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Properties

Label 5610.2.a.p.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)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +3.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +1.00000 q^{11} +1.00000 q^{12} -3.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} -1.00000 q^{18} -1.00000 q^{20} +3.00000 q^{21} -1.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.00000 q^{27} +3.00000 q^{28} -9.00000 q^{29} +1.00000 q^{30} +5.00000 q^{31} -1.00000 q^{32} +1.00000 q^{33} -1.00000 q^{34} -3.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} +1.00000 q^{40} +8.00000 q^{41} -3.00000 q^{42} +1.00000 q^{43} +1.00000 q^{44} -1.00000 q^{45} -1.00000 q^{46} +1.00000 q^{48} +2.00000 q^{49} -1.00000 q^{50} +1.00000 q^{51} -1.00000 q^{54} -1.00000 q^{55} -3.00000 q^{56} +9.00000 q^{58} +10.0000 q^{59} -1.00000 q^{60} +14.0000 q^{61} -5.00000 q^{62} +3.00000 q^{63} +1.00000 q^{64} -1.00000 q^{66} +1.00000 q^{68} +1.00000 q^{69} +3.00000 q^{70} -10.0000 q^{71} -1.00000 q^{72} -2.00000 q^{73} -2.00000 q^{74} +1.00000 q^{75} +3.00000 q^{77} -1.00000 q^{80} +1.00000 q^{81} -8.00000 q^{82} +3.00000 q^{84} -1.00000 q^{85} -1.00000 q^{86} -9.00000 q^{87} -1.00000 q^{88} -4.00000 q^{89} +1.00000 q^{90} +1.00000 q^{92} +5.00000 q^{93} -1.00000 q^{96} +9.00000 q^{97} -2.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −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 \(-0.308125\pi\)
0.566947 + 0.823754i \(0.308125\pi\)
\(8\) −1.00000 −0.353553
\(9\) 1.00000 0.333333
\(10\) 1.00000 0.316228
\(11\) 1.00000 0.301511
\(12\) 1.00000 0.288675
\(13\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) −3.00000 −0.801784
\(15\) −1.00000 −0.258199
\(16\) 1.00000 0.250000
\(17\) 1.00000 0.242536
\(18\) −1.00000 −0.235702
\(19\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) −1.00000 −0.223607
\(21\) 3.00000 0.654654
\(22\) −1.00000 −0.213201
\(23\) 1.00000 0.208514 0.104257 − 0.994550i \(-0.466753\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(24\) −1.00000 −0.204124
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 3.00000 0.566947
\(29\) −9.00000 −1.67126 −0.835629 − 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) 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
\(35\) −3.00000 −0.507093
\(36\) 1.00000 0.166667
\(37\) 2.00000 0.328798 0.164399 − 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 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
\(43\) 1.00000 0.152499 0.0762493 − 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 1.00000 0.150756
\(45\) −1.00000 −0.149071
\(46\) −1.00000 −0.147442
\(47\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) 1.00000 0.144338
\(49\) 2.00000 0.285714
\(50\) −1.00000 −0.141421
\(51\) 1.00000 0.140028
\(52\) 0 0
\(53\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(54\) −1.00000 −0.136083
\(55\) −1.00000 −0.134840
\(56\) −3.00000 −0.400892
\(57\) 0 0
\(58\) 9.00000 1.18176
\(59\) 10.0000 1.30189 0.650945 − 0.759125i \(-0.274373\pi\)
0.650945 + 0.759125i \(0.274373\pi\)
\(60\) −1.00000 −0.129099
\(61\) 14.0000 1.79252 0.896258 − 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) −5.00000 −0.635001
\(63\) 3.00000 0.377964
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) −1.00000 −0.123091
\(67\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 1.00000 0.121268
\(69\) 1.00000 0.120386
\(70\) 3.00000 0.358569
\(71\) −10.0000 −1.18678 −0.593391 − 0.804914i \(-0.702211\pi\)
−0.593391 + 0.804914i \(0.702211\pi\)
\(72\) −1.00000 −0.117851
\(73\) −2.00000 −0.234082 −0.117041 − 0.993127i \(-0.537341\pi\)
−0.117041 + 0.993127i \(0.537341\pi\)
\(74\) −2.00000 −0.232495
\(75\) 1.00000 0.115470
\(76\) 0 0
\(77\) 3.00000 0.341882
\(78\) 0 0
\(79\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) −1.00000 −0.111803
\(81\) 1.00000 0.111111
\(82\) −8.00000 −0.883452
\(83\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 3.00000 0.327327
\(85\) −1.00000 −0.108465
\(86\) −1.00000 −0.107833
\(87\) −9.00000 −0.964901
\(88\) −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
\(91\) 0 0
\(92\) 1.00000 0.104257
\(93\) 5.00000 0.518476
\(94\) 0 0
\(95\) 0 0
\(96\) −1.00000 −0.102062
\(97\) 9.00000 0.913812 0.456906 − 0.889515i \(-0.348958\pi\)
0.456906 + 0.889515i \(0.348958\pi\)
\(98\) −2.00000 −0.202031
\(99\) 1.00000 0.100504
\(100\) 1.00000 0.100000
\(101\) 10.0000 0.995037 0.497519 − 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) −1.00000 −0.0990148
\(103\) 13.0000 1.28093 0.640464 − 0.767988i \(-0.278742\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 0 0
\(105\) −3.00000 −0.292770
\(106\) 0 0
\(107\) −9.00000 −0.870063 −0.435031 − 0.900415i \(-0.643263\pi\)
−0.435031 + 0.900415i \(0.643263\pi\)
\(108\) 1.00000 0.0962250
\(109\) −4.00000 −0.383131 −0.191565 − 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 1.00000 0.0953463
\(111\) 2.00000 0.189832
\(112\) 3.00000 0.283473
\(113\) −10.0000 −0.940721 −0.470360 − 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) −1.00000 −0.0932505
\(116\) −9.00000 −0.835629
\(117\) 0 0
\(118\) −10.0000 −0.920575
\(119\) 3.00000 0.275010
\(120\) 1.00000 0.0912871
\(121\) 1.00000 0.0909091
\(122\) −14.0000 −1.26750
\(123\) 8.00000 0.721336
\(124\) 5.00000 0.449013
\(125\) −1.00000 −0.0894427
\(126\) −3.00000 −0.267261
\(127\) 2.00000 0.177471 0.0887357 − 0.996055i \(-0.471717\pi\)
0.0887357 + 0.996055i \(0.471717\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 1.00000 0.0880451
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 − 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 1.00000 0.0870388
\(133\) 0 0
\(134\) 0 0
\(135\) −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
\(139\) 19.0000 1.61156 0.805779 − 0.592216i \(-0.201747\pi\)
0.805779 + 0.592216i \(0.201747\pi\)
\(140\) −3.00000 −0.253546
\(141\) 0 0
\(142\) 10.0000 0.839181
\(143\) 0 0
\(144\) 1.00000 0.0833333
\(145\) 9.00000 0.747409
\(146\) 2.00000 0.165521
\(147\) 2.00000 0.164957
\(148\) 2.00000 0.164399
\(149\) −8.00000 −0.655386 −0.327693 − 0.944784i \(-0.606271\pi\)
−0.327693 + 0.944784i \(0.606271\pi\)
\(150\) −1.00000 −0.0816497
\(151\) −20.0000 −1.62758 −0.813788 − 0.581161i \(-0.802599\pi\)
−0.813788 + 0.581161i \(0.802599\pi\)
\(152\) 0 0
\(153\) 1.00000 0.0808452
\(154\) −3.00000 −0.241747
\(155\) −5.00000 −0.401610
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 − 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 1.00000 0.0790569
\(161\) 3.00000 0.236433
\(162\) −1.00000 −0.0785674
\(163\) −1.00000 −0.0783260 −0.0391630 − 0.999233i \(-0.512469\pi\)
−0.0391630 + 0.999233i \(0.512469\pi\)
\(164\) 8.00000 0.624695
\(165\) −1.00000 −0.0778499
\(166\) 0 0
\(167\) −14.0000 −1.08335 −0.541676 − 0.840587i \(-0.682210\pi\)
−0.541676 + 0.840587i \(0.682210\pi\)
\(168\) −3.00000 −0.231455
\(169\) −13.0000 −1.00000
\(170\) 1.00000 0.0766965
\(171\) 0 0
\(172\) 1.00000 0.0762493
\(173\) 2.00000 0.152057 0.0760286 − 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 9.00000 0.682288
\(175\) 3.00000 0.226779
\(176\) 1.00000 0.0753778
\(177\) 10.0000 0.751646
\(178\) 4.00000 0.299813
\(179\) 6.00000 0.448461 0.224231 − 0.974536i \(-0.428013\pi\)
0.224231 + 0.974536i \(0.428013\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 9.00000 0.668965 0.334482 − 0.942402i \(-0.391439\pi\)
0.334482 + 0.942402i \(0.391439\pi\)
\(182\) 0 0
\(183\) 14.0000 1.03491
\(184\) −1.00000 −0.0737210
\(185\) −2.00000 −0.147043
\(186\) −5.00000 −0.366618
\(187\) 1.00000 0.0731272
\(188\) 0 0
\(189\) 3.00000 0.218218
\(190\) 0 0
\(191\) −9.00000 −0.651217 −0.325609 − 0.945505i \(-0.605569\pi\)
−0.325609 + 0.945505i \(0.605569\pi\)
\(192\) 1.00000 0.0721688
\(193\) 18.0000 1.29567 0.647834 − 0.761781i \(-0.275675\pi\)
0.647834 + 0.761781i \(0.275675\pi\)
\(194\) −9.00000 −0.646162
\(195\) 0 0
\(196\) 2.00000 0.142857
\(197\) 8.00000 0.569976 0.284988 − 0.958531i \(-0.408010\pi\)
0.284988 + 0.958531i \(0.408010\pi\)
\(198\) −1.00000 −0.0710669
\(199\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) −1.00000 −0.0707107
\(201\) 0 0
\(202\) −10.0000 −0.703598
\(203\) −27.0000 −1.89503
\(204\) 1.00000 0.0700140
\(205\) −8.00000 −0.558744
\(206\) −13.0000 −0.905753
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 0 0
\(210\) 3.00000 0.207020
\(211\) −11.0000 −0.757271 −0.378636 − 0.925546i \(-0.623607\pi\)
−0.378636 + 0.925546i \(0.623607\pi\)
\(212\) 0 0
\(213\) −10.0000 −0.685189
\(214\) 9.00000 0.615227
\(215\) −1.00000 −0.0681994
\(216\) −1.00000 −0.0680414
\(217\) 15.0000 1.01827
\(218\) 4.00000 0.270914
\(219\) −2.00000 −0.135147
\(220\) −1.00000 −0.0674200
\(221\) 0 0
\(222\) −2.00000 −0.134231
\(223\) −3.00000 −0.200895 −0.100447 − 0.994942i \(-0.532027\pi\)
−0.100447 + 0.994942i \(0.532027\pi\)
\(224\) −3.00000 −0.200446
\(225\) 1.00000 0.0666667
\(226\) 10.0000 0.665190
\(227\) 15.0000 0.995585 0.497792 − 0.867296i \(-0.334144\pi\)
0.497792 + 0.867296i \(0.334144\pi\)
\(228\) 0 0
\(229\) 16.0000 1.05731 0.528655 − 0.848837i \(-0.322697\pi\)
0.528655 + 0.848837i \(0.322697\pi\)
\(230\) 1.00000 0.0659380
\(231\) 3.00000 0.197386
\(232\) 9.00000 0.590879
\(233\) −15.0000 −0.982683 −0.491341 − 0.870967i \(-0.663493\pi\)
−0.491341 + 0.870967i \(0.663493\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 10.0000 0.650945
\(237\) 0 0
\(238\) −3.00000 −0.194461
\(239\) −18.0000 −1.16432 −0.582162 − 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) −1.00000 −0.0645497
\(241\) −7.00000 −0.450910 −0.225455 − 0.974254i \(-0.572387\pi\)
−0.225455 + 0.974254i \(0.572387\pi\)
\(242\) −1.00000 −0.0642824
\(243\) 1.00000 0.0641500
\(244\) 14.0000 0.896258
\(245\) −2.00000 −0.127775
\(246\) −8.00000 −0.510061
\(247\) 0 0
\(248\) −5.00000 −0.317500
\(249\) 0 0
\(250\) 1.00000 0.0632456
\(251\) −8.00000 −0.504956 −0.252478 − 0.967603i \(-0.581245\pi\)
−0.252478 + 0.967603i \(0.581245\pi\)
\(252\) 3.00000 0.188982
\(253\) 1.00000 0.0628695
\(254\) −2.00000 −0.125491
\(255\) −1.00000 −0.0626224
\(256\) 1.00000 0.0625000
\(257\) 15.0000 0.935674 0.467837 − 0.883815i \(-0.345033\pi\)
0.467837 + 0.883815i \(0.345033\pi\)
\(258\) −1.00000 −0.0622573
\(259\) 6.00000 0.372822
\(260\) 0 0
\(261\) −9.00000 −0.557086
\(262\) −4.00000 −0.247121
\(263\) 19.0000 1.17159 0.585795 − 0.810459i \(-0.300782\pi\)
0.585795 + 0.810459i \(0.300782\pi\)
\(264\) −1.00000 −0.0615457
\(265\) 0 0
\(266\) 0 0
\(267\) −4.00000 −0.244796
\(268\) 0 0
\(269\) 30.0000 1.82913 0.914566 − 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(270\) 1.00000 0.0608581
\(271\) 23.0000 1.39715 0.698575 − 0.715537i \(-0.253818\pi\)
0.698575 + 0.715537i \(0.253818\pi\)
\(272\) 1.00000 0.0606339
\(273\) 0 0
\(274\) −17.0000 −1.02701
\(275\) 1.00000 0.0603023
\(276\) 1.00000 0.0601929
\(277\) 2.00000 0.120168 0.0600842 − 0.998193i \(-0.480863\pi\)
0.0600842 + 0.998193i \(0.480863\pi\)
\(278\) −19.0000 −1.13954
\(279\) 5.00000 0.299342
\(280\) 3.00000 0.179284
\(281\) −13.0000 −0.775515 −0.387757 − 0.921761i \(-0.626750\pi\)
−0.387757 + 0.921761i \(0.626750\pi\)
\(282\) 0 0
\(283\) 14.0000 0.832214 0.416107 − 0.909316i \(-0.363394\pi\)
0.416107 + 0.909316i \(0.363394\pi\)
\(284\) −10.0000 −0.593391
\(285\) 0 0
\(286\) 0 0
\(287\) 24.0000 1.41668
\(288\) −1.00000 −0.0589256
\(289\) 1.00000 0.0588235
\(290\) −9.00000 −0.528498
\(291\) 9.00000 0.527589
\(292\) −2.00000 −0.117041
\(293\) 1.00000 0.0584206 0.0292103 − 0.999573i \(-0.490701\pi\)
0.0292103 + 0.999573i \(0.490701\pi\)
\(294\) −2.00000 −0.116642
\(295\) −10.0000 −0.582223
\(296\) −2.00000 −0.116248
\(297\) 1.00000 0.0580259
\(298\) 8.00000 0.463428
\(299\) 0 0
\(300\) 1.00000 0.0577350
\(301\) 3.00000 0.172917
\(302\) 20.0000 1.15087
\(303\) 10.0000 0.574485
\(304\) 0 0
\(305\) −14.0000 −0.801638
\(306\) −1.00000 −0.0571662
\(307\) 12.0000 0.684876 0.342438 − 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 3.00000 0.170941
\(309\) 13.0000 0.739544
\(310\) 5.00000 0.283981
\(311\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 31.0000 1.75222 0.876112 − 0.482108i \(-0.160129\pi\)
0.876112 + 0.482108i \(0.160129\pi\)
\(314\) 2.00000 0.112867
\(315\) −3.00000 −0.169031
\(316\) 0 0
\(317\) 3.00000 0.168497 0.0842484 − 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) 0 0
\(319\) −9.00000 −0.503903
\(320\) −1.00000 −0.0559017
\(321\) −9.00000 −0.502331
\(322\) −3.00000 −0.167183
\(323\) 0 0
\(324\) 1.00000 0.0555556
\(325\) 0 0
\(326\) 1.00000 0.0553849
\(327\) −4.00000 −0.221201
\(328\) −8.00000 −0.441726
\(329\) 0 0
\(330\) 1.00000 0.0550482
\(331\) 25.0000 1.37412 0.687062 − 0.726599i \(-0.258900\pi\)
0.687062 + 0.726599i \(0.258900\pi\)
\(332\) 0 0
\(333\) 2.00000 0.109599
\(334\) 14.0000 0.766046
\(335\) 0 0
\(336\) 3.00000 0.163663
\(337\) −6.00000 −0.326841 −0.163420 − 0.986557i \(-0.552253\pi\)
−0.163420 + 0.986557i \(0.552253\pi\)
\(338\) 13.0000 0.707107
\(339\) −10.0000 −0.543125
\(340\) −1.00000 −0.0542326
\(341\) 5.00000 0.270765
\(342\) 0 0
\(343\) −15.0000 −0.809924
\(344\) −1.00000 −0.0539164
\(345\) −1.00000 −0.0538382
\(346\) −2.00000 −0.107521
\(347\) −4.00000 −0.214731 −0.107366 − 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) −9.00000 −0.482451
\(349\) −22.0000 −1.17763 −0.588817 − 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) −3.00000 −0.160357
\(351\) 0 0
\(352\) −1.00000 −0.0533002
\(353\) −23.0000 −1.22417 −0.612083 − 0.790793i \(-0.709668\pi\)
−0.612083 + 0.790793i \(0.709668\pi\)
\(354\) −10.0000 −0.531494
\(355\) 10.0000 0.530745
\(356\) −4.00000 −0.212000
\(357\) 3.00000 0.158777
\(358\) −6.00000 −0.317110
\(359\) −6.00000 −0.316668 −0.158334 − 0.987386i \(-0.550612\pi\)
−0.158334 + 0.987386i \(0.550612\pi\)
\(360\) 1.00000 0.0527046
\(361\) −19.0000 −1.00000
\(362\) −9.00000 −0.473029
\(363\) 1.00000 0.0524864
\(364\) 0 0
\(365\) 2.00000 0.104685
\(366\) −14.0000 −0.731792
\(367\) −10.0000 −0.521996 −0.260998 − 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) 1.00000 0.0521286
\(369\) 8.00000 0.416463
\(370\) 2.00000 0.103975
\(371\) 0 0
\(372\) 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
\(376\) 0 0
\(377\) 0 0
\(378\) −3.00000 −0.154303
\(379\) 32.0000 1.64373 0.821865 − 0.569683i \(-0.192934\pi\)
0.821865 + 0.569683i \(0.192934\pi\)
\(380\) 0 0
\(381\) 2.00000 0.102463
\(382\) 9.00000 0.460480
\(383\) −4.00000 −0.204390 −0.102195 − 0.994764i \(-0.532587\pi\)
−0.102195 + 0.994764i \(0.532587\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −3.00000 −0.152894
\(386\) −18.0000 −0.916176
\(387\) 1.00000 0.0508329
\(388\) 9.00000 0.456906
\(389\) −10.0000 −0.507020 −0.253510 − 0.967333i \(-0.581585\pi\)
−0.253510 + 0.967333i \(0.581585\pi\)
\(390\) 0 0
\(391\) 1.00000 0.0505722
\(392\) −2.00000 −0.101015
\(393\) 4.00000 0.201773
\(394\) −8.00000 −0.403034
\(395\) 0 0
\(396\) 1.00000 0.0502519
\(397\) −2.00000 −0.100377 −0.0501886 − 0.998740i \(-0.515982\pi\)
−0.0501886 + 0.998740i \(0.515982\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −11.0000 −0.549314 −0.274657 − 0.961542i \(-0.588564\pi\)
−0.274657 + 0.961542i \(0.588564\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 10.0000 0.497519
\(405\) −1.00000 −0.0496904
\(406\) 27.0000 1.33999
\(407\) 2.00000 0.0991363
\(408\) −1.00000 −0.0495074
\(409\) −20.0000 −0.988936 −0.494468 − 0.869196i \(-0.664637\pi\)
−0.494468 + 0.869196i \(0.664637\pi\)
\(410\) 8.00000 0.395092
\(411\) 17.0000 0.838548
\(412\) 13.0000 0.640464
\(413\) 30.0000 1.47620
\(414\) −1.00000 −0.0491473
\(415\) 0 0
\(416\) 0 0
\(417\) 19.0000 0.930434
\(418\) 0 0
\(419\) −37.0000 −1.80757 −0.903784 − 0.427989i \(-0.859222\pi\)
−0.903784 + 0.427989i \(0.859222\pi\)
\(420\) −3.00000 −0.146385
\(421\) 24.0000 1.16969 0.584844 − 0.811146i \(-0.301156\pi\)
0.584844 + 0.811146i \(0.301156\pi\)
\(422\) 11.0000 0.535472
\(423\) 0 0
\(424\) 0 0
\(425\) 1.00000 0.0485071
\(426\) 10.0000 0.484502
\(427\) 42.0000 2.03252
\(428\) −9.00000 −0.435031
\(429\) 0 0
\(430\) 1.00000 0.0482243
\(431\) 37.0000 1.78223 0.891114 − 0.453780i \(-0.149925\pi\)
0.891114 + 0.453780i \(0.149925\pi\)
\(432\) 1.00000 0.0481125
\(433\) 20.0000 0.961139 0.480569 − 0.876957i \(-0.340430\pi\)
0.480569 + 0.876957i \(0.340430\pi\)
\(434\) −15.0000 −0.720023
\(435\) 9.00000 0.431517
\(436\) −4.00000 −0.191565
\(437\) 0 0
\(438\) 2.00000 0.0955637
\(439\) −10.0000 −0.477274 −0.238637 − 0.971109i \(-0.576701\pi\)
−0.238637 + 0.971109i \(0.576701\pi\)
\(440\) 1.00000 0.0476731
\(441\) 2.00000 0.0952381
\(442\) 0 0
\(443\) 9.00000 0.427603 0.213801 − 0.976877i \(-0.431415\pi\)
0.213801 + 0.976877i \(0.431415\pi\)
\(444\) 2.00000 0.0949158
\(445\) 4.00000 0.189618
\(446\) 3.00000 0.142054
\(447\) −8.00000 −0.378387
\(448\) 3.00000 0.141737
\(449\) 31.0000 1.46298 0.731490 − 0.681852i \(-0.238825\pi\)
0.731490 + 0.681852i \(0.238825\pi\)
\(450\) −1.00000 −0.0471405
\(451\) 8.00000 0.376705
\(452\) −10.0000 −0.470360
\(453\) −20.0000 −0.939682
\(454\) −15.0000 −0.703985
\(455\) 0 0
\(456\) 0 0
\(457\) 10.0000 0.467780 0.233890 − 0.972263i \(-0.424854\pi\)
0.233890 + 0.972263i \(0.424854\pi\)
\(458\) −16.0000 −0.747631
\(459\) 1.00000 0.0466760
\(460\) −1.00000 −0.0466252
\(461\) 14.0000 0.652045 0.326023 − 0.945362i \(-0.394291\pi\)
0.326023 + 0.945362i \(0.394291\pi\)
\(462\) −3.00000 −0.139573
\(463\) −40.0000 −1.85896 −0.929479 − 0.368875i \(-0.879743\pi\)
−0.929479 + 0.368875i \(0.879743\pi\)
\(464\) −9.00000 −0.417815
\(465\) −5.00000 −0.231869
\(466\) 15.0000 0.694862
\(467\) 28.0000 1.29569 0.647843 − 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −2.00000 −0.0921551
\(472\) −10.0000 −0.460287
\(473\) 1.00000 0.0459800
\(474\) 0 0
\(475\) 0 0
\(476\) 3.00000 0.137505
\(477\) 0 0
\(478\) 18.0000 0.823301
\(479\) −21.0000 −0.959514 −0.479757 − 0.877401i \(-0.659275\pi\)
−0.479757 + 0.877401i \(0.659275\pi\)
\(480\) 1.00000 0.0456435
\(481\) 0 0
\(482\) 7.00000 0.318841
\(483\) 3.00000 0.136505
\(484\) 1.00000 0.0454545
\(485\) −9.00000 −0.408669
\(486\) −1.00000 −0.0453609
\(487\) −42.0000 −1.90320 −0.951601 − 0.307337i \(-0.900562\pi\)
−0.951601 + 0.307337i \(0.900562\pi\)
\(488\) −14.0000 −0.633750
\(489\) −1.00000 −0.0452216
\(490\) 2.00000 0.0903508
\(491\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(492\) 8.00000 0.360668
\(493\) −9.00000 −0.405340
\(494\) 0 0
\(495\) −1.00000 −0.0449467
\(496\) 5.00000 0.224507
\(497\) −30.0000 −1.34568
\(498\) 0 0
\(499\) −28.0000 −1.25345 −0.626726 − 0.779240i \(-0.715605\pi\)
−0.626726 + 0.779240i \(0.715605\pi\)
\(500\) −1.00000 −0.0447214
\(501\) −14.0000 −0.625474
\(502\) 8.00000 0.357057
\(503\) 4.00000 0.178351 0.0891756 − 0.996016i \(-0.471577\pi\)
0.0891756 + 0.996016i \(0.471577\pi\)
\(504\) −3.00000 −0.133631
\(505\) −10.0000 −0.444994
\(506\) −1.00000 −0.0444554
\(507\) −13.0000 −0.577350
\(508\) 2.00000 0.0887357
\(509\) 14.0000 0.620539 0.310270 − 0.950649i \(-0.399581\pi\)
0.310270 + 0.950649i \(0.399581\pi\)
\(510\) 1.00000 0.0442807
\(511\) −6.00000 −0.265424
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −15.0000 −0.661622
\(515\) −13.0000 −0.572848
\(516\) 1.00000 0.0440225
\(517\) 0 0
\(518\) −6.00000 −0.263625
\(519\) 2.00000 0.0877903
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 − 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 9.00000 0.393919
\(523\) −23.0000 −1.00572 −0.502860 − 0.864368i \(-0.667719\pi\)
−0.502860 + 0.864368i \(0.667719\pi\)
\(524\) 4.00000 0.174741
\(525\) 3.00000 0.130931
\(526\) −19.0000 −0.828439
\(527\) 5.00000 0.217803
\(528\) 1.00000 0.0435194
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) 10.0000 0.433963
\(532\) 0 0
\(533\) 0 0
\(534\) 4.00000 0.173097
\(535\) 9.00000 0.389104
\(536\) 0 0
\(537\) 6.00000 0.258919
\(538\) −30.0000 −1.29339
\(539\) 2.00000 0.0861461
\(540\) −1.00000 −0.0430331
\(541\) 12.0000 0.515920 0.257960 − 0.966156i \(-0.416950\pi\)
0.257960 + 0.966156i \(0.416950\pi\)
\(542\) −23.0000 −0.987935
\(543\) 9.00000 0.386227
\(544\) −1.00000 −0.0428746
\(545\) 4.00000 0.171341
\(546\) 0 0
\(547\) −6.00000 −0.256541 −0.128271 − 0.991739i \(-0.540943\pi\)
−0.128271 + 0.991739i \(0.540943\pi\)
\(548\) 17.0000 0.726204
\(549\) 14.0000 0.597505
\(550\) −1.00000 −0.0426401
\(551\) 0 0
\(552\) −1.00000 −0.0425628
\(553\) 0 0
\(554\) −2.00000 −0.0849719
\(555\) −2.00000 −0.0848953
\(556\) 19.0000 0.805779
\(557\) 23.0000 0.974541 0.487271 − 0.873251i \(-0.337993\pi\)
0.487271 + 0.873251i \(0.337993\pi\)
\(558\) −5.00000 −0.211667
\(559\) 0 0
\(560\) −3.00000 −0.126773
\(561\) 1.00000 0.0422200
\(562\) 13.0000 0.548372
\(563\) 20.0000 0.842900 0.421450 − 0.906852i \(-0.361521\pi\)
0.421450 + 0.906852i \(0.361521\pi\)
\(564\) 0 0
\(565\) 10.0000 0.420703
\(566\) −14.0000 −0.588464
\(567\) 3.00000 0.125988
\(568\) 10.0000 0.419591
\(569\) −22.0000 −0.922288 −0.461144 − 0.887325i \(-0.652561\pi\)
−0.461144 + 0.887325i \(0.652561\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 − 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 0 0
\(573\) −9.00000 −0.375980
\(574\) −24.0000 −1.00174
\(575\) 1.00000 0.0417029
\(576\) 1.00000 0.0416667
\(577\) 42.0000 1.74848 0.874241 − 0.485491i \(-0.161359\pi\)
0.874241 + 0.485491i \(0.161359\pi\)
\(578\) −1.00000 −0.0415945
\(579\) 18.0000 0.748054
\(580\) 9.00000 0.373705
\(581\) 0 0
\(582\) −9.00000 −0.373062
\(583\) 0 0
\(584\) 2.00000 0.0827606
\(585\) 0 0
\(586\) −1.00000 −0.0413096
\(587\) 31.0000 1.27951 0.639753 − 0.768580i \(-0.279036\pi\)
0.639753 + 0.768580i \(0.279036\pi\)
\(588\) 2.00000 0.0824786
\(589\) 0 0
\(590\) 10.0000 0.411693
\(591\) 8.00000 0.329076
\(592\) 2.00000 0.0821995
\(593\) 6.00000 0.246390 0.123195 − 0.992382i \(-0.460686\pi\)
0.123195 + 0.992382i \(0.460686\pi\)
\(594\) −1.00000 −0.0410305
\(595\) −3.00000 −0.122988
\(596\) −8.00000 −0.327693
\(597\) 0 0
\(598\) 0 0
\(599\) 9.00000 0.367730 0.183865 − 0.982952i \(-0.441139\pi\)
0.183865 + 0.982952i \(0.441139\pi\)
\(600\) −1.00000 −0.0408248
\(601\) −2.00000 −0.0815817 −0.0407909 − 0.999168i \(-0.512988\pi\)
−0.0407909 + 0.999168i \(0.512988\pi\)
\(602\) −3.00000 −0.122271
\(603\) 0 0
\(604\) −20.0000 −0.813788
\(605\) −1.00000 −0.0406558
\(606\) −10.0000 −0.406222
\(607\) −8.00000 −0.324710 −0.162355 − 0.986732i \(-0.551909\pi\)
−0.162355 + 0.986732i \(0.551909\pi\)
\(608\) 0 0
\(609\) −27.0000 −1.09410
\(610\) 14.0000 0.566843
\(611\) 0 0
\(612\) 1.00000 0.0404226
\(613\) −26.0000 −1.05013 −0.525065 − 0.851062i \(-0.675959\pi\)
−0.525065 + 0.851062i \(0.675959\pi\)
\(614\) −12.0000 −0.484281
\(615\) −8.00000 −0.322591
\(616\) −3.00000 −0.120873
\(617\) 6.00000 0.241551 0.120775 − 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) −13.0000 −0.522937
\(619\) −6.00000 −0.241160 −0.120580 − 0.992704i \(-0.538475\pi\)
−0.120580 + 0.992704i \(0.538475\pi\)
\(620\) −5.00000 −0.200805
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) −12.0000 −0.480770
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −31.0000 −1.23901
\(627\) 0 0
\(628\) −2.00000 −0.0798087
\(629\) 2.00000 0.0797452
\(630\) 3.00000 0.119523
\(631\) −30.0000 −1.19428 −0.597141 − 0.802137i \(-0.703697\pi\)
−0.597141 + 0.802137i \(0.703697\pi\)
\(632\) 0 0
\(633\) −11.0000 −0.437211
\(634\) −3.00000 −0.119145
\(635\) −2.00000 −0.0793676
\(636\) 0 0
\(637\) 0 0
\(638\) 9.00000 0.356313
\(639\) −10.0000 −0.395594
\(640\) 1.00000 0.0395285
\(641\) 3.00000 0.118493 0.0592464 − 0.998243i \(-0.481130\pi\)
0.0592464 + 0.998243i \(0.481130\pi\)
\(642\) 9.00000 0.355202
\(643\) 25.0000 0.985904 0.492952 − 0.870057i \(-0.335918\pi\)
0.492952 + 0.870057i \(0.335918\pi\)
\(644\) 3.00000 0.118217
\(645\) −1.00000 −0.0393750
\(646\) 0 0
\(647\) −34.0000 −1.33668 −0.668339 − 0.743857i \(-0.732994\pi\)
−0.668339 + 0.743857i \(0.732994\pi\)
\(648\) −1.00000 −0.0392837
\(649\) 10.0000 0.392534
\(650\) 0 0
\(651\) 15.0000 0.587896
\(652\) −1.00000 −0.0391630
\(653\) 27.0000 1.05659 0.528296 − 0.849060i \(-0.322831\pi\)
0.528296 + 0.849060i \(0.322831\pi\)
\(654\) 4.00000 0.156412
\(655\) −4.00000 −0.156293
\(656\) 8.00000 0.312348
\(657\) −2.00000 −0.0780274
\(658\) 0 0
\(659\) 5.00000 0.194772 0.0973862 − 0.995247i \(-0.468952\pi\)
0.0973862 + 0.995247i \(0.468952\pi\)
\(660\) −1.00000 −0.0389249
\(661\) 8.00000 0.311164 0.155582 − 0.987823i \(-0.450275\pi\)
0.155582 + 0.987823i \(0.450275\pi\)
\(662\) −25.0000 −0.971653
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) −9.00000 −0.348481
\(668\) −14.0000 −0.541676
\(669\) −3.00000 −0.115987
\(670\) 0 0
\(671\) 14.0000 0.540464
\(672\) −3.00000 −0.115728
\(673\) 16.0000 0.616755 0.308377 − 0.951264i \(-0.400214\pi\)
0.308377 + 0.951264i \(0.400214\pi\)
\(674\) 6.00000 0.231111
\(675\) 1.00000 0.0384900
\(676\) −13.0000 −0.500000
\(677\) 30.0000 1.15299 0.576497 − 0.817099i \(-0.304419\pi\)
0.576497 + 0.817099i \(0.304419\pi\)
\(678\) 10.0000 0.384048
\(679\) 27.0000 1.03616
\(680\) 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 \(0.426264\pi\)
\(684\) 0 0
\(685\) −17.0000 −0.649537
\(686\) 15.0000 0.572703
\(687\) 16.0000 0.610438
\(688\) 1.00000 0.0381246
\(689\) 0 0
\(690\) 1.00000 0.0380693
\(691\) 32.0000 1.21734 0.608669 − 0.793424i \(-0.291704\pi\)
0.608669 + 0.793424i \(0.291704\pi\)
\(692\) 2.00000 0.0760286
\(693\) 3.00000 0.113961
\(694\) 4.00000 0.151838
\(695\) −19.0000 −0.720711
\(696\) 9.00000 0.341144
\(697\) 8.00000 0.303022
\(698\) 22.0000 0.832712
\(699\) −15.0000 −0.567352
\(700\) 3.00000 0.113389
\(701\) −18.0000 −0.679851 −0.339925 − 0.940452i \(-0.610402\pi\)
−0.339925 + 0.940452i \(0.610402\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) 23.0000 0.865616
\(707\) 30.0000 1.12827
\(708\) 10.0000 0.375823
\(709\) −34.0000 −1.27690 −0.638448 − 0.769665i \(-0.720423\pi\)
−0.638448 + 0.769665i \(0.720423\pi\)
\(710\) −10.0000 −0.375293
\(711\) 0 0
\(712\) 4.00000 0.149906
\(713\) 5.00000 0.187251
\(714\) −3.00000 −0.112272
\(715\) 0 0
\(716\) 6.00000 0.224231
\(717\) −18.0000 −0.672222
\(718\) 6.00000 0.223918
\(719\) −26.0000 −0.969636 −0.484818 − 0.874615i \(-0.661114\pi\)
−0.484818 + 0.874615i \(0.661114\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 39.0000 1.45244
\(722\) 19.0000 0.707107
\(723\) −7.00000 −0.260333
\(724\) 9.00000 0.334482
\(725\) −9.00000 −0.334252
\(726\) −1.00000 −0.0371135
\(727\) 45.0000 1.66896 0.834479 − 0.551040i \(-0.185769\pi\)
0.834479 + 0.551040i \(0.185769\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −2.00000 −0.0740233
\(731\) 1.00000 0.0369863
\(732\) 14.0000 0.517455
\(733\) −28.0000 −1.03420 −0.517102 − 0.855924i \(-0.672989\pi\)
−0.517102 + 0.855924i \(0.672989\pi\)
\(734\) 10.0000 0.369107
\(735\) −2.00000 −0.0737711
\(736\) −1.00000 −0.0368605
\(737\) 0 0
\(738\) −8.00000 −0.294484
\(739\) −26.0000 −0.956425 −0.478213 − 0.878244i \(-0.658715\pi\)
−0.478213 + 0.878244i \(0.658715\pi\)
\(740\) −2.00000 −0.0735215
\(741\) 0 0
\(742\) 0 0
\(743\) −12.0000 −0.440237 −0.220119 − 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) −5.00000 −0.183309
\(745\) 8.00000 0.293097
\(746\) −22.0000 −0.805477
\(747\) 0 0
\(748\) 1.00000 0.0365636
\(749\) −27.0000 −0.986559
\(750\) 1.00000 0.0365148
\(751\) 43.0000 1.56909 0.784546 − 0.620070i \(-0.212896\pi\)
0.784546 + 0.620070i \(0.212896\pi\)
\(752\) 0 0
\(753\) −8.00000 −0.291536
\(754\) 0 0
\(755\) 20.0000 0.727875
\(756\) 3.00000 0.109109
\(757\) 29.0000 1.05402 0.527011 − 0.849858i \(-0.323312\pi\)
0.527011 + 0.849858i \(0.323312\pi\)
\(758\) −32.0000 −1.16229
\(759\) 1.00000 0.0362977
\(760\) 0 0
\(761\) −27.0000 −0.978749 −0.489375 − 0.872074i \(-0.662775\pi\)
−0.489375 + 0.872074i \(0.662775\pi\)
\(762\) −2.00000 −0.0724524
\(763\) −12.0000 −0.434429
\(764\) −9.00000 −0.325609
\(765\) −1.00000 −0.0361551
\(766\) 4.00000 0.144526
\(767\) 0 0
\(768\) 1.00000 0.0360844
\(769\) −14.0000 −0.504853 −0.252426 − 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 3.00000 0.108112
\(771\) 15.0000 0.540212
\(772\) 18.0000 0.647834
\(773\) −8.00000 −0.287740 −0.143870 − 0.989597i \(-0.545955\pi\)
−0.143870 + 0.989597i \(0.545955\pi\)
\(774\) −1.00000 −0.0359443
\(775\) 5.00000 0.179605
\(776\) −9.00000 −0.323081
\(777\) 6.00000 0.215249
\(778\) 10.0000 0.358517
\(779\) 0 0
\(780\) 0 0
\(781\) −10.0000 −0.357828
\(782\) −1.00000 −0.0357599
\(783\) −9.00000 −0.321634
\(784\) 2.00000 0.0714286
\(785\) 2.00000 0.0713831
\(786\) −4.00000 −0.142675
\(787\) 32.0000 1.14068 0.570338 − 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) 8.00000 0.284988
\(789\) 19.0000 0.676418
\(790\) 0 0
\(791\) −30.0000 −1.06668
\(792\) −1.00000 −0.0355335
\(793\) 0 0
\(794\) 2.00000 0.0709773
\(795\) 0 0
\(796\) 0 0
\(797\) 36.0000 1.27519 0.637593 − 0.770374i \(-0.279930\pi\)
0.637593 + 0.770374i \(0.279930\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −1.00000 −0.0353553
\(801\) −4.00000 −0.141333
\(802\) 11.0000 0.388424
\(803\) −2.00000 −0.0705785
\(804\) 0 0
\(805\) −3.00000 −0.105736
\(806\) 0 0
\(807\) 30.0000 1.05605
\(808\) −10.0000 −0.351799
\(809\) 2.00000 0.0703163 0.0351581 − 0.999382i \(-0.488807\pi\)
0.0351581 + 0.999382i \(0.488807\pi\)
\(810\) 1.00000 0.0351364
\(811\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) −27.0000 −0.947514
\(813\) 23.0000 0.806645
\(814\) −2.00000 −0.0701000
\(815\) 1.00000 0.0350285
\(816\) 1.00000 0.0350070
\(817\) 0 0
\(818\) 20.0000 0.699284
\(819\) 0 0
\(820\) −8.00000 −0.279372
\(821\) −3.00000 −0.104701 −0.0523504 − 0.998629i \(-0.516671\pi\)
−0.0523504 + 0.998629i \(0.516671\pi\)
\(822\) −17.0000 −0.592943
\(823\) 10.0000 0.348578 0.174289 − 0.984695i \(-0.444237\pi\)
0.174289 + 0.984695i \(0.444237\pi\)
\(824\) −13.0000 −0.452876
\(825\) 1.00000 0.0348155
\(826\) −30.0000 −1.04383
\(827\) −23.0000 −0.799788 −0.399894 − 0.916561i \(-0.630953\pi\)
−0.399894 + 0.916561i \(0.630953\pi\)
\(828\) 1.00000 0.0347524
\(829\) −2.00000 −0.0694629 −0.0347314 − 0.999397i \(-0.511058\pi\)
−0.0347314 + 0.999397i \(0.511058\pi\)
\(830\) 0 0
\(831\) 2.00000 0.0693792
\(832\) 0 0
\(833\) 2.00000 0.0692959
\(834\) −19.0000 −0.657916
\(835\) 14.0000 0.484490
\(836\) 0 0
\(837\) 5.00000 0.172825
\(838\) 37.0000 1.27814
\(839\) −26.0000 −0.897620 −0.448810 − 0.893627i \(-0.648152\pi\)
−0.448810 + 0.893627i \(0.648152\pi\)
\(840\) 3.00000 0.103510
\(841\) 52.0000 1.79310
\(842\) −24.0000 −0.827095
\(843\) −13.0000 −0.447744
\(844\) −11.0000 −0.378636
\(845\) 13.0000 0.447214
\(846\) 0 0
\(847\) 3.00000 0.103081
\(848\) 0 0
\(849\) 14.0000 0.480479
\(850\) −1.00000 −0.0342997
\(851\) 2.00000 0.0685591
\(852\) −10.0000 −0.342594
\(853\) −25.0000 −0.855984 −0.427992 − 0.903783i \(-0.640779\pi\)
−0.427992 + 0.903783i \(0.640779\pi\)
\(854\) −42.0000 −1.43721
\(855\) 0 0
\(856\) 9.00000 0.307614
\(857\) 7.00000 0.239115 0.119558 − 0.992827i \(-0.461852\pi\)
0.119558 + 0.992827i \(0.461852\pi\)
\(858\) 0 0
\(859\) −49.0000 −1.67186 −0.835929 − 0.548837i \(-0.815071\pi\)
−0.835929 + 0.548837i \(0.815071\pi\)
\(860\) −1.00000 −0.0340997
\(861\) 24.0000 0.817918
\(862\) −37.0000 −1.26023
\(863\) 28.0000 0.953131 0.476566 − 0.879139i \(-0.341881\pi\)
0.476566 + 0.879139i \(0.341881\pi\)
\(864\) −1.00000 −0.0340207
\(865\) −2.00000 −0.0680020
\(866\) −20.0000 −0.679628
\(867\) 1.00000 0.0339618
\(868\) 15.0000 0.509133
\(869\) 0 0
\(870\) −9.00000 −0.305129
\(871\) 0 0
\(872\) 4.00000 0.135457
\(873\) 9.00000 0.304604
\(874\) 0 0
\(875\) −3.00000 −0.101419
\(876\) −2.00000 −0.0675737
\(877\) 23.0000 0.776655 0.388327 − 0.921521i \(-0.373053\pi\)
0.388327 + 0.921521i \(0.373053\pi\)
\(878\) 10.0000 0.337484
\(879\) 1.00000 0.0337292
\(880\) −1.00000 −0.0337100
\(881\) −27.0000 −0.909653 −0.454827 − 0.890580i \(-0.650299\pi\)
−0.454827 + 0.890580i \(0.650299\pi\)
\(882\) −2.00000 −0.0673435
\(883\) 20.0000 0.673054 0.336527 − 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 0 0
\(885\) −10.0000 −0.336146
\(886\) −9.00000 −0.302361
\(887\) −4.00000 −0.134307 −0.0671534 − 0.997743i \(-0.521392\pi\)
−0.0671534 + 0.997743i \(0.521392\pi\)
\(888\) −2.00000 −0.0671156
\(889\) 6.00000 0.201234
\(890\) −4.00000 −0.134080
\(891\) 1.00000 0.0335013
\(892\) −3.00000 −0.100447
\(893\) 0 0
\(894\) 8.00000 0.267560
\(895\) −6.00000 −0.200558
\(896\) −3.00000 −0.100223
\(897\) 0 0
\(898\) −31.0000 −1.03448
\(899\) −45.0000 −1.50083
\(900\) 1.00000 0.0333333
\(901\) 0 0
\(902\) −8.00000 −0.266371
\(903\) 3.00000 0.0998337
\(904\) 10.0000 0.332595
\(905\) −9.00000 −0.299170
\(906\) 20.0000 0.664455
\(907\) 33.0000 1.09575 0.547874 − 0.836561i \(-0.315438\pi\)
0.547874 + 0.836561i \(0.315438\pi\)
\(908\) 15.0000 0.497792
\(909\) 10.0000 0.331679
\(910\) 0 0
\(911\) 40.0000 1.32526 0.662630 − 0.748947i \(-0.269440\pi\)
0.662630 + 0.748947i \(0.269440\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −10.0000 −0.330771
\(915\) −14.0000 −0.462826
\(916\) 16.0000 0.528655
\(917\) 12.0000 0.396275
\(918\) −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
\(921\) 12.0000 0.395413
\(922\) −14.0000 −0.461065
\(923\) 0 0
\(924\) 3.00000 0.0986928
\(925\) 2.00000 0.0657596
\(926\) 40.0000 1.31448
\(927\) 13.0000 0.426976
\(928\) 9.00000 0.295439
\(929\) −49.0000 −1.60764 −0.803819 − 0.594874i \(-0.797202\pi\)
−0.803819 + 0.594874i \(0.797202\pi\)
\(930\) 5.00000 0.163956
\(931\) 0 0
\(932\) −15.0000 −0.491341
\(933\) 0 0
\(934\) −28.0000 −0.916188
\(935\) −1.00000 −0.0327035
\(936\) 0 0
\(937\) −38.0000 −1.24141 −0.620703 − 0.784046i \(-0.713153\pi\)
−0.620703 + 0.784046i \(0.713153\pi\)
\(938\) 0 0
\(939\) 31.0000 1.01165
\(940\) 0 0
\(941\) −30.0000 −0.977972 −0.488986 − 0.872292i \(-0.662633\pi\)
−0.488986 + 0.872292i \(0.662633\pi\)
\(942\) 2.00000 0.0651635
\(943\) 8.00000 0.260516
\(944\) 10.0000 0.325472
\(945\) −3.00000 −0.0975900
\(946\) −1.00000 −0.0325128
\(947\) 30.0000 0.974869 0.487435 − 0.873160i \(-0.337933\pi\)
0.487435 + 0.873160i \(0.337933\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 3.00000 0.0972817
\(952\) −3.00000 −0.0972306
\(953\) −46.0000 −1.49009 −0.745043 − 0.667016i \(-0.767571\pi\)
−0.745043 + 0.667016i \(0.767571\pi\)
\(954\) 0 0
\(955\) 9.00000 0.291233
\(956\) −18.0000 −0.582162
\(957\) −9.00000 −0.290929
\(958\) 21.0000 0.678479
\(959\) 51.0000 1.64688
\(960\) −1.00000 −0.0322749
\(961\) −6.00000 −0.193548
\(962\) 0 0
\(963\) −9.00000 −0.290021
\(964\) −7.00000 −0.225455
\(965\) −18.0000 −0.579441
\(966\) −3.00000 −0.0965234
\(967\) 2.00000 0.0643157 0.0321578 − 0.999483i \(-0.489762\pi\)
0.0321578 + 0.999483i \(0.489762\pi\)
\(968\) −1.00000 −0.0321412
\(969\) 0 0
\(970\) 9.00000 0.288973
\(971\) −20.0000 −0.641831 −0.320915 − 0.947108i \(-0.603990\pi\)
−0.320915 + 0.947108i \(0.603990\pi\)
\(972\) 1.00000 0.0320750
\(973\) 57.0000 1.82734
\(974\) 42.0000 1.34577
\(975\) 0 0
\(976\) 14.0000 0.448129
\(977\) 34.0000 1.08776 0.543878 − 0.839164i \(-0.316955\pi\)
0.543878 + 0.839164i \(0.316955\pi\)
\(978\) 1.00000 0.0319765
\(979\) −4.00000 −0.127841
\(980\) −2.00000 −0.0638877
\(981\) −4.00000 −0.127710
\(982\) 0 0
\(983\) 9.00000 0.287055 0.143528 − 0.989646i \(-0.454155\pi\)
0.143528 + 0.989646i \(0.454155\pi\)
\(984\) −8.00000 −0.255031
\(985\) −8.00000 −0.254901
\(986\) 9.00000 0.286618
\(987\) 0 0
\(988\) 0 0
\(989\) 1.00000 0.0317982
\(990\) 1.00000 0.0317821
\(991\) 7.00000 0.222362 0.111181 − 0.993800i \(-0.464537\pi\)
0.111181 + 0.993800i \(0.464537\pi\)
\(992\) −5.00000 −0.158750
\(993\) 25.0000 0.793351
\(994\) 30.0000 0.951542
\(995\) 0 0
\(996\) 0 0
\(997\) −3.00000 −0.0950110 −0.0475055 − 0.998871i \(-0.515127\pi\)
−0.0475055 + 0.998871i \(0.515127\pi\)
\(998\) 28.0000 0.886325
\(999\) 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.p.1.1 ✓ 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
5610.2.a.p.1.1 ✓ 1 1.1 even 1 trivial