\(484\) 1.00000 0.0454545
\(485\) −1.00000 −0.0454077
\(486\) 1.00000 0.0453609
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) 10.0000 0.452679
\(489\) −21.0000 −0.949653
\(490\) −2.00000 −0.0903508
\(491\) 8.00000 0.361035 0.180517 0.983572i \(-0.442223\pi\)
0.180517 + 0.983572i \(0.442223\pi\)
\(492\) −8.00000 −0.360668
\(493\) 3.00000 0.135113
\(494\) 16.0000 0.719874
\(495\) −1.00000 −0.0449467
\(496\) −5.00000 −0.224507
\(497\) −42.0000 −1.88396
\(498\) −8.00000 −0.358489
\(499\) 4.00000 0.179065 0.0895323 0.995984i \(-0.471463\pi\)
0.0895323 + 0.995984i \(0.471463\pi\)
\(500\) 1.00000 0.0447214
\(501\) −18.0000 −0.804181
\(502\) 0 0
\(503\) 28.0000 1.24846 0.624229 0.781241i \(-0.285413\pi\)
0.624229 + 0.781241i \(0.285413\pi\)
\(504\) 3.00000 0.133631
\(505\) −2.00000 −0.0889988
\(506\) −1.00000 −0.0444554
\(507\) −3.00000 −0.133235
\(508\) −6.00000 −0.266207
\(509\) 30.0000 1.32973 0.664863 0.746965i \(-0.268490\pi\)
0.664863 + 0.746965i \(0.268490\pi\)
\(510\) −1.00000 −0.0442807
\(511\) 18.0000 0.796273
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 −0.176604
\(514\) 17.0000 0.749838
\(515\) −11.0000 −0.484718
\(516\) −13.0000 −0.572293
\(517\) 12.0000 0.527759
\(518\) −18.0000 −0.790875
\(519\) 6.00000 0.263371
\(520\) 4.00000 0.175412
\(521\) −18.0000 −0.788594 −0.394297 0.918983i \(-0.629012\pi\)
−0.394297 + 0.918983i \(0.629012\pi\)
\(522\) 3.00000 0.131306
\(523\) −11.0000 −0.480996 −0.240498 0.970650i \(-0.577311\pi\)
−0.240498 + 0.970650i \(0.577311\pi\)
\(524\) 12.0000 0.524222
\(525\) 3.00000 0.130931
\(526\) −11.0000 −0.479623
\(527\) 5.00000 0.217803
\(528\) 1.00000 0.0435194
\(529\) −22.0000 −0.956522
\(530\) 4.00000 0.173749
\(531\) −6.00000 −0.260378
\(532\) −12.0000 −0.520266
\(533\) −32.0000 −1.38607
\(534\) −4.00000 −0.173097
\(535\) 5.00000 0.216169
\(536\) −8.00000 −0.345547
\(537\) 6.00000 0.258919
\(538\) −26.0000 −1.12094
\(539\) −2.00000 −0.0861461
\(540\) −1.00000 −0.0430331
\(541\) −28.0000 −1.20381 −0.601907 0.798566i \(-0.705592\pi\)
−0.601907 + 0.798566i \(0.705592\pi\)
\(542\) 25.0000 1.07384
\(543\) 5.00000 0.214571
\(544\) 1.00000 0.0428746
\(545\) 8.00000 0.342682
\(546\) 12.0000 0.513553
\(547\) 2.00000 0.0855138 0.0427569 0.999086i \(-0.486386\pi\)
0.0427569 + 0.999086i \(0.486386\pi\)
\(548\) 17.0000 0.726204
\(549\) −10.0000 −0.426790
\(550\) 1.00000 0.0426401
\(551\) −12.0000 −0.511217
\(552\) −1.00000 −0.0425628
\(553\) −12.0000 −0.510292
\(554\) 2.00000 0.0849719
\(555\) 6.00000 0.254686
\(556\) 1.00000 0.0424094
\(557\) −5.00000 −0.211857 −0.105928 0.994374i \(-0.533781\pi\)
−0.105928 + 0.994374i \(0.533781\pi\)
\(558\) 5.00000 0.211667
\(559\) −52.0000 −2.19937
\(560\) −3.00000 −0.126773
\(561\) −1.00000 −0.0422200
\(562\) −3.00000 −0.126547
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 12.0000 0.505291
\(565\) 10.0000 0.420703
\(566\) 2.00000 0.0840663
\(567\) −3.00000 −0.125988
\(568\) −14.0000 −0.587427
\(569\) 34.0000 1.42535 0.712677 0.701492i \(-0.247483\pi\)
0.712677 + 0.701492i \(0.247483\pi\)
\(570\) 4.00000 0.167542
\(571\) 44.0000 1.84134 0.920671 0.390339i \(-0.127642\pi\)
0.920671 + 0.390339i \(0.127642\pi\)
\(572\) 4.00000 0.167248
\(573\) 9.00000 0.375980
\(574\) 24.0000 1.00174
\(575\) −1.00000 −0.0417029
\(576\) 1.00000 0.0416667
\(577\) 38.0000 1.58196 0.790980 0.611842i \(-0.209571\pi\)
0.790980 + 0.611842i \(0.209571\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 6.00000 0.249351
\(580\) −3.00000 −0.124568
\(581\) 24.0000 0.995688
\(582\) −1.00000 −0.0414513
\(583\) 4.00000 0.165663
\(584\) 6.00000 0.248282
\(585\) −4.00000 −0.165380
\(586\) 3.00000 0.123929
\(587\) 27.0000 1.11441 0.557205 0.830375i \(-0.311874\pi\)
0.557205 + 0.830375i \(0.311874\pi\)
\(588\) −2.00000 −0.0824786
\(589\) −20.0000 −0.824086
\(590\) 6.00000 0.247016
\(591\) 12.0000 0.493614
\(592\) −6.00000 −0.246598
\(593\) −6.00000 −0.246390 −0.123195 0.992382i \(-0.539314\pi\)
−0.123195 + 0.992382i \(0.539314\pi\)
\(594\) −1.00000 −0.0410305
\(595\) 3.00000 0.122988
\(596\) 16.0000 0.655386
\(597\) −8.00000 −0.327418
\(598\) −4.00000 −0.163572
\(599\) 1.00000 0.0408589 0.0204294 0.999791i \(-0.493497\pi\)
0.0204294 + 0.999791i \(0.493497\pi\)
\(600\) 1.00000 0.0408248
\(601\) −46.0000 −1.87638 −0.938190 0.346122i \(-0.887498\pi\)
−0.938190 + 0.346122i \(0.887498\pi\)
\(602\) 39.0000 1.58952
\(603\) 8.00000 0.325785
\(604\) 12.0000 0.488273
\(605\) 1.00000 0.0406558
\(606\) −2.00000 −0.0812444
\(607\) 40.0000 1.62355 0.811775 0.583970i \(-0.198502\pi\)
0.811775 + 0.583970i \(0.198502\pi\)
\(608\) −4.00000 −0.162221
\(609\) −9.00000 −0.364698
\(610\) 10.0000 0.404888
\(611\) 48.0000 1.94187
\(612\) −1.00000 −0.0404226
\(613\) 10.0000 0.403896 0.201948 0.979396i \(-0.435273\pi\)
0.201948 + 0.979396i \(0.435273\pi\)
\(614\) −20.0000 −0.807134
\(615\) −8.00000 −0.322591
\(616\) −3.00000 −0.120873
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) −11.0000 −0.442485
\(619\) 14.0000 0.562708 0.281354 0.959604i \(-0.409217\pi\)
0.281354 + 0.959604i \(0.409217\pi\)
\(620\) −5.00000 −0.200805
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 12.0000 0.480770
\(624\) 4.00000 0.160128
\(625\) 1.00000 0.0400000
\(626\) −17.0000 −0.679457
\(627\) 4.00000 0.159745
\(628\) −18.0000 −0.718278
\(629\) 6.00000 0.239236
\(630\) 3.00000 0.119523
\(631\) −22.0000 −0.875806 −0.437903 0.899022i \(-0.644279\pi\)
−0.437903 + 0.899022i \(0.644279\pi\)
\(632\) −4.00000 −0.159111
\(633\) −15.0000 −0.596196
\(634\) 31.0000 1.23117
\(635\) −6.00000 −0.238103
\(636\) 4.00000 0.158610
\(637\) −8.00000 −0.316972
\(638\) −3.00000 −0.118771
\(639\) 14.0000 0.553831
\(640\) −1.00000 −0.0395285
\(641\) −27.0000 −1.06644 −0.533218 0.845978i \(-0.679017\pi\)
−0.533218 + 0.845978i \(0.679017\pi\)
\(642\) 5.00000 0.197334
\(643\) 11.0000 0.433798 0.216899 0.976194i \(-0.430406\pi\)
0.216899 + 0.976194i \(0.430406\pi\)
\(644\) 3.00000 0.118217
\(645\) −13.0000 −0.511875
\(646\) 4.00000 0.157378
\(647\) 22.0000 0.864909 0.432455 0.901656i \(-0.357648\pi\)
0.432455 + 0.901656i \(0.357648\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 6.00000 0.235521
\(650\) 4.00000 0.156893
\(651\) −15.0000 −0.587896
\(652\) 21.0000 0.822423
\(653\) −39.0000 −1.52619 −0.763094 0.646288i \(-0.776321\pi\)
−0.763094 + 0.646288i \(0.776321\pi\)
\(654\) 8.00000 0.312825
\(655\) 12.0000 0.468879
\(656\) 8.00000 0.312348
\(657\) −6.00000 −0.234082
\(658\) −36.0000 −1.40343
\(659\) −23.0000 −0.895953 −0.447976 0.894045i \(-0.647855\pi\)
−0.447976 + 0.894045i \(0.647855\pi\)
\(660\) 1.00000 0.0389249
\(661\) −16.0000 −0.622328 −0.311164 0.950356i \(-0.600719\pi\)
−0.311164 + 0.950356i \(0.600719\pi\)
\(662\) 11.0000 0.427527
\(663\) −4.00000 −0.155347
\(664\) 8.00000 0.310460
\(665\) −12.0000 −0.465340
\(666\) 6.00000 0.232495
\(667\) 3.00000 0.116160
\(668\) 18.0000 0.696441
\(669\) 19.0000 0.734582
\(670\) −8.00000 −0.309067
\(671\) 10.0000 0.386046
\(672\) −3.00000 −0.115728
\(673\) −8.00000 −0.308377 −0.154189 0.988041i \(-0.549276\pi\)
−0.154189 + 0.988041i \(0.549276\pi\)
\(674\) −18.0000 −0.693334
\(675\) −1.00000 −0.0384900
\(676\) 3.00000 0.115385
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 10.0000 0.384048
\(679\) 3.00000 0.115129
\(680\) 1.00000 0.0383482
\(681\) −21.0000 −0.804722
\(682\) −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
\(685\) 17.0000 0.649537
\(686\) −15.0000 −0.572703
\(687\) 24.0000 0.915657
\(688\) 13.0000 0.495620
\(689\) 16.0000 0.609551
\(690\) −1.00000 −0.0380693
\(691\) 12.0000 0.456502 0.228251 0.973602i \(-0.426699\pi\)
0.228251 + 0.973602i \(0.426699\pi\)
\(692\) −6.00000 −0.228086
\(693\) 3.00000 0.113961
\(694\) −12.0000 −0.455514
\(695\) 1.00000 0.0379322
\(696\) −3.00000 −0.113715
\(697\) −8.00000 −0.303022
\(698\) −26.0000 −0.984115
\(699\) −23.0000 −0.869940
\(700\) −3.00000 −0.113389
\(701\) 46.0000 1.73740 0.868698 0.495342i \(-0.164957\pi\)
0.868698 + 0.495342i \(0.164957\pi\)
\(702\) −4.00000 −0.150970
\(703\) −24.0000 −0.905177
\(704\) −1.00000 −0.0376889
\(705\) 12.0000 0.451946
\(706\) −25.0000 −0.940887
\(707\) 6.00000 0.225653
\(708\) 6.00000 0.225494
\(709\) 50.0000 1.87779 0.938895 0.344204i \(-0.111851\pi\)
0.938895 + 0.344204i \(0.111851\pi\)
\(710\) −14.0000 −0.525411
\(711\) 4.00000 0.150012
\(712\) 4.00000 0.149906
\(713\) 5.00000 0.187251
\(714\) 3.00000 0.112272
\(715\) 4.00000 0.149592
\(716\) −6.00000 −0.224231
\(717\) −6.00000 −0.224074
\(718\) −14.0000 −0.522475
\(719\) −6.00000 −0.223762 −0.111881 0.993722i \(-0.535688\pi\)
−0.111881 + 0.993722i \(0.535688\pi\)
\(720\) 1.00000 0.0372678
\(721\) 33.0000 1.22898
\(722\) 3.00000 0.111648
\(723\) 9.00000 0.334714
\(724\) −5.00000 −0.185824
\(725\) −3.00000 −0.111417
\(726\) 1.00000 0.0371135
\(727\) 5.00000 0.185440 0.0927199 0.995692i \(-0.470444\pi\)
0.0927199 + 0.995692i \(0.470444\pi\)
\(728\) −12.0000 −0.444750
\(729\) 1.00000 0.0370370
\(730\) 6.00000 0.222070
\(731\) −13.0000 −0.480822
\(732\) 10.0000 0.369611
\(733\) 44.0000 1.62518 0.812589 0.582838i \(-0.198058\pi\)
0.812589 + 0.582838i \(0.198058\pi\)
\(734\) −22.0000 −0.812035
\(735\) −2.00000 −0.0737711
\(736\) 1.00000 0.0368605
\(737\) −8.00000 −0.294684
\(738\) −8.00000 −0.294484
\(739\) −10.0000 −0.367856 −0.183928 0.982940i \(-0.558881\pi\)
−0.183928 + 0.982940i \(0.558881\pi\)
\(740\) −6.00000 −0.220564
\(741\) 16.0000 0.587775
\(742\) −12.0000 −0.440534
\(743\) 8.00000 0.293492 0.146746 0.989174i \(-0.453120\pi\)
0.146746 + 0.989174i \(0.453120\pi\)
\(744\) −5.00000 −0.183309
\(745\) 16.0000 0.586195
\(746\) −22.0000 −0.805477
\(747\) −8.00000 −0.292705
\(748\) 1.00000 0.0365636
\(749\) −15.0000 −0.548088
\(750\) 1.00000 0.0365148
\(751\) 45.0000 1.64207 0.821037 0.570875i \(-0.193396\pi\)
0.821037 + 0.570875i \(0.193396\pi\)
\(752\) −12.0000 −0.437595
\(753\) 0 0
\(754\) −12.0000 −0.437014
\(755\) 12.0000 0.436725
\(756\) 3.00000 0.109109
\(757\) −23.0000 −0.835949 −0.417975 0.908459i \(-0.637260\pi\)
−0.417975 + 0.908459i \(0.637260\pi\)
\(758\) 8.00000 0.290573
\(759\) −1.00000 −0.0362977
\(760\) −4.00000 −0.145095
\(761\) −3.00000 −0.108750 −0.0543750 0.998521i \(-0.517317\pi\)
−0.0543750 + 0.998521i \(0.517317\pi\)
\(762\) −6.00000 −0.217357
\(763\) −24.0000 −0.868858
\(764\) −9.00000 −0.325609
\(765\) −1.00000 −0.0361551
\(766\) −8.00000 −0.289052
\(767\) 24.0000 0.866590
\(768\) −1.00000 −0.0360844
\(769\) 2.00000 0.0721218 0.0360609 0.999350i \(-0.488519\pi\)
0.0360609 + 0.999350i \(0.488519\pi\)
\(770\) −3.00000 −0.108112
\(771\) 17.0000 0.612240
\(772\) −6.00000 −0.215945
\(773\) 48.0000 1.72644 0.863220 0.504828i \(-0.168444\pi\)
0.863220 + 0.504828i \(0.168444\pi\)
\(774\) −13.0000 −0.467275
\(775\) −5.00000 −0.179605
\(776\) 1.00000 0.0358979
\(777\) −18.0000 −0.645746
\(778\) −22.0000 −0.788738
\(779\) 32.0000 1.14652
\(780\) 4.00000 0.143223
\(781\) −14.0000 −0.500959
\(782\) −1.00000 −0.0357599
\(783\) 3.00000 0.107211
\(784\) 2.00000 0.0714286
\(785\) −18.0000 −0.642448
\(786\) 12.0000 0.428026
\(787\) −12.0000 −0.427754 −0.213877 0.976861i \(-0.568609\pi\)
−0.213877 + 0.976861i \(0.568609\pi\)
\(788\) −12.0000 −0.427482
\(789\) −11.0000 −0.391610
\(790\) −4.00000 −0.142314
\(791\) −30.0000 −1.06668
\(792\) 1.00000 0.0355335
\(793\) 40.0000 1.42044
\(794\) 18.0000 0.638796
\(795\) 4.00000 0.141865
\(796\) 8.00000 0.283552
\(797\) −52.0000 −1.84193 −0.920967 0.389640i \(-0.872599\pi\)
−0.920967 + 0.389640i \(0.872599\pi\)
\(798\) −12.0000 −0.424795
\(799\) 12.0000 0.424529
\(800\) −1.00000 −0.0353553
\(801\) −4.00000 −0.141333
\(802\) −3.00000 −0.105934
\(803\) 6.00000 0.211735
\(804\) −8.00000 −0.282138
\(805\) 3.00000 0.105736
\(806\) −20.0000 −0.704470
\(807\) −26.0000 −0.915243
\(808\) 2.00000 0.0703598
\(809\) −54.0000 −1.89854 −0.949269 0.314464i \(-0.898175\pi\)
−0.949269 + 0.314464i \(0.898175\pi\)
\(810\) −1.00000 −0.0351364
\(811\) 8.00000 0.280918 0.140459 0.990086i \(-0.455142\pi\)
0.140459 + 0.990086i \(0.455142\pi\)
\(812\) 9.00000 0.315838
\(813\) 25.0000 0.876788
\(814\) −6.00000 −0.210300
\(815\) 21.0000 0.735598
\(816\) 1.00000 0.0350070
\(817\) 52.0000 1.81925
\(818\) −8.00000 −0.279713
\(819\) 12.0000 0.419314
\(820\) 8.00000 0.279372
\(821\) −33.0000 −1.15171 −0.575854 0.817553i \(-0.695330\pi\)
−0.575854 + 0.817553i \(0.695330\pi\)
\(822\) 17.0000 0.592943
\(823\) 10.0000 0.348578 0.174289 0.984695i \(-0.444237\pi\)
0.174289 + 0.984695i \(0.444237\pi\)
\(824\) 11.0000 0.383203
\(825\) 1.00000 0.0348155
\(826\) −18.0000 −0.626300
\(827\) −37.0000 −1.28662 −0.643308 0.765607i \(-0.722439\pi\)
−0.643308 + 0.765607i \(0.722439\pi\)
\(828\) −1.00000 −0.0347524
\(829\) 34.0000 1.18087 0.590434 0.807086i \(-0.298956\pi\)
0.590434 + 0.807086i \(0.298956\pi\)
\(830\) 8.00000 0.277684
\(831\) 2.00000 0.0693792
\(832\) −4.00000 −0.138675
\(833\) −2.00000 −0.0692959
\(834\) 1.00000 0.0346272
\(835\) 18.0000 0.622916
\(836\) −4.00000 −0.138343
\(837\) 5.00000 0.172825
\(838\) −25.0000 −0.863611
\(839\) 18.0000 0.621429 0.310715 0.950503i \(-0.399432\pi\)
0.310715 + 0.950503i \(0.399432\pi\)
\(840\) −3.00000 −0.103510
\(841\) −20.0000 −0.689655
\(842\) −8.00000 −0.275698
\(843\) −3.00000 −0.103325
\(844\) 15.0000 0.516321
\(845\) 3.00000 0.103203
\(846\) 12.0000 0.412568
\(847\) −3.00000 −0.103081
\(848\) −4.00000 −0.137361
\(849\) 2.00000 0.0686398
\(850\) 1.00000 0.0342997
\(851\) 6.00000 0.205677
\(852\) −14.0000 −0.479632
\(853\) −51.0000 −1.74621 −0.873103 0.487535i \(-0.837896\pi\)
−0.873103 + 0.487535i \(0.837896\pi\)
\(854\) −30.0000 −1.02658
\(855\) 4.00000 0.136797
\(856\) −5.00000 −0.170896
\(857\) −7.00000 −0.239115 −0.119558 0.992827i \(-0.538148\pi\)
−0.119558 + 0.992827i \(0.538148\pi\)
\(858\) 4.00000 0.136558
\(859\) 35.0000 1.19418 0.597092 0.802173i \(-0.296323\pi\)
0.597092 + 0.802173i \(0.296323\pi\)
\(860\) 13.0000 0.443296
\(861\) 24.0000 0.817918
\(862\) −35.0000 −1.19210
\(863\) 32.0000 1.08929 0.544646 0.838666i \(-0.316664\pi\)
0.544646 + 0.838666i \(0.316664\pi\)
\(864\) 1.00000 0.0340207
\(865\) −6.00000 −0.204006
\(866\) −12.0000 −0.407777
\(867\) −1.00000 −0.0339618
\(868\) 15.0000 0.509133
\(869\) −4.00000 −0.135691
\(870\) −3.00000 −0.101710
\(871\) −32.0000 −1.08428
\(872\) −8.00000 −0.270914
\(873\) −1.00000 −0.0338449
\(874\) 4.00000 0.135302
\(875\) −3.00000 −0.101419
\(876\) 6.00000 0.202721
\(877\) 13.0000 0.438979 0.219489 0.975615i \(-0.429561\pi\)
0.219489 + 0.975615i \(0.429561\pi\)
\(878\) 34.0000 1.14744
\(879\) 3.00000 0.101187
\(880\) −1.00000 −0.0337100
\(881\) 19.0000 0.640126 0.320063 0.947396i \(-0.396296\pi\)
0.320063 + 0.947396i \(0.396296\pi\)
\(882\) −2.00000 −0.0673435
\(883\) −24.0000 −0.807664 −0.403832 0.914833i \(-0.632322\pi\)
−0.403832 + 0.914833i \(0.632322\pi\)
\(884\) 4.00000 0.134535
\(885\) 6.00000 0.201688
\(886\) −13.0000 −0.436744
\(887\) 24.0000 0.805841 0.402921 0.915235i \(-0.367995\pi\)
0.402921 + 0.915235i \(0.367995\pi\)
\(888\) −6.00000 −0.201347
\(889\) 18.0000 0.603701
\(890\) 4.00000 0.134080
\(891\) −1.00000 −0.0335013
\(892\) −19.0000 −0.636167
\(893\) −48.0000 −1.60626
\(894\) 16.0000 0.535120
\(895\) −6.00000 −0.200558
\(896\) 3.00000 0.100223
\(897\) −4.00000 −0.133556
\(898\) −41.0000 −1.36819
\(899\) 15.0000 0.500278
\(900\) 1.00000 0.0333333
\(901\) 4.00000 0.133259
\(902\) 8.00000 0.266371
\(903\) 39.0000 1.29784
\(904\) −10.0000 −0.332595
\(905\) −5.00000 −0.166206
\(906\) 12.0000 0.398673
\(907\) −37.0000 −1.22856 −0.614282 0.789086i \(-0.710554\pi\)
−0.614282 + 0.789086i \(0.710554\pi\)
\(908\) 21.0000 0.696909
\(909\) −2.00000 −0.0663358
\(910\) −12.0000 −0.397796
\(911\) −32.0000 −1.06021 −0.530104 0.847933i \(-0.677847\pi\)
−0.530104 + 0.847933i \(0.677847\pi\)
\(912\) −4.00000 −0.132453
\(913\) 8.00000 0.264761
\(914\) 22.0000 0.727695
\(915\) 10.0000 0.330590
\(916\) −24.0000 −0.792982
\(917\) −36.0000 −1.18882
\(918\) −1.00000 −0.0330049
\(919\) 1.00000 0.0329870 0.0164935 0.999864i \(-0.494750\pi\)
0.0164935 + 0.999864i \(0.494750\pi\)
\(920\) 1.00000 0.0329690
\(921\) −20.0000 −0.659022
\(922\) 26.0000 0.856264
\(923\) −56.0000 −1.84326
\(924\) −3.00000 −0.0986928
\(925\) −6.00000 −0.197279
\(926\) 24.0000 0.788689
\(927\) −11.0000 −0.361287
\(928\) 3.00000 0.0984798
\(929\) −7.00000 −0.229663 −0.114831 0.993385i \(-0.536633\pi\)
−0.114831 + 0.993385i \(0.536633\pi\)
\(930\) −5.00000 −0.163956
\(931\) 8.00000 0.262189
\(932\) 23.0000 0.753390
\(933\) 0 0
\(934\) −12.0000 −0.392652
\(935\) 1.00000 0.0327035
\(936\) 4.00000 0.130744
\(937\) −38.0000 −1.24141 −0.620703 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(938\) 24.0000 0.783628
\(939\) −17.0000 −0.554774
\(940\) −12.0000 −0.391397
\(941\) 46.0000 1.49956 0.749779 0.661689i \(-0.230160\pi\)
0.749779 + 0.661689i \(0.230160\pi\)
\(942\) −18.0000 −0.586472
\(943\) −8.00000 −0.260516
\(944\) −6.00000 −0.195283
\(945\) 3.00000 0.0975900
\(946\) 13.0000 0.422666
\(947\) 18.0000 0.584921 0.292461 0.956278i \(-0.405526\pi\)
0.292461 + 0.956278i \(0.405526\pi\)
\(948\) −4.00000 −0.129914
\(949\) 24.0000 0.779073
\(950\) −4.00000 −0.129777
\(951\) 31.0000 1.00524
\(952\) −3.00000 −0.0972306
\(953\) −38.0000 −1.23094 −0.615470 0.788160i \(-0.711034\pi\)
−0.615470 + 0.788160i \(0.711034\pi\)
\(954\) 4.00000 0.129505
\(955\) −9.00000 −0.291233
\(956\) 6.00000 0.194054
\(957\) −3.00000 −0.0969762
\(958\) −29.0000 −0.936947
\(959\) −51.0000 −1.64688
\(960\) −1.00000 −0.0322749
\(961\) −6.00000 −0.193548
\(962\) −24.0000 −0.773791
\(963\) 5.00000 0.161123
\(964\) −9.00000 −0.289870
\(965\) −6.00000 −0.193147
\(966\) 3.00000 0.0965234
\(967\) −42.0000 −1.35063 −0.675314 0.737530i \(-0.735992\pi\)
−0.675314 + 0.737530i \(0.735992\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 4.00000 0.128499
\(970\) 1.00000 0.0321081
\(971\) −12.0000 −0.385098 −0.192549 0.981287i \(-0.561675\pi\)
−0.192549 + 0.981287i \(0.561675\pi\)
\(972\) −1.00000 −0.0320750
\(973\) −3.00000 −0.0961756
\(974\) −2.00000 −0.0640841
\(975\) 4.00000 0.128103
\(976\) −10.0000 −0.320092
\(977\) 2.00000 0.0639857 0.0319928 0.999488i \(-0.489815\pi\)
0.0319928 + 0.999488i \(0.489815\pi\)
\(978\) 21.0000 0.671506
\(979\) 4.00000 0.127841
\(980\) 2.00000 0.0638877
\(981\) 8.00000 0.255420
\(982\) −8.00000 −0.255290
\(983\) −41.0000 −1.30770 −0.653848 0.756626i \(-0.726847\pi\)
−0.653848 + 0.756626i \(0.726847\pi\)
\(984\) 8.00000 0.255031
\(985\) −12.0000 −0.382352
\(986\) −3.00000 −0.0955395
\(987\) −36.0000 −1.14589
\(988\) −16.0000 −0.509028
\(989\) −13.0000 −0.413376
\(990\) 1.00000 0.0317821
\(991\) −47.0000 −1.49300 −0.746502 0.665383i \(-0.768268\pi\)
−0.746502 + 0.665383i \(0.768268\pi\)
\(992\) 5.00000 0.158750
\(993\) 11.0000 0.349074
\(994\) 42.0000 1.33216
\(995\) 8.00000 0.253617
\(996\) 8.00000 0.253490
\(997\) 7.00000 0.221692 0.110846 0.993838i \(-0.464644\pi\)
0.110846 + 0.993838i \(0.464644\pi\)
\(998\) −4.00000 −0.126618
\(999\) 6.00000 0.189832
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.f.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.f.1.1 1 1.1 even 1 trivial