Properties

Label 4014.2.a.v.1.1
Level $4014$
Weight $2$
Character 4014.1
Self dual yes
Analytic conductor $32.052$
Analytic rank $0$
Dimension $7$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [4014,2,Mod(1,4014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4014, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("4014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4014 = 2 \cdot 3^{2} \cdot 223 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4014.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: \(32.0519513713\)
Analytic rank: \(0\)
Dimension: \(7\)
Coefficient field: \(\mathbb{Q}[x]/(x^{7} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{7} - 18x^{5} - 8x^{4} + 51x^{3} + 47x^{2} - 2x - 8 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 1338)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.01737\) of defining polynomial
Character \(\chi\) \(=\) 4014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{4} -3.79108 q^{5} -2.04653 q^{7} -1.00000 q^{8} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{4} -3.79108 q^{5} -2.04653 q^{7} -1.00000 q^{8} +3.79108 q^{10} +3.58410 q^{11} -1.68304 q^{13} +2.04653 q^{14} +1.00000 q^{16} -7.06098 q^{17} +6.27006 q^{19} -3.79108 q^{20} -3.58410 q^{22} -5.91836 q^{23} +9.37227 q^{25} +1.68304 q^{26} -2.04653 q^{28} -1.71227 q^{29} -6.59661 q^{31} -1.00000 q^{32} +7.06098 q^{34} +7.75855 q^{35} -6.84027 q^{37} -6.27006 q^{38} +3.79108 q^{40} -7.17153 q^{41} +8.20919 q^{43} +3.58410 q^{44} +5.91836 q^{46} -4.20034 q^{47} -2.81172 q^{49} -9.37227 q^{50} -1.68304 q^{52} -2.24115 q^{53} -13.5876 q^{55} +2.04653 q^{56} +1.71227 q^{58} +11.2120 q^{59} +2.28773 q^{61} +6.59661 q^{62} +1.00000 q^{64} +6.38054 q^{65} -9.15716 q^{67} -7.06098 q^{68} -7.75855 q^{70} -10.1516 q^{71} +0.168150 q^{73} +6.84027 q^{74} +6.27006 q^{76} -7.33497 q^{77} +4.46545 q^{79} -3.79108 q^{80} +7.17153 q^{82} +17.1161 q^{83} +26.7687 q^{85} -8.20919 q^{86} -3.58410 q^{88} -8.00626 q^{89} +3.44439 q^{91} -5.91836 q^{92} +4.20034 q^{94} -23.7703 q^{95} -17.4161 q^{97} +2.81172 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q - 7 q^{2} + 7 q^{4} - 6 q^{5} + 3 q^{7} - 7 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 7 q - 7 q^{2} + 7 q^{4} - 6 q^{5} + 3 q^{7} - 7 q^{8} + 6 q^{10} + q^{11} + 8 q^{13} - 3 q^{14} + 7 q^{16} - 16 q^{17} + 2 q^{19} - 6 q^{20} - q^{22} - 8 q^{23} + 19 q^{25} - 8 q^{26} + 3 q^{28} - 4 q^{29} + 11 q^{31} - 7 q^{32} + 16 q^{34} + 17 q^{37} - 2 q^{38} + 6 q^{40} - 18 q^{41} - q^{43} + q^{44} + 8 q^{46} - 5 q^{47} + 24 q^{49} - 19 q^{50} + 8 q^{52} - 6 q^{53} + 21 q^{55} - 3 q^{56} + 4 q^{58} + 7 q^{59} + 24 q^{61} - 11 q^{62} + 7 q^{64} - 11 q^{65} - 4 q^{67} - 16 q^{68} + 7 q^{71} + 28 q^{73} - 17 q^{74} + 2 q^{76} + 2 q^{77} - 6 q^{80} + 18 q^{82} + 2 q^{83} + 4 q^{85} + q^{86} - q^{88} - 5 q^{89} + 2 q^{91} - 8 q^{92} + 5 q^{94} + 14 q^{95} + 23 q^{97} - 24 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) −3.79108 −1.69542 −0.847711 0.530459i \(-0.822020\pi\)
−0.847711 + 0.530459i \(0.822020\pi\)
\(6\) 0 0
\(7\) −2.04653 −0.773515 −0.386758 0.922181i \(-0.626405\pi\)
−0.386758 + 0.922181i \(0.626405\pi\)
\(8\) −1.00000 −0.353553
\(9\) 0 0
\(10\) 3.79108 1.19884
\(11\) 3.58410 1.08065 0.540324 0.841457i \(-0.318302\pi\)
0.540324 + 0.841457i \(0.318302\pi\)
\(12\) 0 0
\(13\) −1.68304 −0.466791 −0.233396 0.972382i \(-0.574984\pi\)
−0.233396 + 0.972382i \(0.574984\pi\)
\(14\) 2.04653 0.546958
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −7.06098 −1.71254 −0.856270 0.516528i \(-0.827224\pi\)
−0.856270 + 0.516528i \(0.827224\pi\)
\(18\) 0 0
\(19\) 6.27006 1.43845 0.719225 0.694777i \(-0.244497\pi\)
0.719225 + 0.694777i \(0.244497\pi\)
\(20\) −3.79108 −0.847711
\(21\) 0 0
\(22\) −3.58410 −0.764133
\(23\) −5.91836 −1.23406 −0.617032 0.786938i \(-0.711665\pi\)
−0.617032 + 0.786938i \(0.711665\pi\)
\(24\) 0 0
\(25\) 9.37227 1.87445
\(26\) 1.68304 0.330071
\(27\) 0 0
\(28\) −2.04653 −0.386758
\(29\) −1.71227 −0.317961 −0.158981 0.987282i \(-0.550821\pi\)
−0.158981 + 0.987282i \(0.550821\pi\)
\(30\) 0 0
\(31\) −6.59661 −1.18479 −0.592393 0.805649i \(-0.701817\pi\)
−0.592393 + 0.805649i \(0.701817\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 7.06098 1.21095
\(35\) 7.75855 1.31143
\(36\) 0 0
\(37\) −6.84027 −1.12453 −0.562267 0.826956i \(-0.690071\pi\)
−0.562267 + 0.826956i \(0.690071\pi\)
\(38\) −6.27006 −1.01714
\(39\) 0 0
\(40\) 3.79108 0.599422
\(41\) −7.17153 −1.12001 −0.560003 0.828491i \(-0.689200\pi\)
−0.560003 + 0.828491i \(0.689200\pi\)
\(42\) 0 0
\(43\) 8.20919 1.25189 0.625945 0.779868i \(-0.284714\pi\)
0.625945 + 0.779868i \(0.284714\pi\)
\(44\) 3.58410 0.540324
\(45\) 0 0
\(46\) 5.91836 0.872614
\(47\) −4.20034 −0.612682 −0.306341 0.951922i \(-0.599105\pi\)
−0.306341 + 0.951922i \(0.599105\pi\)
\(48\) 0 0
\(49\) −2.81172 −0.401674
\(50\) −9.37227 −1.32544
\(51\) 0 0
\(52\) −1.68304 −0.233396
\(53\) −2.24115 −0.307845 −0.153923 0.988083i \(-0.549191\pi\)
−0.153923 + 0.988083i \(0.549191\pi\)
\(54\) 0 0
\(55\) −13.5876 −1.83215
\(56\) 2.04653 0.273479
\(57\) 0 0
\(58\) 1.71227 0.224832
\(59\) 11.2120 1.45968 0.729841 0.683617i \(-0.239594\pi\)
0.729841 + 0.683617i \(0.239594\pi\)
\(60\) 0 0
\(61\) 2.28773 0.292913 0.146457 0.989217i \(-0.453213\pi\)
0.146457 + 0.989217i \(0.453213\pi\)
\(62\) 6.59661 0.837770
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 6.38054 0.791408
\(66\) 0 0
\(67\) −9.15716 −1.11872 −0.559362 0.828923i \(-0.688954\pi\)
−0.559362 + 0.828923i \(0.688954\pi\)
\(68\) −7.06098 −0.856270
\(69\) 0 0
\(70\) −7.75855 −0.927324
\(71\) −10.1516 −1.20477 −0.602384 0.798207i \(-0.705782\pi\)
−0.602384 + 0.798207i \(0.705782\pi\)
\(72\) 0 0
\(73\) 0.168150 0.0196804 0.00984022 0.999952i \(-0.496868\pi\)
0.00984022 + 0.999952i \(0.496868\pi\)
\(74\) 6.84027 0.795165
\(75\) 0 0
\(76\) 6.27006 0.719225
\(77\) −7.33497 −0.835898
\(78\) 0 0
\(79\) 4.46545 0.502402 0.251201 0.967935i \(-0.419174\pi\)
0.251201 + 0.967935i \(0.419174\pi\)
\(80\) −3.79108 −0.423855
\(81\) 0 0
\(82\) 7.17153 0.791964
\(83\) 17.1161 1.87873 0.939367 0.342913i \(-0.111414\pi\)
0.939367 + 0.342913i \(0.111414\pi\)
\(84\) 0 0
\(85\) 26.7687 2.90348
\(86\) −8.20919 −0.885219
\(87\) 0 0
\(88\) −3.58410 −0.382067
\(89\) −8.00626 −0.848662 −0.424331 0.905507i \(-0.639491\pi\)
−0.424331 + 0.905507i \(0.639491\pi\)
\(90\) 0 0
\(91\) 3.44439 0.361070
\(92\) −5.91836 −0.617032
\(93\) 0 0
\(94\) 4.20034 0.433232
\(95\) −23.7703 −2.43878
\(96\) 0 0
\(97\) −17.4161 −1.76834 −0.884171 0.467164i \(-0.845276\pi\)
−0.884171 + 0.467164i \(0.845276\pi\)
\(98\) 2.81172 0.284026
\(99\) 0 0
\(100\) 9.37227 0.937227
\(101\) −6.54042 −0.650796 −0.325398 0.945577i \(-0.605498\pi\)
−0.325398 + 0.945577i \(0.605498\pi\)
\(102\) 0 0
\(103\) −2.14277 −0.211134 −0.105567 0.994412i \(-0.533666\pi\)
−0.105567 + 0.994412i \(0.533666\pi\)
\(104\) 1.68304 0.165036
\(105\) 0 0
\(106\) 2.24115 0.217679
\(107\) 3.51417 0.339728 0.169864 0.985468i \(-0.445667\pi\)
0.169864 + 0.985468i \(0.445667\pi\)
\(108\) 0 0
\(109\) 1.51709 0.145311 0.0726554 0.997357i \(-0.476853\pi\)
0.0726554 + 0.997357i \(0.476853\pi\)
\(110\) 13.5876 1.29553
\(111\) 0 0
\(112\) −2.04653 −0.193379
\(113\) −7.71445 −0.725714 −0.362857 0.931845i \(-0.618199\pi\)
−0.362857 + 0.931845i \(0.618199\pi\)
\(114\) 0 0
\(115\) 22.4370 2.09226
\(116\) −1.71227 −0.158981
\(117\) 0 0
\(118\) −11.2120 −1.03215
\(119\) 14.4505 1.32468
\(120\) 0 0
\(121\) 1.84579 0.167799
\(122\) −2.28773 −0.207121
\(123\) 0 0
\(124\) −6.59661 −0.592393
\(125\) −16.5756 −1.48257
\(126\) 0 0
\(127\) 4.13695 0.367095 0.183548 0.983011i \(-0.441242\pi\)
0.183548 + 0.983011i \(0.441242\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) −6.38054 −0.559610
\(131\) 18.2131 1.59129 0.795644 0.605765i \(-0.207133\pi\)
0.795644 + 0.605765i \(0.207133\pi\)
\(132\) 0 0
\(133\) −12.8319 −1.11266
\(134\) 9.15716 0.791058
\(135\) 0 0
\(136\) 7.06098 0.605474
\(137\) −2.56030 −0.218741 −0.109370 0.994001i \(-0.534883\pi\)
−0.109370 + 0.994001i \(0.534883\pi\)
\(138\) 0 0
\(139\) 13.5289 1.14750 0.573752 0.819029i \(-0.305487\pi\)
0.573752 + 0.819029i \(0.305487\pi\)
\(140\) 7.75855 0.655717
\(141\) 0 0
\(142\) 10.1516 0.851899
\(143\) −6.03219 −0.504437
\(144\) 0 0
\(145\) 6.49136 0.539078
\(146\) −0.168150 −0.0139162
\(147\) 0 0
\(148\) −6.84027 −0.562267
\(149\) 16.9096 1.38529 0.692646 0.721278i \(-0.256445\pi\)
0.692646 + 0.721278i \(0.256445\pi\)
\(150\) 0 0
\(151\) 7.75657 0.631220 0.315610 0.948889i \(-0.397791\pi\)
0.315610 + 0.948889i \(0.397791\pi\)
\(152\) −6.27006 −0.508569
\(153\) 0 0
\(154\) 7.33497 0.591069
\(155\) 25.0083 2.00871
\(156\) 0 0
\(157\) 10.7828 0.860565 0.430283 0.902694i \(-0.358414\pi\)
0.430283 + 0.902694i \(0.358414\pi\)
\(158\) −4.46545 −0.355252
\(159\) 0 0
\(160\) 3.79108 0.299711
\(161\) 12.1121 0.954567
\(162\) 0 0
\(163\) 11.0330 0.864173 0.432087 0.901832i \(-0.357777\pi\)
0.432087 + 0.901832i \(0.357777\pi\)
\(164\) −7.17153 −0.560003
\(165\) 0 0
\(166\) −17.1161 −1.32847
\(167\) 24.3706 1.88585 0.942926 0.333002i \(-0.108062\pi\)
0.942926 + 0.333002i \(0.108062\pi\)
\(168\) 0 0
\(169\) −10.1674 −0.782106
\(170\) −26.7687 −2.05307
\(171\) 0 0
\(172\) 8.20919 0.625945
\(173\) 12.3663 0.940193 0.470096 0.882615i \(-0.344219\pi\)
0.470096 + 0.882615i \(0.344219\pi\)
\(174\) 0 0
\(175\) −19.1806 −1.44992
\(176\) 3.58410 0.270162
\(177\) 0 0
\(178\) 8.00626 0.600095
\(179\) 10.6717 0.797639 0.398819 0.917030i \(-0.369420\pi\)
0.398819 + 0.917030i \(0.369420\pi\)
\(180\) 0 0
\(181\) −4.07663 −0.303013 −0.151507 0.988456i \(-0.548412\pi\)
−0.151507 + 0.988456i \(0.548412\pi\)
\(182\) −3.44439 −0.255315
\(183\) 0 0
\(184\) 5.91836 0.436307
\(185\) 25.9320 1.90656
\(186\) 0 0
\(187\) −25.3073 −1.85065
\(188\) −4.20034 −0.306341
\(189\) 0 0
\(190\) 23.7703 1.72448
\(191\) 19.2883 1.39566 0.697828 0.716265i \(-0.254150\pi\)
0.697828 + 0.716265i \(0.254150\pi\)
\(192\) 0 0
\(193\) 7.82656 0.563368 0.281684 0.959507i \(-0.409107\pi\)
0.281684 + 0.959507i \(0.409107\pi\)
\(194\) 17.4161 1.25041
\(195\) 0 0
\(196\) −2.81172 −0.200837
\(197\) −17.9536 −1.27914 −0.639569 0.768734i \(-0.720887\pi\)
−0.639569 + 0.768734i \(0.720887\pi\)
\(198\) 0 0
\(199\) 5.34926 0.379199 0.189600 0.981862i \(-0.439281\pi\)
0.189600 + 0.981862i \(0.439281\pi\)
\(200\) −9.37227 −0.662719
\(201\) 0 0
\(202\) 6.54042 0.460182
\(203\) 3.50422 0.245948
\(204\) 0 0
\(205\) 27.1878 1.89888
\(206\) 2.14277 0.149294
\(207\) 0 0
\(208\) −1.68304 −0.116698
\(209\) 22.4725 1.55446
\(210\) 0 0
\(211\) −11.8871 −0.818344 −0.409172 0.912457i \(-0.634182\pi\)
−0.409172 + 0.912457i \(0.634182\pi\)
\(212\) −2.24115 −0.153923
\(213\) 0 0
\(214\) −3.51417 −0.240224
\(215\) −31.1217 −2.12248
\(216\) 0 0
\(217\) 13.5002 0.916450
\(218\) −1.51709 −0.102750
\(219\) 0 0
\(220\) −13.5876 −0.916076
\(221\) 11.8839 0.799399
\(222\) 0 0
\(223\) −1.00000 −0.0669650
\(224\) 2.04653 0.136740
\(225\) 0 0
\(226\) 7.71445 0.513157
\(227\) −6.81249 −0.452161 −0.226080 0.974109i \(-0.572591\pi\)
−0.226080 + 0.974109i \(0.572591\pi\)
\(228\) 0 0
\(229\) −17.2778 −1.14175 −0.570874 0.821037i \(-0.693396\pi\)
−0.570874 + 0.821037i \(0.693396\pi\)
\(230\) −22.4370 −1.47945
\(231\) 0 0
\(232\) 1.71227 0.112416
\(233\) 25.8848 1.69577 0.847886 0.530179i \(-0.177875\pi\)
0.847886 + 0.530179i \(0.177875\pi\)
\(234\) 0 0
\(235\) 15.9238 1.03875
\(236\) 11.2120 0.729841
\(237\) 0 0
\(238\) −14.4505 −0.936688
\(239\) 26.1645 1.69244 0.846219 0.532835i \(-0.178873\pi\)
0.846219 + 0.532835i \(0.178873\pi\)
\(240\) 0 0
\(241\) 9.73250 0.626926 0.313463 0.949600i \(-0.398511\pi\)
0.313463 + 0.949600i \(0.398511\pi\)
\(242\) −1.84579 −0.118652
\(243\) 0 0
\(244\) 2.28773 0.146457
\(245\) 10.6594 0.681006
\(246\) 0 0
\(247\) −10.5528 −0.671456
\(248\) 6.59661 0.418885
\(249\) 0 0
\(250\) 16.5756 1.04833
\(251\) −5.46503 −0.344950 −0.172475 0.985014i \(-0.555176\pi\)
−0.172475 + 0.985014i \(0.555176\pi\)
\(252\) 0 0
\(253\) −21.2120 −1.33359
\(254\) −4.13695 −0.259576
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 0.0155642 0.000970868 0 0.000485434 1.00000i \(-0.499845\pi\)
0.000485434 1.00000i \(0.499845\pi\)
\(258\) 0 0
\(259\) 13.9988 0.869844
\(260\) 6.38054 0.395704
\(261\) 0 0
\(262\) −18.2131 −1.12521
\(263\) −21.7779 −1.34288 −0.671442 0.741057i \(-0.734325\pi\)
−0.671442 + 0.741057i \(0.734325\pi\)
\(264\) 0 0
\(265\) 8.49636 0.521927
\(266\) 12.8319 0.786772
\(267\) 0 0
\(268\) −9.15716 −0.559362
\(269\) −19.9425 −1.21592 −0.607959 0.793969i \(-0.708011\pi\)
−0.607959 + 0.793969i \(0.708011\pi\)
\(270\) 0 0
\(271\) −15.6300 −0.949452 −0.474726 0.880134i \(-0.657453\pi\)
−0.474726 + 0.880134i \(0.657453\pi\)
\(272\) −7.06098 −0.428135
\(273\) 0 0
\(274\) 2.56030 0.154673
\(275\) 33.5912 2.02562
\(276\) 0 0
\(277\) −26.1815 −1.57309 −0.786547 0.617531i \(-0.788133\pi\)
−0.786547 + 0.617531i \(0.788133\pi\)
\(278\) −13.5289 −0.811407
\(279\) 0 0
\(280\) −7.75855 −0.463662
\(281\) 32.8035 1.95689 0.978446 0.206505i \(-0.0662089\pi\)
0.978446 + 0.206505i \(0.0662089\pi\)
\(282\) 0 0
\(283\) 10.8724 0.646294 0.323147 0.946349i \(-0.395259\pi\)
0.323147 + 0.946349i \(0.395259\pi\)
\(284\) −10.1516 −0.602384
\(285\) 0 0
\(286\) 6.03219 0.356691
\(287\) 14.6768 0.866342
\(288\) 0 0
\(289\) 32.8575 1.93279
\(290\) −6.49136 −0.381186
\(291\) 0 0
\(292\) 0.168150 0.00984022
\(293\) 20.3692 1.18998 0.594990 0.803733i \(-0.297156\pi\)
0.594990 + 0.803733i \(0.297156\pi\)
\(294\) 0 0
\(295\) −42.5057 −2.47478
\(296\) 6.84027 0.397583
\(297\) 0 0
\(298\) −16.9096 −0.979549
\(299\) 9.96084 0.576050
\(300\) 0 0
\(301\) −16.8003 −0.968356
\(302\) −7.75657 −0.446340
\(303\) 0 0
\(304\) 6.27006 0.359612
\(305\) −8.67295 −0.496612
\(306\) 0 0
\(307\) 18.7120 1.06795 0.533975 0.845500i \(-0.320698\pi\)
0.533975 + 0.845500i \(0.320698\pi\)
\(308\) −7.33497 −0.417949
\(309\) 0 0
\(310\) −25.0083 −1.42037
\(311\) −0.0834666 −0.00473296 −0.00236648 0.999997i \(-0.500753\pi\)
−0.00236648 + 0.999997i \(0.500753\pi\)
\(312\) 0 0
\(313\) −22.4273 −1.26766 −0.633832 0.773471i \(-0.718519\pi\)
−0.633832 + 0.773471i \(0.718519\pi\)
\(314\) −10.7828 −0.608511
\(315\) 0 0
\(316\) 4.46545 0.251201
\(317\) 6.63887 0.372876 0.186438 0.982467i \(-0.440306\pi\)
0.186438 + 0.982467i \(0.440306\pi\)
\(318\) 0 0
\(319\) −6.13696 −0.343604
\(320\) −3.79108 −0.211928
\(321\) 0 0
\(322\) −12.1121 −0.674981
\(323\) −44.2728 −2.46340
\(324\) 0 0
\(325\) −15.7739 −0.874979
\(326\) −11.0330 −0.611063
\(327\) 0 0
\(328\) 7.17153 0.395982
\(329\) 8.59612 0.473919
\(330\) 0 0
\(331\) −11.4184 −0.627614 −0.313807 0.949487i \(-0.601605\pi\)
−0.313807 + 0.949487i \(0.601605\pi\)
\(332\) 17.1161 0.939367
\(333\) 0 0
\(334\) −24.3706 −1.33350
\(335\) 34.7155 1.89671
\(336\) 0 0
\(337\) −2.45042 −0.133483 −0.0667414 0.997770i \(-0.521260\pi\)
−0.0667414 + 0.997770i \(0.521260\pi\)
\(338\) 10.1674 0.553032
\(339\) 0 0
\(340\) 26.7687 1.45174
\(341\) −23.6429 −1.28034
\(342\) 0 0
\(343\) 20.0800 1.08422
\(344\) −8.20919 −0.442610
\(345\) 0 0
\(346\) −12.3663 −0.664817
\(347\) −23.4542 −1.25909 −0.629543 0.776965i \(-0.716758\pi\)
−0.629543 + 0.776965i \(0.716758\pi\)
\(348\) 0 0
\(349\) −11.6132 −0.621642 −0.310821 0.950469i \(-0.600604\pi\)
−0.310821 + 0.950469i \(0.600604\pi\)
\(350\) 19.1806 1.02525
\(351\) 0 0
\(352\) −3.58410 −0.191033
\(353\) −29.0016 −1.54360 −0.771800 0.635866i \(-0.780643\pi\)
−0.771800 + 0.635866i \(0.780643\pi\)
\(354\) 0 0
\(355\) 38.4853 2.04259
\(356\) −8.00626 −0.424331
\(357\) 0 0
\(358\) −10.6717 −0.564016
\(359\) 5.42796 0.286477 0.143238 0.989688i \(-0.454248\pi\)
0.143238 + 0.989688i \(0.454248\pi\)
\(360\) 0 0
\(361\) 20.3136 1.06914
\(362\) 4.07663 0.214263
\(363\) 0 0
\(364\) 3.44439 0.180535
\(365\) −0.637468 −0.0333666
\(366\) 0 0
\(367\) 34.5582 1.80392 0.901961 0.431817i \(-0.142127\pi\)
0.901961 + 0.431817i \(0.142127\pi\)
\(368\) −5.91836 −0.308516
\(369\) 0 0
\(370\) −25.9320 −1.34814
\(371\) 4.58657 0.238123
\(372\) 0 0
\(373\) 15.9829 0.827563 0.413781 0.910376i \(-0.364208\pi\)
0.413781 + 0.910376i \(0.364208\pi\)
\(374\) 25.3073 1.30861
\(375\) 0 0
\(376\) 4.20034 0.216616
\(377\) 2.88182 0.148421
\(378\) 0 0
\(379\) 3.69996 0.190054 0.0950272 0.995475i \(-0.469706\pi\)
0.0950272 + 0.995475i \(0.469706\pi\)
\(380\) −23.7703 −1.21939
\(381\) 0 0
\(382\) −19.2883 −0.986878
\(383\) −5.53886 −0.283023 −0.141511 0.989937i \(-0.545196\pi\)
−0.141511 + 0.989937i \(0.545196\pi\)
\(384\) 0 0
\(385\) 27.8074 1.41720
\(386\) −7.82656 −0.398361
\(387\) 0 0
\(388\) −17.4161 −0.884171
\(389\) −10.0091 −0.507480 −0.253740 0.967273i \(-0.581661\pi\)
−0.253740 + 0.967273i \(0.581661\pi\)
\(390\) 0 0
\(391\) 41.7894 2.11338
\(392\) 2.81172 0.142013
\(393\) 0 0
\(394\) 17.9536 0.904487
\(395\) −16.9289 −0.851783
\(396\) 0 0
\(397\) −5.11076 −0.256501 −0.128251 0.991742i \(-0.540936\pi\)
−0.128251 + 0.991742i \(0.540936\pi\)
\(398\) −5.34926 −0.268134
\(399\) 0 0
\(400\) 9.37227 0.468613
\(401\) 10.8760 0.543122 0.271561 0.962421i \(-0.412460\pi\)
0.271561 + 0.962421i \(0.412460\pi\)
\(402\) 0 0
\(403\) 11.1024 0.553048
\(404\) −6.54042 −0.325398
\(405\) 0 0
\(406\) −3.50422 −0.173911
\(407\) −24.5162 −1.21522
\(408\) 0 0
\(409\) −35.1322 −1.73718 −0.868588 0.495535i \(-0.834972\pi\)
−0.868588 + 0.495535i \(0.834972\pi\)
\(410\) −27.1878 −1.34271
\(411\) 0 0
\(412\) −2.14277 −0.105567
\(413\) −22.9457 −1.12909
\(414\) 0 0
\(415\) −64.8884 −3.18525
\(416\) 1.68304 0.0825178
\(417\) 0 0
\(418\) −22.4725 −1.09917
\(419\) −28.4444 −1.38960 −0.694800 0.719203i \(-0.744507\pi\)
−0.694800 + 0.719203i \(0.744507\pi\)
\(420\) 0 0
\(421\) 29.6070 1.44296 0.721478 0.692437i \(-0.243463\pi\)
0.721478 + 0.692437i \(0.243463\pi\)
\(422\) 11.8871 0.578656
\(423\) 0 0
\(424\) 2.24115 0.108840
\(425\) −66.1774 −3.21008
\(426\) 0 0
\(427\) −4.68190 −0.226573
\(428\) 3.51417 0.169864
\(429\) 0 0
\(430\) 31.1217 1.50082
\(431\) 24.5257 1.18136 0.590682 0.806905i \(-0.298859\pi\)
0.590682 + 0.806905i \(0.298859\pi\)
\(432\) 0 0
\(433\) −4.31750 −0.207486 −0.103743 0.994604i \(-0.533082\pi\)
−0.103743 + 0.994604i \(0.533082\pi\)
\(434\) −13.5002 −0.648028
\(435\) 0 0
\(436\) 1.51709 0.0726554
\(437\) −37.1084 −1.77514
\(438\) 0 0
\(439\) 10.1308 0.483517 0.241759 0.970336i \(-0.422276\pi\)
0.241759 + 0.970336i \(0.422276\pi\)
\(440\) 13.5876 0.647764
\(441\) 0 0
\(442\) −11.8839 −0.565260
\(443\) 38.9310 1.84967 0.924834 0.380370i \(-0.124203\pi\)
0.924834 + 0.380370i \(0.124203\pi\)
\(444\) 0 0
\(445\) 30.3524 1.43884
\(446\) 1.00000 0.0473514
\(447\) 0 0
\(448\) −2.04653 −0.0966894
\(449\) 29.2856 1.38207 0.691037 0.722820i \(-0.257154\pi\)
0.691037 + 0.722820i \(0.257154\pi\)
\(450\) 0 0
\(451\) −25.7035 −1.21033
\(452\) −7.71445 −0.362857
\(453\) 0 0
\(454\) 6.81249 0.319726
\(455\) −13.0580 −0.612166
\(456\) 0 0
\(457\) 10.9698 0.513148 0.256574 0.966525i \(-0.417406\pi\)
0.256574 + 0.966525i \(0.417406\pi\)
\(458\) 17.2778 0.807338
\(459\) 0 0
\(460\) 22.4370 1.04613
\(461\) 19.4524 0.905989 0.452994 0.891513i \(-0.350356\pi\)
0.452994 + 0.891513i \(0.350356\pi\)
\(462\) 0 0
\(463\) 23.6650 1.09980 0.549902 0.835229i \(-0.314665\pi\)
0.549902 + 0.835229i \(0.314665\pi\)
\(464\) −1.71227 −0.0794903
\(465\) 0 0
\(466\) −25.8848 −1.19909
\(467\) 7.36165 0.340656 0.170328 0.985387i \(-0.445517\pi\)
0.170328 + 0.985387i \(0.445517\pi\)
\(468\) 0 0
\(469\) 18.7404 0.865351
\(470\) −15.9238 −0.734510
\(471\) 0 0
\(472\) −11.2120 −0.516075
\(473\) 29.4226 1.35285
\(474\) 0 0
\(475\) 58.7646 2.69631
\(476\) 14.4505 0.662338
\(477\) 0 0
\(478\) −26.1645 −1.19673
\(479\) −13.0356 −0.595611 −0.297805 0.954627i \(-0.596255\pi\)
−0.297805 + 0.954627i \(0.596255\pi\)
\(480\) 0 0
\(481\) 11.5124 0.524922
\(482\) −9.73250 −0.443303
\(483\) 0 0
\(484\) 1.84579 0.0838996
\(485\) 66.0259 2.99808
\(486\) 0 0
\(487\) 26.1666 1.18572 0.592860 0.805305i \(-0.297999\pi\)
0.592860 + 0.805305i \(0.297999\pi\)
\(488\) −2.28773 −0.103561
\(489\) 0 0
\(490\) −10.6594 −0.481544
\(491\) 14.1175 0.637112 0.318556 0.947904i \(-0.396802\pi\)
0.318556 + 0.947904i \(0.396802\pi\)
\(492\) 0 0
\(493\) 12.0903 0.544521
\(494\) 10.5528 0.474791
\(495\) 0 0
\(496\) −6.59661 −0.296196
\(497\) 20.7754 0.931906
\(498\) 0 0
\(499\) −16.8191 −0.752929 −0.376464 0.926431i \(-0.622860\pi\)
−0.376464 + 0.926431i \(0.622860\pi\)
\(500\) −16.5756 −0.741283
\(501\) 0 0
\(502\) 5.46503 0.243916
\(503\) −35.2287 −1.57077 −0.785385 0.619008i \(-0.787535\pi\)
−0.785385 + 0.619008i \(0.787535\pi\)
\(504\) 0 0
\(505\) 24.7952 1.10337
\(506\) 21.2120 0.942989
\(507\) 0 0
\(508\) 4.13695 0.183548
\(509\) 19.5271 0.865522 0.432761 0.901509i \(-0.357539\pi\)
0.432761 + 0.901509i \(0.357539\pi\)
\(510\) 0 0
\(511\) −0.344123 −0.0152231
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −0.0155642 −0.000686507 0
\(515\) 8.12342 0.357961
\(516\) 0 0
\(517\) −15.0544 −0.662094
\(518\) −13.9988 −0.615073
\(519\) 0 0
\(520\) −6.38054 −0.279805
\(521\) −5.15078 −0.225660 −0.112830 0.993614i \(-0.535991\pi\)
−0.112830 + 0.993614i \(0.535991\pi\)
\(522\) 0 0
\(523\) −31.9064 −1.39517 −0.697585 0.716502i \(-0.745742\pi\)
−0.697585 + 0.716502i \(0.745742\pi\)
\(524\) 18.2131 0.795644
\(525\) 0 0
\(526\) 21.7779 0.949563
\(527\) 46.5786 2.02899
\(528\) 0 0
\(529\) 12.0270 0.522912
\(530\) −8.49636 −0.369058
\(531\) 0 0
\(532\) −12.8319 −0.556332
\(533\) 12.0700 0.522809
\(534\) 0 0
\(535\) −13.3225 −0.575981
\(536\) 9.15716 0.395529
\(537\) 0 0
\(538\) 19.9425 0.859784
\(539\) −10.0775 −0.434068
\(540\) 0 0
\(541\) 34.2955 1.47448 0.737239 0.675632i \(-0.236129\pi\)
0.737239 + 0.675632i \(0.236129\pi\)
\(542\) 15.6300 0.671364
\(543\) 0 0
\(544\) 7.06098 0.302737
\(545\) −5.75140 −0.246363
\(546\) 0 0
\(547\) 23.1609 0.990288 0.495144 0.868811i \(-0.335115\pi\)
0.495144 + 0.868811i \(0.335115\pi\)
\(548\) −2.56030 −0.109370
\(549\) 0 0
\(550\) −33.5912 −1.43233
\(551\) −10.7360 −0.457371
\(552\) 0 0
\(553\) −9.13867 −0.388616
\(554\) 26.1815 1.11234
\(555\) 0 0
\(556\) 13.5289 0.573752
\(557\) −25.1057 −1.06376 −0.531881 0.846819i \(-0.678515\pi\)
−0.531881 + 0.846819i \(0.678515\pi\)
\(558\) 0 0
\(559\) −13.8164 −0.584371
\(560\) 7.75855 0.327859
\(561\) 0 0
\(562\) −32.8035 −1.38373
\(563\) −12.9346 −0.545130 −0.272565 0.962137i \(-0.587872\pi\)
−0.272565 + 0.962137i \(0.587872\pi\)
\(564\) 0 0
\(565\) 29.2461 1.23039
\(566\) −10.8724 −0.456999
\(567\) 0 0
\(568\) 10.1516 0.425950
\(569\) 24.2386 1.01613 0.508067 0.861318i \(-0.330360\pi\)
0.508067 + 0.861318i \(0.330360\pi\)
\(570\) 0 0
\(571\) −27.1667 −1.13689 −0.568446 0.822720i \(-0.692455\pi\)
−0.568446 + 0.822720i \(0.692455\pi\)
\(572\) −6.03219 −0.252218
\(573\) 0 0
\(574\) −14.6768 −0.612596
\(575\) −55.4684 −2.31319
\(576\) 0 0
\(577\) 12.3175 0.512786 0.256393 0.966573i \(-0.417466\pi\)
0.256393 + 0.966573i \(0.417466\pi\)
\(578\) −32.8575 −1.36669
\(579\) 0 0
\(580\) 6.49136 0.269539
\(581\) −35.0286 −1.45323
\(582\) 0 0
\(583\) −8.03250 −0.332672
\(584\) −0.168150 −0.00695808
\(585\) 0 0
\(586\) −20.3692 −0.841443
\(587\) −30.0582 −1.24064 −0.620318 0.784350i \(-0.712997\pi\)
−0.620318 + 0.784350i \(0.712997\pi\)
\(588\) 0 0
\(589\) −41.3611 −1.70425
\(590\) 42.5057 1.74993
\(591\) 0 0
\(592\) −6.84027 −0.281133
\(593\) −21.2323 −0.871907 −0.435953 0.899969i \(-0.643589\pi\)
−0.435953 + 0.899969i \(0.643589\pi\)
\(594\) 0 0
\(595\) −54.7830 −2.24588
\(596\) 16.9096 0.692646
\(597\) 0 0
\(598\) −9.96084 −0.407329
\(599\) 22.3975 0.915136 0.457568 0.889175i \(-0.348721\pi\)
0.457568 + 0.889175i \(0.348721\pi\)
\(600\) 0 0
\(601\) −13.0705 −0.533156 −0.266578 0.963813i \(-0.585893\pi\)
−0.266578 + 0.963813i \(0.585893\pi\)
\(602\) 16.8003 0.684731
\(603\) 0 0
\(604\) 7.75657 0.315610
\(605\) −6.99753 −0.284490
\(606\) 0 0
\(607\) 24.0034 0.974270 0.487135 0.873327i \(-0.338042\pi\)
0.487135 + 0.873327i \(0.338042\pi\)
\(608\) −6.27006 −0.254284
\(609\) 0 0
\(610\) 8.67295 0.351158
\(611\) 7.06934 0.285995
\(612\) 0 0
\(613\) −24.2075 −0.977731 −0.488866 0.872359i \(-0.662589\pi\)
−0.488866 + 0.872359i \(0.662589\pi\)
\(614\) −18.7120 −0.755155
\(615\) 0 0
\(616\) 7.33497 0.295534
\(617\) 9.48916 0.382019 0.191010 0.981588i \(-0.438824\pi\)
0.191010 + 0.981588i \(0.438824\pi\)
\(618\) 0 0
\(619\) 15.2784 0.614093 0.307046 0.951695i \(-0.400659\pi\)
0.307046 + 0.951695i \(0.400659\pi\)
\(620\) 25.0083 1.00436
\(621\) 0 0
\(622\) 0.0834666 0.00334670
\(623\) 16.3851 0.656453
\(624\) 0 0
\(625\) 15.9780 0.639121
\(626\) 22.4273 0.896374
\(627\) 0 0
\(628\) 10.7828 0.430283
\(629\) 48.2990 1.92581
\(630\) 0 0
\(631\) −34.4001 −1.36945 −0.684724 0.728803i \(-0.740077\pi\)
−0.684724 + 0.728803i \(0.740077\pi\)
\(632\) −4.46545 −0.177626
\(633\) 0 0
\(634\) −6.63887 −0.263663
\(635\) −15.6835 −0.622381
\(636\) 0 0
\(637\) 4.73223 0.187498
\(638\) 6.13696 0.242965
\(639\) 0 0
\(640\) 3.79108 0.149855
\(641\) −14.9350 −0.589897 −0.294948 0.955513i \(-0.595302\pi\)
−0.294948 + 0.955513i \(0.595302\pi\)
\(642\) 0 0
\(643\) 8.53019 0.336398 0.168199 0.985753i \(-0.446205\pi\)
0.168199 + 0.985753i \(0.446205\pi\)
\(644\) 12.1121 0.477283
\(645\) 0 0
\(646\) 44.2728 1.74189
\(647\) 7.45426 0.293057 0.146529 0.989206i \(-0.453190\pi\)
0.146529 + 0.989206i \(0.453190\pi\)
\(648\) 0 0
\(649\) 40.1851 1.57740
\(650\) 15.7739 0.618703
\(651\) 0 0
\(652\) 11.0330 0.432087
\(653\) −27.5619 −1.07858 −0.539291 0.842120i \(-0.681308\pi\)
−0.539291 + 0.842120i \(0.681308\pi\)
\(654\) 0 0
\(655\) −69.0473 −2.69790
\(656\) −7.17153 −0.280001
\(657\) 0 0
\(658\) −8.59612 −0.335112
\(659\) 38.8035 1.51157 0.755786 0.654819i \(-0.227255\pi\)
0.755786 + 0.654819i \(0.227255\pi\)
\(660\) 0 0
\(661\) −3.27956 −0.127560 −0.0637800 0.997964i \(-0.520316\pi\)
−0.0637800 + 0.997964i \(0.520316\pi\)
\(662\) 11.4184 0.443790
\(663\) 0 0
\(664\) −17.1161 −0.664233
\(665\) 48.6466 1.88643
\(666\) 0 0
\(667\) 10.1338 0.392384
\(668\) 24.3706 0.942926
\(669\) 0 0
\(670\) −34.7155 −1.34118
\(671\) 8.19945 0.316536
\(672\) 0 0
\(673\) 24.6978 0.952030 0.476015 0.879437i \(-0.342081\pi\)
0.476015 + 0.879437i \(0.342081\pi\)
\(674\) 2.45042 0.0943866
\(675\) 0 0
\(676\) −10.1674 −0.391053
\(677\) 25.6722 0.986664 0.493332 0.869841i \(-0.335779\pi\)
0.493332 + 0.869841i \(0.335779\pi\)
\(678\) 0 0
\(679\) 35.6427 1.36784
\(680\) −26.7687 −1.02653
\(681\) 0 0
\(682\) 23.6429 0.905334
\(683\) 2.96766 0.113554 0.0567772 0.998387i \(-0.481918\pi\)
0.0567772 + 0.998387i \(0.481918\pi\)
\(684\) 0 0
\(685\) 9.70629 0.370858
\(686\) −20.0800 −0.766657
\(687\) 0 0
\(688\) 8.20919 0.312972
\(689\) 3.77194 0.143700
\(690\) 0 0
\(691\) −14.4367 −0.549198 −0.274599 0.961559i \(-0.588545\pi\)
−0.274599 + 0.961559i \(0.588545\pi\)
\(692\) 12.3663 0.470096
\(693\) 0 0
\(694\) 23.4542 0.890309
\(695\) −51.2890 −1.94550
\(696\) 0 0
\(697\) 50.6381 1.91805
\(698\) 11.6132 0.439567
\(699\) 0 0
\(700\) −19.1806 −0.724959
\(701\) 10.1930 0.384986 0.192493 0.981298i \(-0.438343\pi\)
0.192493 + 0.981298i \(0.438343\pi\)
\(702\) 0 0
\(703\) −42.8889 −1.61758
\(704\) 3.58410 0.135081
\(705\) 0 0
\(706\) 29.0016 1.09149
\(707\) 13.3852 0.503400
\(708\) 0 0
\(709\) −1.53923 −0.0578069 −0.0289034 0.999582i \(-0.509202\pi\)
−0.0289034 + 0.999582i \(0.509202\pi\)
\(710\) −38.4853 −1.44433
\(711\) 0 0
\(712\) 8.00626 0.300047
\(713\) 39.0411 1.46210
\(714\) 0 0
\(715\) 22.8685 0.855233
\(716\) 10.6717 0.398819
\(717\) 0 0
\(718\) −5.42796 −0.202570
\(719\) −25.2733 −0.942535 −0.471267 0.881990i \(-0.656203\pi\)
−0.471267 + 0.881990i \(0.656203\pi\)
\(720\) 0 0
\(721\) 4.38525 0.163315
\(722\) −20.3136 −0.755994
\(723\) 0 0
\(724\) −4.07663 −0.151507
\(725\) −16.0479 −0.596003
\(726\) 0 0
\(727\) 35.8379 1.32915 0.664576 0.747220i \(-0.268612\pi\)
0.664576 + 0.747220i \(0.268612\pi\)
\(728\) −3.44439 −0.127658
\(729\) 0 0
\(730\) 0.637468 0.0235938
\(731\) −57.9649 −2.14391
\(732\) 0 0
\(733\) −50.5067 −1.86551 −0.932754 0.360514i \(-0.882601\pi\)
−0.932754 + 0.360514i \(0.882601\pi\)
\(734\) −34.5582 −1.27557
\(735\) 0 0
\(736\) 5.91836 0.218154
\(737\) −32.8202 −1.20895
\(738\) 0 0
\(739\) 29.7084 1.09284 0.546420 0.837511i \(-0.315990\pi\)
0.546420 + 0.837511i \(0.315990\pi\)
\(740\) 25.9320 0.953279
\(741\) 0 0
\(742\) −4.58657 −0.168378
\(743\) −20.6363 −0.757071 −0.378535 0.925587i \(-0.623572\pi\)
−0.378535 + 0.925587i \(0.623572\pi\)
\(744\) 0 0
\(745\) −64.1057 −2.34865
\(746\) −15.9829 −0.585175
\(747\) 0 0
\(748\) −25.3073 −0.925326
\(749\) −7.19185 −0.262784
\(750\) 0 0
\(751\) 15.8799 0.579466 0.289733 0.957108i \(-0.406434\pi\)
0.289733 + 0.957108i \(0.406434\pi\)
\(752\) −4.20034 −0.153171
\(753\) 0 0
\(754\) −2.88182 −0.104950
\(755\) −29.4057 −1.07018
\(756\) 0 0
\(757\) 46.4774 1.68925 0.844624 0.535359i \(-0.179824\pi\)
0.844624 + 0.535359i \(0.179824\pi\)
\(758\) −3.69996 −0.134389
\(759\) 0 0
\(760\) 23.7703 0.862238
\(761\) −27.1864 −0.985507 −0.492754 0.870169i \(-0.664010\pi\)
−0.492754 + 0.870169i \(0.664010\pi\)
\(762\) 0 0
\(763\) −3.10477 −0.112400
\(764\) 19.2883 0.697828
\(765\) 0 0
\(766\) 5.53886 0.200127
\(767\) −18.8703 −0.681367
\(768\) 0 0
\(769\) −32.9323 −1.18757 −0.593784 0.804625i \(-0.702367\pi\)
−0.593784 + 0.804625i \(0.702367\pi\)
\(770\) −27.8074 −1.00211
\(771\) 0 0
\(772\) 7.82656 0.281684
\(773\) 45.5182 1.63718 0.818588 0.574382i \(-0.194758\pi\)
0.818588 + 0.574382i \(0.194758\pi\)
\(774\) 0 0
\(775\) −61.8252 −2.22083
\(776\) 17.4161 0.625203
\(777\) 0 0
\(778\) 10.0091 0.358842
\(779\) −44.9659 −1.61107
\(780\) 0 0
\(781\) −36.3842 −1.30193
\(782\) −41.7894 −1.49439
\(783\) 0 0
\(784\) −2.81172 −0.100418
\(785\) −40.8786 −1.45902
\(786\) 0 0
\(787\) −13.1542 −0.468898 −0.234449 0.972128i \(-0.575329\pi\)
−0.234449 + 0.972128i \(0.575329\pi\)
\(788\) −17.9536 −0.639569
\(789\) 0 0
\(790\) 16.9289 0.602302
\(791\) 15.7878 0.561351
\(792\) 0 0
\(793\) −3.85034 −0.136729
\(794\) 5.11076 0.181374
\(795\) 0 0
\(796\) 5.34926 0.189600
\(797\) 4.81033 0.170391 0.0851953 0.996364i \(-0.472849\pi\)
0.0851953 + 0.996364i \(0.472849\pi\)
\(798\) 0 0
\(799\) 29.6585 1.04924
\(800\) −9.37227 −0.331360
\(801\) 0 0
\(802\) −10.8760 −0.384045
\(803\) 0.602666 0.0212676
\(804\) 0 0
\(805\) −45.9179 −1.61839
\(806\) −11.1024 −0.391064
\(807\) 0 0
\(808\) 6.54042 0.230091
\(809\) −31.7294 −1.11554 −0.557772 0.829994i \(-0.688344\pi\)
−0.557772 + 0.829994i \(0.688344\pi\)
\(810\) 0 0
\(811\) −45.5222 −1.59850 −0.799251 0.600997i \(-0.794770\pi\)
−0.799251 + 0.600997i \(0.794770\pi\)
\(812\) 3.50422 0.122974
\(813\) 0 0
\(814\) 24.5162 0.859293
\(815\) −41.8270 −1.46514
\(816\) 0 0
\(817\) 51.4721 1.80078
\(818\) 35.1322 1.22837
\(819\) 0 0
\(820\) 27.1878 0.949441
\(821\) 5.66307 0.197643 0.0988213 0.995105i \(-0.468493\pi\)
0.0988213 + 0.995105i \(0.468493\pi\)
\(822\) 0 0
\(823\) −48.9183 −1.70519 −0.852593 0.522576i \(-0.824971\pi\)
−0.852593 + 0.522576i \(0.824971\pi\)
\(824\) 2.14277 0.0746471
\(825\) 0 0
\(826\) 22.9457 0.798385
\(827\) −46.4492 −1.61520 −0.807599 0.589733i \(-0.799233\pi\)
−0.807599 + 0.589733i \(0.799233\pi\)
\(828\) 0 0
\(829\) −35.9868 −1.24987 −0.624936 0.780676i \(-0.714875\pi\)
−0.624936 + 0.780676i \(0.714875\pi\)
\(830\) 64.8884 2.25231
\(831\) 0 0
\(832\) −1.68304 −0.0583489
\(833\) 19.8535 0.687883
\(834\) 0 0
\(835\) −92.3908 −3.19731
\(836\) 22.4725 0.777229
\(837\) 0 0
\(838\) 28.4444 0.982595
\(839\) −29.6956 −1.02521 −0.512604 0.858625i \(-0.671319\pi\)
−0.512604 + 0.858625i \(0.671319\pi\)
\(840\) 0 0
\(841\) −26.0681 −0.898901
\(842\) −29.6070 −1.02032
\(843\) 0 0
\(844\) −11.8871 −0.409172
\(845\) 38.5453 1.32600
\(846\) 0 0
\(847\) −3.77746 −0.129795
\(848\) −2.24115 −0.0769613
\(849\) 0 0
\(850\) 66.1774 2.26987
\(851\) 40.4832 1.38775
\(852\) 0 0
\(853\) −16.7681 −0.574130 −0.287065 0.957911i \(-0.592680\pi\)
−0.287065 + 0.957911i \(0.592680\pi\)
\(854\) 4.68190 0.160211
\(855\) 0 0
\(856\) −3.51417 −0.120112
\(857\) 25.2913 0.863934 0.431967 0.901889i \(-0.357820\pi\)
0.431967 + 0.901889i \(0.357820\pi\)
\(858\) 0 0
\(859\) 39.6717 1.35358 0.676790 0.736176i \(-0.263370\pi\)
0.676790 + 0.736176i \(0.263370\pi\)
\(860\) −31.1217 −1.06124
\(861\) 0 0
\(862\) −24.5257 −0.835350
\(863\) −2.95874 −0.100717 −0.0503583 0.998731i \(-0.516036\pi\)
−0.0503583 + 0.998731i \(0.516036\pi\)
\(864\) 0 0
\(865\) −46.8816 −1.59402
\(866\) 4.31750 0.146715
\(867\) 0 0
\(868\) 13.5002 0.458225
\(869\) 16.0046 0.542920
\(870\) 0 0
\(871\) 15.4119 0.522211
\(872\) −1.51709 −0.0513751
\(873\) 0 0
\(874\) 37.1084 1.25521
\(875\) 33.9224 1.14679
\(876\) 0 0
\(877\) 47.0556 1.58896 0.794478 0.607293i \(-0.207745\pi\)
0.794478 + 0.607293i \(0.207745\pi\)
\(878\) −10.1308 −0.341899
\(879\) 0 0
\(880\) −13.5876 −0.458038
\(881\) −56.0650 −1.88888 −0.944439 0.328686i \(-0.893394\pi\)
−0.944439 + 0.328686i \(0.893394\pi\)
\(882\) 0 0
\(883\) 37.9775 1.27805 0.639023 0.769188i \(-0.279339\pi\)
0.639023 + 0.769188i \(0.279339\pi\)
\(884\) 11.8839 0.399700
\(885\) 0 0
\(886\) −38.9310 −1.30791
\(887\) −39.0844 −1.31233 −0.656163 0.754619i \(-0.727822\pi\)
−0.656163 + 0.754619i \(0.727822\pi\)
\(888\) 0 0
\(889\) −8.46640 −0.283954
\(890\) −30.3524 −1.01741
\(891\) 0 0
\(892\) −1.00000 −0.0334825
\(893\) −26.3364 −0.881313
\(894\) 0 0
\(895\) −40.4572 −1.35233
\(896\) 2.04653 0.0683698
\(897\) 0 0
\(898\) −29.2856 −0.977273
\(899\) 11.2952 0.376716
\(900\) 0 0
\(901\) 15.8247 0.527197
\(902\) 25.7035 0.855833
\(903\) 0 0
\(904\) 7.71445 0.256579
\(905\) 15.4548 0.513735
\(906\) 0 0
\(907\) −31.4930 −1.04571 −0.522854 0.852422i \(-0.675133\pi\)
−0.522854 + 0.852422i \(0.675133\pi\)
\(908\) −6.81249 −0.226080
\(909\) 0 0
\(910\) 13.0580 0.432867
\(911\) 27.7005 0.917759 0.458880 0.888498i \(-0.348251\pi\)
0.458880 + 0.888498i \(0.348251\pi\)
\(912\) 0 0
\(913\) 61.3458 2.03025
\(914\) −10.9698 −0.362850
\(915\) 0 0
\(916\) −17.2778 −0.570874
\(917\) −37.2737 −1.23089
\(918\) 0 0
\(919\) −23.5430 −0.776612 −0.388306 0.921531i \(-0.626940\pi\)
−0.388306 + 0.921531i \(0.626940\pi\)
\(920\) −22.4370 −0.739725
\(921\) 0 0
\(922\) −19.4524 −0.640631
\(923\) 17.0855 0.562375
\(924\) 0 0
\(925\) −64.1088 −2.10789
\(926\) −23.6650 −0.777679
\(927\) 0 0
\(928\) 1.71227 0.0562081
\(929\) −60.0063 −1.96874 −0.984372 0.176102i \(-0.943651\pi\)
−0.984372 + 0.176102i \(0.943651\pi\)
\(930\) 0 0
\(931\) −17.6296 −0.577788
\(932\) 25.8848 0.847886
\(933\) 0 0
\(934\) −7.36165 −0.240880
\(935\) 95.9419 3.13764
\(936\) 0 0
\(937\) 57.7590 1.88690 0.943452 0.331511i \(-0.107558\pi\)
0.943452 + 0.331511i \(0.107558\pi\)
\(938\) −18.7404 −0.611896
\(939\) 0 0
\(940\) 15.9238 0.519377
\(941\) −14.4905 −0.472378 −0.236189 0.971707i \(-0.575898\pi\)
−0.236189 + 0.971707i \(0.575898\pi\)
\(942\) 0 0
\(943\) 42.4437 1.38216
\(944\) 11.2120 0.364920
\(945\) 0 0
\(946\) −29.4226 −0.956610
\(947\) 49.5458 1.61002 0.805012 0.593259i \(-0.202159\pi\)
0.805012 + 0.593259i \(0.202159\pi\)
\(948\) 0 0
\(949\) −0.283003 −0.00918666
\(950\) −58.7646 −1.90658
\(951\) 0 0
\(952\) −14.4505 −0.468344
\(953\) −15.2950 −0.495452 −0.247726 0.968830i \(-0.579683\pi\)
−0.247726 + 0.968830i \(0.579683\pi\)
\(954\) 0 0
\(955\) −73.1236 −2.36622
\(956\) 26.1645 0.846219
\(957\) 0 0
\(958\) 13.0356 0.421161
\(959\) 5.23972 0.169200
\(960\) 0 0
\(961\) 12.5153 0.403718
\(962\) −11.5124 −0.371176
\(963\) 0 0
\(964\) 9.73250 0.313463
\(965\) −29.6711 −0.955146
\(966\) 0 0
\(967\) 30.2994 0.974364 0.487182 0.873300i \(-0.338025\pi\)
0.487182 + 0.873300i \(0.338025\pi\)
\(968\) −1.84579 −0.0593260
\(969\) 0 0
\(970\) −66.0259 −2.11997
\(971\) 33.9790 1.09044 0.545219 0.838294i \(-0.316446\pi\)
0.545219 + 0.838294i \(0.316446\pi\)
\(972\) 0 0
\(973\) −27.6872 −0.887612
\(974\) −26.1666 −0.838431
\(975\) 0 0
\(976\) 2.28773 0.0732284
\(977\) 5.13359 0.164238 0.0821191 0.996623i \(-0.473831\pi\)
0.0821191 + 0.996623i \(0.473831\pi\)
\(978\) 0 0
\(979\) −28.6953 −0.917105
\(980\) 10.6594 0.340503
\(981\) 0 0
\(982\) −14.1175 −0.450506
\(983\) 23.1353 0.737901 0.368950 0.929449i \(-0.379717\pi\)
0.368950 + 0.929449i \(0.379717\pi\)
\(984\) 0 0
\(985\) 68.0633 2.16868
\(986\) −12.0903 −0.385035
\(987\) 0 0
\(988\) −10.5528 −0.335728
\(989\) −48.5849 −1.54491
\(990\) 0 0
\(991\) 20.4476 0.649540 0.324770 0.945793i \(-0.394713\pi\)
0.324770 + 0.945793i \(0.394713\pi\)
\(992\) 6.59661 0.209443
\(993\) 0 0
\(994\) −20.7754 −0.658957
\(995\) −20.2795 −0.642902
\(996\) 0 0
\(997\) 16.5682 0.524721 0.262360 0.964970i \(-0.415499\pi\)
0.262360 + 0.964970i \(0.415499\pi\)
\(998\) 16.8191 0.532401
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 4014.2.a.v.1.1 7
3.2 odd 2 1338.2.a.j.1.7 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1338.2.a.j.1.7 7 3.2 odd 2
4014.2.a.v.1.1 7 1.1 even 1 trivial