Properties

Label 5225.2.a.n.1.6
Level $5225$
Weight $2$
Character 5225.1
Self dual yes
Analytic conductor $41.722$
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] = [5225,2,Mod(1,5225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5225, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("5225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5225 = 5^{2} \cdot 11 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5225.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: \(41.7218350561\)
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: \( x^{7} - x^{6} - 14x^{5} + 10x^{4} + 59x^{3} - 27x^{2} - 66x + 30 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 209)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(2.61330\) of defining polynomial
Character \(\chi\) \(=\) 5225.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.61330 q^{2} -1.19599 q^{3} +4.82936 q^{4} -3.12549 q^{6} -3.61829 q^{7} +7.39397 q^{8} -1.56960 q^{9} +O(q^{10})\) \(q+2.61330 q^{2} -1.19599 q^{3} +4.82936 q^{4} -3.12549 q^{6} -3.61829 q^{7} +7.39397 q^{8} -1.56960 q^{9} -1.00000 q^{11} -5.77587 q^{12} +1.47857 q^{13} -9.45570 q^{14} +9.66398 q^{16} +3.27003 q^{17} -4.10185 q^{18} +1.00000 q^{19} +4.32745 q^{21} -2.61330 q^{22} +7.45793 q^{23} -8.84313 q^{24} +3.86395 q^{26} +5.46521 q^{27} -17.4740 q^{28} +1.02535 q^{29} +1.64921 q^{31} +10.4670 q^{32} +1.19599 q^{33} +8.54558 q^{34} -7.58018 q^{36} +6.71293 q^{37} +2.61330 q^{38} -1.76836 q^{39} -3.92451 q^{41} +11.3089 q^{42} -5.38113 q^{43} -4.82936 q^{44} +19.4898 q^{46} +3.71597 q^{47} -11.5580 q^{48} +6.09205 q^{49} -3.91093 q^{51} +7.14054 q^{52} +0.102902 q^{53} +14.2823 q^{54} -26.7536 q^{56} -1.19599 q^{57} +2.67955 q^{58} +13.2986 q^{59} -6.49664 q^{61} +4.30989 q^{62} +5.67929 q^{63} +8.02543 q^{64} +3.12549 q^{66} +3.70989 q^{67} +15.7921 q^{68} -8.91962 q^{69} +6.32968 q^{71} -11.6056 q^{72} +1.37759 q^{73} +17.5429 q^{74} +4.82936 q^{76} +3.61829 q^{77} -4.62125 q^{78} +13.6725 q^{79} -1.82753 q^{81} -10.2559 q^{82} -5.44061 q^{83} +20.8988 q^{84} -14.0625 q^{86} -1.22631 q^{87} -7.39397 q^{88} +12.1357 q^{89} -5.34990 q^{91} +36.0170 q^{92} -1.97244 q^{93} +9.71096 q^{94} -12.5184 q^{96} +13.7910 q^{97} +15.9204 q^{98} +1.56960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + q^{2} - 2 q^{3} + 15 q^{4} - 2 q^{6} - 10 q^{7} + 9 q^{8} + 11 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + q^{2} - 2 q^{3} + 15 q^{4} - 2 q^{6} - 10 q^{7} + 9 q^{8} + 11 q^{9} - 7 q^{11} + 16 q^{12} + 4 q^{13} + 6 q^{14} + 27 q^{16} - 2 q^{17} - 9 q^{18} + 7 q^{19} - 14 q^{21} - q^{22} - 10 q^{23} - 2 q^{24} - 8 q^{26} + 4 q^{27} - 26 q^{28} - 18 q^{29} + 24 q^{31} + 49 q^{32} + 2 q^{33} - 6 q^{34} + 29 q^{36} + q^{38} + 24 q^{39} - 12 q^{41} + 44 q^{42} - 2 q^{43} - 15 q^{44} - 4 q^{46} - 8 q^{47} + 72 q^{48} + 17 q^{49} - 24 q^{51} + 60 q^{52} - 2 q^{53} - 52 q^{54} + 26 q^{56} - 2 q^{57} + 8 q^{58} - 10 q^{59} + 14 q^{61} - 14 q^{62} + 55 q^{64} + 2 q^{66} - 8 q^{67} + 18 q^{68} - 6 q^{69} + 10 q^{71} - 53 q^{72} + 6 q^{73} + 26 q^{74} + 15 q^{76} + 10 q^{77} - 22 q^{78} + 52 q^{79} - q^{81} - 24 q^{82} + 10 q^{83} - 6 q^{84} + 8 q^{86} - 6 q^{87} - 9 q^{88} + 12 q^{91} - 2 q^{93} + 24 q^{94} + 6 q^{96} + 24 q^{97} - 19 q^{98} - 11 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.61330 1.84789 0.923943 0.382531i \(-0.124948\pi\)
0.923943 + 0.382531i \(0.124948\pi\)
\(3\) −1.19599 −0.690506 −0.345253 0.938510i \(-0.612207\pi\)
−0.345253 + 0.938510i \(0.612207\pi\)
\(4\) 4.82936 2.41468
\(5\) 0 0
\(6\) −3.12549 −1.27598
\(7\) −3.61829 −1.36759 −0.683793 0.729676i \(-0.739671\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(8\) 7.39397 2.61416
\(9\) −1.56960 −0.523201
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) −5.77587 −1.66735
\(13\) 1.47857 0.410081 0.205041 0.978753i \(-0.434267\pi\)
0.205041 + 0.978753i \(0.434267\pi\)
\(14\) −9.45570 −2.52714
\(15\) 0 0
\(16\) 9.66398 2.41600
\(17\) 3.27003 0.793099 0.396549 0.918013i \(-0.370208\pi\)
0.396549 + 0.918013i \(0.370208\pi\)
\(18\) −4.10185 −0.966816
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) 4.32745 0.944327
\(22\) −2.61330 −0.557158
\(23\) 7.45793 1.55509 0.777543 0.628830i \(-0.216466\pi\)
0.777543 + 0.628830i \(0.216466\pi\)
\(24\) −8.84313 −1.80510
\(25\) 0 0
\(26\) 3.86395 0.757783
\(27\) 5.46521 1.05178
\(28\) −17.4740 −3.30228
\(29\) 1.02535 0.190403 0.0952013 0.995458i \(-0.469651\pi\)
0.0952013 + 0.995458i \(0.469651\pi\)
\(30\) 0 0
\(31\) 1.64921 0.296207 0.148104 0.988972i \(-0.452683\pi\)
0.148104 + 0.988972i \(0.452683\pi\)
\(32\) 10.4670 1.85032
\(33\) 1.19599 0.208195
\(34\) 8.54558 1.46556
\(35\) 0 0
\(36\) −7.58018 −1.26336
\(37\) 6.71293 1.10360 0.551799 0.833977i \(-0.313941\pi\)
0.551799 + 0.833977i \(0.313941\pi\)
\(38\) 2.61330 0.423934
\(39\) −1.76836 −0.283164
\(40\) 0 0
\(41\) −3.92451 −0.612905 −0.306453 0.951886i \(-0.599142\pi\)
−0.306453 + 0.951886i \(0.599142\pi\)
\(42\) 11.3089 1.74501
\(43\) −5.38113 −0.820614 −0.410307 0.911947i \(-0.634578\pi\)
−0.410307 + 0.911947i \(0.634578\pi\)
\(44\) −4.82936 −0.728053
\(45\) 0 0
\(46\) 19.4898 2.87362
\(47\) 3.71597 0.542030 0.271015 0.962575i \(-0.412641\pi\)
0.271015 + 0.962575i \(0.412641\pi\)
\(48\) −11.5580 −1.66826
\(49\) 6.09205 0.870292
\(50\) 0 0
\(51\) −3.91093 −0.547640
\(52\) 7.14054 0.990215
\(53\) 0.102902 0.0141347 0.00706733 0.999975i \(-0.497750\pi\)
0.00706733 + 0.999975i \(0.497750\pi\)
\(54\) 14.2823 1.94357
\(55\) 0 0
\(56\) −26.7536 −3.57509
\(57\) −1.19599 −0.158413
\(58\) 2.67955 0.351842
\(59\) 13.2986 1.73134 0.865668 0.500619i \(-0.166894\pi\)
0.865668 + 0.500619i \(0.166894\pi\)
\(60\) 0 0
\(61\) −6.49664 −0.831809 −0.415905 0.909408i \(-0.636535\pi\)
−0.415905 + 0.909408i \(0.636535\pi\)
\(62\) 4.30989 0.547357
\(63\) 5.67929 0.715523
\(64\) 8.02543 1.00318
\(65\) 0 0
\(66\) 3.12549 0.384721
\(67\) 3.70989 0.453235 0.226618 0.973984i \(-0.427233\pi\)
0.226618 + 0.973984i \(0.427233\pi\)
\(68\) 15.7921 1.91508
\(69\) −8.91962 −1.07380
\(70\) 0 0
\(71\) 6.32968 0.751194 0.375597 0.926783i \(-0.377438\pi\)
0.375597 + 0.926783i \(0.377438\pi\)
\(72\) −11.6056 −1.36773
\(73\) 1.37759 0.161235 0.0806173 0.996745i \(-0.474311\pi\)
0.0806173 + 0.996745i \(0.474311\pi\)
\(74\) 17.5429 2.03932
\(75\) 0 0
\(76\) 4.82936 0.553965
\(77\) 3.61829 0.412343
\(78\) −4.62125 −0.523254
\(79\) 13.6725 1.53828 0.769141 0.639079i \(-0.220684\pi\)
0.769141 + 0.639079i \(0.220684\pi\)
\(80\) 0 0
\(81\) −1.82753 −0.203059
\(82\) −10.2559 −1.13258
\(83\) −5.44061 −0.597184 −0.298592 0.954381i \(-0.596517\pi\)
−0.298592 + 0.954381i \(0.596517\pi\)
\(84\) 20.8988 2.28025
\(85\) 0 0
\(86\) −14.0625 −1.51640
\(87\) −1.22631 −0.131474
\(88\) −7.39397 −0.788200
\(89\) 12.1357 1.28638 0.643191 0.765706i \(-0.277610\pi\)
0.643191 + 0.765706i \(0.277610\pi\)
\(90\) 0 0
\(91\) −5.34990 −0.560822
\(92\) 36.0170 3.75503
\(93\) −1.97244 −0.204533
\(94\) 9.71096 1.00161
\(95\) 0 0
\(96\) −12.5184 −1.27766
\(97\) 13.7910 1.40026 0.700131 0.714014i \(-0.253125\pi\)
0.700131 + 0.714014i \(0.253125\pi\)
\(98\) 15.9204 1.60820
\(99\) 1.56960 0.157751
\(100\) 0 0
\(101\) −11.0029 −1.09483 −0.547413 0.836863i \(-0.684387\pi\)
−0.547413 + 0.836863i \(0.684387\pi\)
\(102\) −10.2204 −1.01198
\(103\) 4.99191 0.491867 0.245934 0.969287i \(-0.420906\pi\)
0.245934 + 0.969287i \(0.420906\pi\)
\(104\) 10.9325 1.07202
\(105\) 0 0
\(106\) 0.268914 0.0261192
\(107\) −7.31345 −0.707018 −0.353509 0.935431i \(-0.615012\pi\)
−0.353509 + 0.935431i \(0.615012\pi\)
\(108\) 26.3934 2.53971
\(109\) −1.44482 −0.138389 −0.0691944 0.997603i \(-0.522043\pi\)
−0.0691944 + 0.997603i \(0.522043\pi\)
\(110\) 0 0
\(111\) −8.02861 −0.762042
\(112\) −34.9671 −3.30408
\(113\) 12.0369 1.13234 0.566169 0.824289i \(-0.308425\pi\)
0.566169 + 0.824289i \(0.308425\pi\)
\(114\) −3.12549 −0.292729
\(115\) 0 0
\(116\) 4.95178 0.459761
\(117\) −2.32077 −0.214555
\(118\) 34.7534 3.19931
\(119\) −11.8319 −1.08463
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) −16.9777 −1.53709
\(123\) 4.69368 0.423215
\(124\) 7.96463 0.715245
\(125\) 0 0
\(126\) 14.8417 1.32220
\(127\) 4.69692 0.416784 0.208392 0.978045i \(-0.433177\pi\)
0.208392 + 0.978045i \(0.433177\pi\)
\(128\) 0.0389415 0.00344197
\(129\) 6.43578 0.566639
\(130\) 0 0
\(131\) 3.74466 0.327173 0.163586 0.986529i \(-0.447694\pi\)
0.163586 + 0.986529i \(0.447694\pi\)
\(132\) 5.77587 0.502725
\(133\) −3.61829 −0.313746
\(134\) 9.69507 0.837526
\(135\) 0 0
\(136\) 24.1785 2.07329
\(137\) 15.7595 1.34643 0.673213 0.739449i \(-0.264914\pi\)
0.673213 + 0.739449i \(0.264914\pi\)
\(138\) −23.3097 −1.98425
\(139\) −2.52822 −0.214440 −0.107220 0.994235i \(-0.534195\pi\)
−0.107220 + 0.994235i \(0.534195\pi\)
\(140\) 0 0
\(141\) −4.44427 −0.374275
\(142\) 16.5414 1.38812
\(143\) −1.47857 −0.123644
\(144\) −15.1686 −1.26405
\(145\) 0 0
\(146\) 3.60006 0.297943
\(147\) −7.28604 −0.600942
\(148\) 32.4191 2.66484
\(149\) 1.84902 0.151477 0.0757387 0.997128i \(-0.475869\pi\)
0.0757387 + 0.997128i \(0.475869\pi\)
\(150\) 0 0
\(151\) −15.3184 −1.24659 −0.623296 0.781986i \(-0.714207\pi\)
−0.623296 + 0.781986i \(0.714207\pi\)
\(152\) 7.39397 0.599730
\(153\) −5.13265 −0.414950
\(154\) 9.45570 0.761962
\(155\) 0 0
\(156\) −8.54003 −0.683750
\(157\) −24.6631 −1.96833 −0.984165 0.177254i \(-0.943278\pi\)
−0.984165 + 0.177254i \(0.943278\pi\)
\(158\) 35.7305 2.84257
\(159\) −0.123070 −0.00976006
\(160\) 0 0
\(161\) −26.9850 −2.12671
\(162\) −4.77590 −0.375230
\(163\) 3.72149 0.291490 0.145745 0.989322i \(-0.453442\pi\)
0.145745 + 0.989322i \(0.453442\pi\)
\(164\) −18.9529 −1.47997
\(165\) 0 0
\(166\) −14.2180 −1.10353
\(167\) −2.64758 −0.204876 −0.102438 0.994739i \(-0.532664\pi\)
−0.102438 + 0.994739i \(0.532664\pi\)
\(168\) 31.9970 2.46863
\(169\) −10.8138 −0.831833
\(170\) 0 0
\(171\) −1.56960 −0.120031
\(172\) −25.9874 −1.98152
\(173\) −7.34552 −0.558469 −0.279235 0.960223i \(-0.590081\pi\)
−0.279235 + 0.960223i \(0.590081\pi\)
\(174\) −3.20472 −0.242949
\(175\) 0 0
\(176\) −9.66398 −0.728450
\(177\) −15.9051 −1.19550
\(178\) 31.7143 2.37708
\(179\) 9.55394 0.714095 0.357047 0.934086i \(-0.383783\pi\)
0.357047 + 0.934086i \(0.383783\pi\)
\(180\) 0 0
\(181\) 6.02638 0.447937 0.223969 0.974596i \(-0.428099\pi\)
0.223969 + 0.974596i \(0.428099\pi\)
\(182\) −13.9809 −1.03633
\(183\) 7.76993 0.574369
\(184\) 55.1437 4.06525
\(185\) 0 0
\(186\) −5.15459 −0.377953
\(187\) −3.27003 −0.239128
\(188\) 17.9458 1.30883
\(189\) −19.7747 −1.43840
\(190\) 0 0
\(191\) 17.7069 1.28123 0.640613 0.767864i \(-0.278680\pi\)
0.640613 + 0.767864i \(0.278680\pi\)
\(192\) −9.59835 −0.692701
\(193\) −3.69348 −0.265863 −0.132931 0.991125i \(-0.542439\pi\)
−0.132931 + 0.991125i \(0.542439\pi\)
\(194\) 36.0400 2.58752
\(195\) 0 0
\(196\) 29.4207 2.10148
\(197\) 25.7789 1.83667 0.918336 0.395802i \(-0.129533\pi\)
0.918336 + 0.395802i \(0.129533\pi\)
\(198\) 4.10185 0.291506
\(199\) 18.8953 1.33945 0.669726 0.742608i \(-0.266411\pi\)
0.669726 + 0.742608i \(0.266411\pi\)
\(200\) 0 0
\(201\) −4.43700 −0.312962
\(202\) −28.7538 −2.02311
\(203\) −3.71002 −0.260392
\(204\) −18.8873 −1.32237
\(205\) 0 0
\(206\) 13.0454 0.908914
\(207\) −11.7060 −0.813623
\(208\) 14.2889 0.990755
\(209\) −1.00000 −0.0691714
\(210\) 0 0
\(211\) −10.1993 −0.702150 −0.351075 0.936347i \(-0.614184\pi\)
−0.351075 + 0.936347i \(0.614184\pi\)
\(212\) 0.496950 0.0341306
\(213\) −7.57024 −0.518704
\(214\) −19.1123 −1.30649
\(215\) 0 0
\(216\) 40.4096 2.74953
\(217\) −5.96733 −0.405089
\(218\) −3.77576 −0.255727
\(219\) −1.64759 −0.111334
\(220\) 0 0
\(221\) 4.83497 0.325235
\(222\) −20.9812 −1.40817
\(223\) 0.262700 0.0175917 0.00879584 0.999961i \(-0.497200\pi\)
0.00879584 + 0.999961i \(0.497200\pi\)
\(224\) −37.8726 −2.53047
\(225\) 0 0
\(226\) 31.4561 2.09243
\(227\) −27.3256 −1.81367 −0.906834 0.421489i \(-0.861508\pi\)
−0.906834 + 0.421489i \(0.861508\pi\)
\(228\) −5.77587 −0.382516
\(229\) −5.53171 −0.365546 −0.182773 0.983155i \(-0.558507\pi\)
−0.182773 + 0.983155i \(0.558507\pi\)
\(230\) 0 0
\(231\) −4.32745 −0.284725
\(232\) 7.58141 0.497744
\(233\) −27.4733 −1.79984 −0.899918 0.436059i \(-0.856374\pi\)
−0.899918 + 0.436059i \(0.856374\pi\)
\(234\) −6.06487 −0.396473
\(235\) 0 0
\(236\) 64.2239 4.18062
\(237\) −16.3523 −1.06219
\(238\) −30.9204 −2.00427
\(239\) 1.40339 0.0907781 0.0453890 0.998969i \(-0.485547\pi\)
0.0453890 + 0.998969i \(0.485547\pi\)
\(240\) 0 0
\(241\) −20.7696 −1.33789 −0.668944 0.743312i \(-0.733254\pi\)
−0.668944 + 0.743312i \(0.733254\pi\)
\(242\) 2.61330 0.167990
\(243\) −14.2099 −0.911566
\(244\) −31.3746 −2.00855
\(245\) 0 0
\(246\) 12.2660 0.782052
\(247\) 1.47857 0.0940791
\(248\) 12.1942 0.774334
\(249\) 6.50692 0.412359
\(250\) 0 0
\(251\) −1.29936 −0.0820148 −0.0410074 0.999159i \(-0.513057\pi\)
−0.0410074 + 0.999159i \(0.513057\pi\)
\(252\) 27.4273 1.72776
\(253\) −7.45793 −0.468876
\(254\) 12.2745 0.770169
\(255\) 0 0
\(256\) −15.9491 −0.996819
\(257\) −3.41219 −0.212847 −0.106423 0.994321i \(-0.533940\pi\)
−0.106423 + 0.994321i \(0.533940\pi\)
\(258\) 16.8187 1.04708
\(259\) −24.2893 −1.50927
\(260\) 0 0
\(261\) −1.60939 −0.0996189
\(262\) 9.78594 0.604577
\(263\) −14.2418 −0.878189 −0.439094 0.898441i \(-0.644701\pi\)
−0.439094 + 0.898441i \(0.644701\pi\)
\(264\) 8.84313 0.544257
\(265\) 0 0
\(266\) −9.45570 −0.579766
\(267\) −14.5142 −0.888254
\(268\) 17.9164 1.09442
\(269\) 5.39477 0.328925 0.164462 0.986383i \(-0.447411\pi\)
0.164462 + 0.986383i \(0.447411\pi\)
\(270\) 0 0
\(271\) −11.0624 −0.671995 −0.335998 0.941863i \(-0.609073\pi\)
−0.335998 + 0.941863i \(0.609073\pi\)
\(272\) 31.6015 1.91612
\(273\) 6.39843 0.387251
\(274\) 41.1844 2.48804
\(275\) 0 0
\(276\) −43.0760 −2.59287
\(277\) −14.0808 −0.846036 −0.423018 0.906121i \(-0.639029\pi\)
−0.423018 + 0.906121i \(0.639029\pi\)
\(278\) −6.60700 −0.396261
\(279\) −2.58861 −0.154976
\(280\) 0 0
\(281\) −10.8199 −0.645459 −0.322729 0.946491i \(-0.604600\pi\)
−0.322729 + 0.946491i \(0.604600\pi\)
\(282\) −11.6142 −0.691617
\(283\) −1.90947 −0.113506 −0.0567532 0.998388i \(-0.518075\pi\)
−0.0567532 + 0.998388i \(0.518075\pi\)
\(284\) 30.5683 1.81389
\(285\) 0 0
\(286\) −3.86395 −0.228480
\(287\) 14.2000 0.838201
\(288\) −16.4290 −0.968089
\(289\) −6.30690 −0.370994
\(290\) 0 0
\(291\) −16.4939 −0.966890
\(292\) 6.65287 0.389330
\(293\) −3.63550 −0.212388 −0.106194 0.994345i \(-0.533867\pi\)
−0.106194 + 0.994345i \(0.533867\pi\)
\(294\) −19.0406 −1.11047
\(295\) 0 0
\(296\) 49.6352 2.88499
\(297\) −5.46521 −0.317124
\(298\) 4.83205 0.279913
\(299\) 11.0271 0.637712
\(300\) 0 0
\(301\) 19.4705 1.12226
\(302\) −40.0316 −2.30356
\(303\) 13.1593 0.755984
\(304\) 9.66398 0.554267
\(305\) 0 0
\(306\) −13.4132 −0.766781
\(307\) 23.5329 1.34310 0.671548 0.740961i \(-0.265630\pi\)
0.671548 + 0.740961i \(0.265630\pi\)
\(308\) 17.4740 0.995675
\(309\) −5.97028 −0.339637
\(310\) 0 0
\(311\) −16.0026 −0.907425 −0.453713 0.891148i \(-0.649901\pi\)
−0.453713 + 0.891148i \(0.649901\pi\)
\(312\) −13.0752 −0.740237
\(313\) −16.0034 −0.904566 −0.452283 0.891875i \(-0.649390\pi\)
−0.452283 + 0.891875i \(0.649390\pi\)
\(314\) −64.4522 −3.63725
\(315\) 0 0
\(316\) 66.0296 3.71446
\(317\) 20.8766 1.17255 0.586273 0.810113i \(-0.300595\pi\)
0.586273 + 0.810113i \(0.300595\pi\)
\(318\) −0.321619 −0.0180355
\(319\) −1.02535 −0.0574086
\(320\) 0 0
\(321\) 8.74683 0.488200
\(322\) −70.5199 −3.92992
\(323\) 3.27003 0.181949
\(324\) −8.82581 −0.490323
\(325\) 0 0
\(326\) 9.72539 0.538640
\(327\) 1.72800 0.0955584
\(328\) −29.0177 −1.60224
\(329\) −13.4455 −0.741273
\(330\) 0 0
\(331\) 15.1136 0.830721 0.415360 0.909657i \(-0.363655\pi\)
0.415360 + 0.909657i \(0.363655\pi\)
\(332\) −26.2746 −1.44201
\(333\) −10.5366 −0.577404
\(334\) −6.91893 −0.378587
\(335\) 0 0
\(336\) 41.8204 2.28149
\(337\) 12.2766 0.668751 0.334376 0.942440i \(-0.391475\pi\)
0.334376 + 0.942440i \(0.391475\pi\)
\(338\) −28.2598 −1.53713
\(339\) −14.3961 −0.781886
\(340\) 0 0
\(341\) −1.64921 −0.0893098
\(342\) −4.10185 −0.221803
\(343\) 3.28525 0.177387
\(344\) −39.7879 −2.14522
\(345\) 0 0
\(346\) −19.1961 −1.03199
\(347\) 30.9067 1.65916 0.829580 0.558387i \(-0.188580\pi\)
0.829580 + 0.558387i \(0.188580\pi\)
\(348\) −5.92229 −0.317468
\(349\) −23.9024 −1.27947 −0.639733 0.768597i \(-0.720955\pi\)
−0.639733 + 0.768597i \(0.720955\pi\)
\(350\) 0 0
\(351\) 8.08069 0.431315
\(352\) −10.4670 −0.557892
\(353\) −15.0158 −0.799210 −0.399605 0.916687i \(-0.630853\pi\)
−0.399605 + 0.916687i \(0.630853\pi\)
\(354\) −41.5648 −2.20914
\(355\) 0 0
\(356\) 58.6076 3.10620
\(357\) 14.1509 0.748945
\(358\) 24.9673 1.31957
\(359\) 14.0826 0.743251 0.371626 0.928383i \(-0.378800\pi\)
0.371626 + 0.928383i \(0.378800\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 15.7488 0.827737
\(363\) −1.19599 −0.0627733
\(364\) −25.8366 −1.35420
\(365\) 0 0
\(366\) 20.3052 1.06137
\(367\) −21.3142 −1.11259 −0.556296 0.830984i \(-0.687778\pi\)
−0.556296 + 0.830984i \(0.687778\pi\)
\(368\) 72.0733 3.75708
\(369\) 6.15992 0.320673
\(370\) 0 0
\(371\) −0.372329 −0.0193304
\(372\) −9.52564 −0.493881
\(373\) 2.42088 0.125349 0.0626743 0.998034i \(-0.480037\pi\)
0.0626743 + 0.998034i \(0.480037\pi\)
\(374\) −8.54558 −0.441882
\(375\) 0 0
\(376\) 27.4758 1.41696
\(377\) 1.51605 0.0780806
\(378\) −51.6774 −2.65800
\(379\) 8.87535 0.455896 0.227948 0.973673i \(-0.426798\pi\)
0.227948 + 0.973673i \(0.426798\pi\)
\(380\) 0 0
\(381\) −5.61748 −0.287792
\(382\) 46.2735 2.36756
\(383\) 3.54065 0.180919 0.0904595 0.995900i \(-0.471166\pi\)
0.0904595 + 0.995900i \(0.471166\pi\)
\(384\) −0.0465737 −0.00237670
\(385\) 0 0
\(386\) −9.65219 −0.491284
\(387\) 8.44624 0.429346
\(388\) 66.6016 3.38118
\(389\) −16.7041 −0.846933 −0.423466 0.905912i \(-0.639187\pi\)
−0.423466 + 0.905912i \(0.639187\pi\)
\(390\) 0 0
\(391\) 24.3877 1.23334
\(392\) 45.0444 2.27509
\(393\) −4.47858 −0.225915
\(394\) 67.3681 3.39396
\(395\) 0 0
\(396\) 7.58018 0.380918
\(397\) −28.2073 −1.41568 −0.707841 0.706372i \(-0.750331\pi\)
−0.707841 + 0.706372i \(0.750331\pi\)
\(398\) 49.3792 2.47515
\(399\) 4.32745 0.216643
\(400\) 0 0
\(401\) −36.2078 −1.80813 −0.904065 0.427395i \(-0.859431\pi\)
−0.904065 + 0.427395i \(0.859431\pi\)
\(402\) −11.5952 −0.578317
\(403\) 2.43847 0.121469
\(404\) −53.1368 −2.64365
\(405\) 0 0
\(406\) −9.69540 −0.481175
\(407\) −6.71293 −0.332748
\(408\) −28.9173 −1.43162
\(409\) 36.9236 1.82576 0.912878 0.408233i \(-0.133855\pi\)
0.912878 + 0.408233i \(0.133855\pi\)
\(410\) 0 0
\(411\) −18.8482 −0.929715
\(412\) 24.1077 1.18770
\(413\) −48.1184 −2.36775
\(414\) −30.5913 −1.50348
\(415\) 0 0
\(416\) 15.4762 0.758781
\(417\) 3.02373 0.148072
\(418\) −2.61330 −0.127821
\(419\) 18.0690 0.882726 0.441363 0.897329i \(-0.354495\pi\)
0.441363 + 0.897329i \(0.354495\pi\)
\(420\) 0 0
\(421\) −8.57629 −0.417983 −0.208991 0.977918i \(-0.567018\pi\)
−0.208991 + 0.977918i \(0.567018\pi\)
\(422\) −26.6539 −1.29749
\(423\) −5.83260 −0.283591
\(424\) 0.760853 0.0369503
\(425\) 0 0
\(426\) −19.7833 −0.958506
\(427\) 23.5067 1.13757
\(428\) −35.3193 −1.70722
\(429\) 1.76836 0.0853771
\(430\) 0 0
\(431\) 4.28147 0.206231 0.103116 0.994669i \(-0.467119\pi\)
0.103116 + 0.994669i \(0.467119\pi\)
\(432\) 52.8157 2.54110
\(433\) −18.2035 −0.874804 −0.437402 0.899266i \(-0.644101\pi\)
−0.437402 + 0.899266i \(0.644101\pi\)
\(434\) −15.5945 −0.748558
\(435\) 0 0
\(436\) −6.97756 −0.334165
\(437\) 7.45793 0.356761
\(438\) −4.30564 −0.205732
\(439\) 29.4442 1.40529 0.702647 0.711538i \(-0.252001\pi\)
0.702647 + 0.711538i \(0.252001\pi\)
\(440\) 0 0
\(441\) −9.56210 −0.455338
\(442\) 12.6352 0.600997
\(443\) 24.3633 1.15753 0.578767 0.815493i \(-0.303534\pi\)
0.578767 + 0.815493i \(0.303534\pi\)
\(444\) −38.7730 −1.84009
\(445\) 0 0
\(446\) 0.686514 0.0325074
\(447\) −2.21141 −0.104596
\(448\) −29.0384 −1.37193
\(449\) 38.7776 1.83003 0.915015 0.403421i \(-0.132179\pi\)
0.915015 + 0.403421i \(0.132179\pi\)
\(450\) 0 0
\(451\) 3.92451 0.184798
\(452\) 58.1306 2.73423
\(453\) 18.3206 0.860779
\(454\) −71.4102 −3.35145
\(455\) 0 0
\(456\) −8.84313 −0.414118
\(457\) 7.47672 0.349746 0.174873 0.984591i \(-0.444048\pi\)
0.174873 + 0.984591i \(0.444048\pi\)
\(458\) −14.4560 −0.675487
\(459\) 17.8714 0.834165
\(460\) 0 0
\(461\) 15.9782 0.744181 0.372091 0.928196i \(-0.378641\pi\)
0.372091 + 0.928196i \(0.378641\pi\)
\(462\) −11.3089 −0.526139
\(463\) 6.10221 0.283594 0.141797 0.989896i \(-0.454712\pi\)
0.141797 + 0.989896i \(0.454712\pi\)
\(464\) 9.90896 0.460012
\(465\) 0 0
\(466\) −71.7961 −3.32589
\(467\) 26.6373 1.23263 0.616313 0.787502i \(-0.288626\pi\)
0.616313 + 0.787502i \(0.288626\pi\)
\(468\) −11.2078 −0.518082
\(469\) −13.4235 −0.619838
\(470\) 0 0
\(471\) 29.4969 1.35914
\(472\) 98.3298 4.52599
\(473\) 5.38113 0.247424
\(474\) −42.7334 −1.96281
\(475\) 0 0
\(476\) −57.1406 −2.61904
\(477\) −0.161515 −0.00739527
\(478\) 3.66750 0.167747
\(479\) −16.2094 −0.740626 −0.370313 0.928907i \(-0.620750\pi\)
−0.370313 + 0.928907i \(0.620750\pi\)
\(480\) 0 0
\(481\) 9.92553 0.452565
\(482\) −54.2773 −2.47226
\(483\) 32.2738 1.46851
\(484\) 4.82936 0.219516
\(485\) 0 0
\(486\) −37.1348 −1.68447
\(487\) 4.82448 0.218618 0.109309 0.994008i \(-0.465136\pi\)
0.109309 + 0.994008i \(0.465136\pi\)
\(488\) −48.0360 −2.17449
\(489\) −4.45088 −0.201276
\(490\) 0 0
\(491\) −8.53579 −0.385215 −0.192607 0.981276i \(-0.561694\pi\)
−0.192607 + 0.981276i \(0.561694\pi\)
\(492\) 22.6675 1.02193
\(493\) 3.35293 0.151008
\(494\) 3.86395 0.173847
\(495\) 0 0
\(496\) 15.9380 0.715635
\(497\) −22.9026 −1.02732
\(498\) 17.0046 0.761993
\(499\) −13.4325 −0.601319 −0.300660 0.953732i \(-0.597207\pi\)
−0.300660 + 0.953732i \(0.597207\pi\)
\(500\) 0 0
\(501\) 3.16648 0.141468
\(502\) −3.39562 −0.151554
\(503\) 1.66487 0.0742327 0.0371163 0.999311i \(-0.488183\pi\)
0.0371163 + 0.999311i \(0.488183\pi\)
\(504\) 41.9925 1.87049
\(505\) 0 0
\(506\) −19.4898 −0.866429
\(507\) 12.9333 0.574386
\(508\) 22.6831 1.00640
\(509\) −14.9684 −0.663463 −0.331731 0.943374i \(-0.607633\pi\)
−0.331731 + 0.943374i \(0.607633\pi\)
\(510\) 0 0
\(511\) −4.98452 −0.220502
\(512\) −41.7577 −1.84545
\(513\) 5.46521 0.241295
\(514\) −8.91709 −0.393316
\(515\) 0 0
\(516\) 31.0807 1.36825
\(517\) −3.71597 −0.163428
\(518\) −63.4754 −2.78895
\(519\) 8.78518 0.385627
\(520\) 0 0
\(521\) −7.89123 −0.345721 −0.172861 0.984946i \(-0.555301\pi\)
−0.172861 + 0.984946i \(0.555301\pi\)
\(522\) −4.20583 −0.184084
\(523\) 22.3062 0.975381 0.487690 0.873017i \(-0.337840\pi\)
0.487690 + 0.873017i \(0.337840\pi\)
\(524\) 18.0843 0.790017
\(525\) 0 0
\(526\) −37.2182 −1.62279
\(527\) 5.39297 0.234922
\(528\) 11.5580 0.502999
\(529\) 32.6207 1.41829
\(530\) 0 0
\(531\) −20.8736 −0.905837
\(532\) −17.4740 −0.757595
\(533\) −5.80266 −0.251341
\(534\) −37.9300 −1.64139
\(535\) 0 0
\(536\) 27.4308 1.18483
\(537\) −11.4264 −0.493087
\(538\) 14.0982 0.607815
\(539\) −6.09205 −0.262403
\(540\) 0 0
\(541\) 38.9694 1.67542 0.837712 0.546112i \(-0.183893\pi\)
0.837712 + 0.546112i \(0.183893\pi\)
\(542\) −28.9095 −1.24177
\(543\) −7.20750 −0.309304
\(544\) 34.2273 1.46749
\(545\) 0 0
\(546\) 16.7211 0.715595
\(547\) −37.7503 −1.61409 −0.807043 0.590492i \(-0.798934\pi\)
−0.807043 + 0.590492i \(0.798934\pi\)
\(548\) 76.1083 3.25119
\(549\) 10.1971 0.435204
\(550\) 0 0
\(551\) 1.02535 0.0436814
\(552\) −65.9514 −2.80708
\(553\) −49.4713 −2.10373
\(554\) −36.7975 −1.56338
\(555\) 0 0
\(556\) −12.2097 −0.517805
\(557\) 3.17436 0.134502 0.0672511 0.997736i \(-0.478577\pi\)
0.0672511 + 0.997736i \(0.478577\pi\)
\(558\) −6.76482 −0.286378
\(559\) −7.95637 −0.336519
\(560\) 0 0
\(561\) 3.91093 0.165120
\(562\) −28.2756 −1.19273
\(563\) 19.9431 0.840503 0.420252 0.907408i \(-0.361942\pi\)
0.420252 + 0.907408i \(0.361942\pi\)
\(564\) −21.4630 −0.903754
\(565\) 0 0
\(566\) −4.99004 −0.209747
\(567\) 6.61255 0.277701
\(568\) 46.8015 1.96375
\(569\) 36.6424 1.53613 0.768064 0.640374i \(-0.221220\pi\)
0.768064 + 0.640374i \(0.221220\pi\)
\(570\) 0 0
\(571\) 11.5300 0.482515 0.241258 0.970461i \(-0.422440\pi\)
0.241258 + 0.970461i \(0.422440\pi\)
\(572\) −7.14054 −0.298561
\(573\) −21.1773 −0.884694
\(574\) 37.1090 1.54890
\(575\) 0 0
\(576\) −12.5968 −0.524865
\(577\) −28.5590 −1.18893 −0.594463 0.804123i \(-0.702635\pi\)
−0.594463 + 0.804123i \(0.702635\pi\)
\(578\) −16.4818 −0.685554
\(579\) 4.41737 0.183580
\(580\) 0 0
\(581\) 19.6857 0.816701
\(582\) −43.1036 −1.78670
\(583\) −0.102902 −0.00426176
\(584\) 10.1859 0.421494
\(585\) 0 0
\(586\) −9.50067 −0.392469
\(587\) −18.1461 −0.748969 −0.374484 0.927233i \(-0.622180\pi\)
−0.374484 + 0.927233i \(0.622180\pi\)
\(588\) −35.1869 −1.45108
\(589\) 1.64921 0.0679546
\(590\) 0 0
\(591\) −30.8314 −1.26823
\(592\) 64.8736 2.66629
\(593\) −15.3085 −0.628644 −0.314322 0.949316i \(-0.601777\pi\)
−0.314322 + 0.949316i \(0.601777\pi\)
\(594\) −14.2823 −0.586008
\(595\) 0 0
\(596\) 8.92957 0.365769
\(597\) −22.5986 −0.924900
\(598\) 28.8171 1.17842
\(599\) 17.8806 0.730580 0.365290 0.930894i \(-0.380970\pi\)
0.365290 + 0.930894i \(0.380970\pi\)
\(600\) 0 0
\(601\) −32.5803 −1.32898 −0.664489 0.747298i \(-0.731351\pi\)
−0.664489 + 0.747298i \(0.731351\pi\)
\(602\) 50.8823 2.07381
\(603\) −5.82306 −0.237133
\(604\) −73.9779 −3.01012
\(605\) 0 0
\(606\) 34.3893 1.39697
\(607\) −43.6494 −1.77167 −0.885837 0.463997i \(-0.846415\pi\)
−0.885837 + 0.463997i \(0.846415\pi\)
\(608\) 10.4670 0.424492
\(609\) 4.43715 0.179802
\(610\) 0 0
\(611\) 5.49432 0.222276
\(612\) −24.7874 −1.00197
\(613\) −0.843061 −0.0340509 −0.0170254 0.999855i \(-0.505420\pi\)
−0.0170254 + 0.999855i \(0.505420\pi\)
\(614\) 61.4987 2.48189
\(615\) 0 0
\(616\) 26.7536 1.07793
\(617\) −4.89882 −0.197219 −0.0986094 0.995126i \(-0.531439\pi\)
−0.0986094 + 0.995126i \(0.531439\pi\)
\(618\) −15.6021 −0.627611
\(619\) −14.8704 −0.597691 −0.298846 0.954301i \(-0.596602\pi\)
−0.298846 + 0.954301i \(0.596602\pi\)
\(620\) 0 0
\(621\) 40.7591 1.63561
\(622\) −41.8197 −1.67682
\(623\) −43.9105 −1.75924
\(624\) −17.0894 −0.684122
\(625\) 0 0
\(626\) −41.8217 −1.67153
\(627\) 1.19599 0.0477633
\(628\) −119.107 −4.75289
\(629\) 21.9515 0.875263
\(630\) 0 0
\(631\) 2.83922 0.113027 0.0565137 0.998402i \(-0.482002\pi\)
0.0565137 + 0.998402i \(0.482002\pi\)
\(632\) 101.094 4.02132
\(633\) 12.1983 0.484839
\(634\) 54.5569 2.16673
\(635\) 0 0
\(636\) −0.594348 −0.0235674
\(637\) 9.00751 0.356891
\(638\) −2.67955 −0.106084
\(639\) −9.93508 −0.393026
\(640\) 0 0
\(641\) 20.6746 0.816599 0.408299 0.912848i \(-0.366122\pi\)
0.408299 + 0.912848i \(0.366122\pi\)
\(642\) 22.8581 0.902138
\(643\) 24.6254 0.971130 0.485565 0.874201i \(-0.338614\pi\)
0.485565 + 0.874201i \(0.338614\pi\)
\(644\) −130.320 −5.13533
\(645\) 0 0
\(646\) 8.54558 0.336222
\(647\) −45.3626 −1.78339 −0.891693 0.452640i \(-0.850482\pi\)
−0.891693 + 0.452640i \(0.850482\pi\)
\(648\) −13.5127 −0.530830
\(649\) −13.2986 −0.522017
\(650\) 0 0
\(651\) 7.13688 0.279716
\(652\) 17.9724 0.703854
\(653\) −26.1012 −1.02142 −0.510710 0.859753i \(-0.670617\pi\)
−0.510710 + 0.859753i \(0.670617\pi\)
\(654\) 4.51578 0.176581
\(655\) 0 0
\(656\) −37.9264 −1.48078
\(657\) −2.16227 −0.0843582
\(658\) −35.1371 −1.36979
\(659\) −45.8507 −1.78609 −0.893045 0.449967i \(-0.851436\pi\)
−0.893045 + 0.449967i \(0.851436\pi\)
\(660\) 0 0
\(661\) −15.4225 −0.599864 −0.299932 0.953961i \(-0.596964\pi\)
−0.299932 + 0.953961i \(0.596964\pi\)
\(662\) 39.4965 1.53508
\(663\) −5.78258 −0.224577
\(664\) −40.2277 −1.56114
\(665\) 0 0
\(666\) −27.5354 −1.06698
\(667\) 7.64698 0.296092
\(668\) −12.7861 −0.494709
\(669\) −0.314187 −0.0121472
\(670\) 0 0
\(671\) 6.49664 0.250800
\(672\) 45.2953 1.74730
\(673\) 37.8633 1.45952 0.729762 0.683702i \(-0.239631\pi\)
0.729762 + 0.683702i \(0.239631\pi\)
\(674\) 32.0826 1.23578
\(675\) 0 0
\(676\) −52.2239 −2.00861
\(677\) 25.3510 0.974320 0.487160 0.873313i \(-0.338033\pi\)
0.487160 + 0.873313i \(0.338033\pi\)
\(678\) −37.6213 −1.44484
\(679\) −49.8998 −1.91498
\(680\) 0 0
\(681\) 32.6812 1.25235
\(682\) −4.30989 −0.165034
\(683\) 21.7513 0.832290 0.416145 0.909298i \(-0.363381\pi\)
0.416145 + 0.909298i \(0.363381\pi\)
\(684\) −7.58018 −0.289835
\(685\) 0 0
\(686\) 8.58534 0.327790
\(687\) 6.61588 0.252412
\(688\) −52.0031 −1.98260
\(689\) 0.152147 0.00579636
\(690\) 0 0
\(691\) 17.3051 0.658318 0.329159 0.944275i \(-0.393235\pi\)
0.329159 + 0.944275i \(0.393235\pi\)
\(692\) −35.4741 −1.34852
\(693\) −5.67929 −0.215738
\(694\) 80.7687 3.06594
\(695\) 0 0
\(696\) −9.06730 −0.343695
\(697\) −12.8333 −0.486095
\(698\) −62.4643 −2.36431
\(699\) 32.8578 1.24280
\(700\) 0 0
\(701\) −29.6923 −1.12146 −0.560732 0.827997i \(-0.689480\pi\)
−0.560732 + 0.827997i \(0.689480\pi\)
\(702\) 21.1173 0.797021
\(703\) 6.71293 0.253183
\(704\) −8.02543 −0.302470
\(705\) 0 0
\(706\) −39.2409 −1.47685
\(707\) 39.8116 1.49727
\(708\) −76.8112 −2.88674
\(709\) −21.4898 −0.807067 −0.403534 0.914965i \(-0.632218\pi\)
−0.403534 + 0.914965i \(0.632218\pi\)
\(710\) 0 0
\(711\) −21.4605 −0.804831
\(712\) 89.7310 3.36281
\(713\) 12.2997 0.460627
\(714\) 36.9806 1.38396
\(715\) 0 0
\(716\) 46.1394 1.72431
\(717\) −1.67845 −0.0626828
\(718\) 36.8021 1.37344
\(719\) 9.61388 0.358537 0.179269 0.983800i \(-0.442627\pi\)
0.179269 + 0.983800i \(0.442627\pi\)
\(720\) 0 0
\(721\) −18.0622 −0.672671
\(722\) 2.61330 0.0972571
\(723\) 24.8403 0.923821
\(724\) 29.1036 1.08163
\(725\) 0 0
\(726\) −3.12549 −0.115998
\(727\) −6.84046 −0.253699 −0.126849 0.991922i \(-0.540486\pi\)
−0.126849 + 0.991922i \(0.540486\pi\)
\(728\) −39.5570 −1.46608
\(729\) 22.4775 0.832501
\(730\) 0 0
\(731\) −17.5965 −0.650828
\(732\) 37.5238 1.38692
\(733\) −38.2277 −1.41197 −0.705987 0.708225i \(-0.749496\pi\)
−0.705987 + 0.708225i \(0.749496\pi\)
\(734\) −55.7005 −2.05594
\(735\) 0 0
\(736\) 78.0620 2.87740
\(737\) −3.70989 −0.136656
\(738\) 16.0978 0.592567
\(739\) −17.7157 −0.651682 −0.325841 0.945425i \(-0.605647\pi\)
−0.325841 + 0.945425i \(0.605647\pi\)
\(740\) 0 0
\(741\) −1.76836 −0.0649622
\(742\) −0.973009 −0.0357203
\(743\) −21.3028 −0.781525 −0.390763 0.920491i \(-0.627789\pi\)
−0.390763 + 0.920491i \(0.627789\pi\)
\(744\) −14.5842 −0.534682
\(745\) 0 0
\(746\) 6.32650 0.231630
\(747\) 8.53960 0.312447
\(748\) −15.7921 −0.577418
\(749\) 26.4622 0.966908
\(750\) 0 0
\(751\) 25.1552 0.917926 0.458963 0.888455i \(-0.348221\pi\)
0.458963 + 0.888455i \(0.348221\pi\)
\(752\) 35.9111 1.30954
\(753\) 1.55402 0.0566317
\(754\) 3.96190 0.144284
\(755\) 0 0
\(756\) −95.4992 −3.47327
\(757\) −15.5116 −0.563780 −0.281890 0.959447i \(-0.590961\pi\)
−0.281890 + 0.959447i \(0.590961\pi\)
\(758\) 23.1940 0.842443
\(759\) 8.91962 0.323762
\(760\) 0 0
\(761\) 35.2085 1.27631 0.638154 0.769908i \(-0.279698\pi\)
0.638154 + 0.769908i \(0.279698\pi\)
\(762\) −14.6802 −0.531807
\(763\) 5.22779 0.189259
\(764\) 85.5129 3.09375
\(765\) 0 0
\(766\) 9.25280 0.334317
\(767\) 19.6630 0.709988
\(768\) 19.0750 0.688310
\(769\) −5.57667 −0.201100 −0.100550 0.994932i \(-0.532060\pi\)
−0.100550 + 0.994932i \(0.532060\pi\)
\(770\) 0 0
\(771\) 4.08095 0.146972
\(772\) −17.8371 −0.641973
\(773\) −35.9175 −1.29186 −0.645931 0.763396i \(-0.723531\pi\)
−0.645931 + 0.763396i \(0.723531\pi\)
\(774\) 22.0726 0.793383
\(775\) 0 0
\(776\) 101.970 3.66052
\(777\) 29.0499 1.04216
\(778\) −43.6530 −1.56503
\(779\) −3.92451 −0.140610
\(780\) 0 0
\(781\) −6.32968 −0.226494
\(782\) 63.7324 2.27906
\(783\) 5.60375 0.200262
\(784\) 58.8734 2.10262
\(785\) 0 0
\(786\) −11.7039 −0.417464
\(787\) −7.53242 −0.268502 −0.134251 0.990947i \(-0.542863\pi\)
−0.134251 + 0.990947i \(0.542863\pi\)
\(788\) 124.496 4.43497
\(789\) 17.0331 0.606395
\(790\) 0 0
\(791\) −43.5531 −1.54857
\(792\) 11.6056 0.412387
\(793\) −9.60573 −0.341110
\(794\) −73.7141 −2.61602
\(795\) 0 0
\(796\) 91.2522 3.23435
\(797\) 49.3837 1.74926 0.874629 0.484792i \(-0.161105\pi\)
0.874629 + 0.484792i \(0.161105\pi\)
\(798\) 11.3089 0.400332
\(799\) 12.1513 0.429883
\(800\) 0 0
\(801\) −19.0482 −0.673036
\(802\) −94.6219 −3.34122
\(803\) −1.37759 −0.0486141
\(804\) −21.4278 −0.755702
\(805\) 0 0
\(806\) 6.37247 0.224461
\(807\) −6.45210 −0.227125
\(808\) −81.3549 −2.86205
\(809\) 34.4637 1.21168 0.605840 0.795587i \(-0.292837\pi\)
0.605840 + 0.795587i \(0.292837\pi\)
\(810\) 0 0
\(811\) 20.0278 0.703272 0.351636 0.936137i \(-0.385625\pi\)
0.351636 + 0.936137i \(0.385625\pi\)
\(812\) −17.9170 −0.628763
\(813\) 13.2306 0.464017
\(814\) −17.5429 −0.614879
\(815\) 0 0
\(816\) −37.7952 −1.32310
\(817\) −5.38113 −0.188262
\(818\) 96.4926 3.37379
\(819\) 8.39722 0.293423
\(820\) 0 0
\(821\) 6.45245 0.225192 0.112596 0.993641i \(-0.464083\pi\)
0.112596 + 0.993641i \(0.464083\pi\)
\(822\) −49.2562 −1.71801
\(823\) 43.0190 1.49955 0.749774 0.661694i \(-0.230162\pi\)
0.749774 + 0.661694i \(0.230162\pi\)
\(824\) 36.9100 1.28582
\(825\) 0 0
\(826\) −125.748 −4.37533
\(827\) 43.1557 1.50067 0.750335 0.661058i \(-0.229892\pi\)
0.750335 + 0.661058i \(0.229892\pi\)
\(828\) −56.5324 −1.96464
\(829\) 13.4937 0.468656 0.234328 0.972158i \(-0.424711\pi\)
0.234328 + 0.972158i \(0.424711\pi\)
\(830\) 0 0
\(831\) 16.8406 0.584193
\(832\) 11.8662 0.411385
\(833\) 19.9212 0.690228
\(834\) 7.90191 0.273621
\(835\) 0 0
\(836\) −4.82936 −0.167027
\(837\) 9.01329 0.311545
\(838\) 47.2197 1.63118
\(839\) −14.6851 −0.506988 −0.253494 0.967337i \(-0.581580\pi\)
−0.253494 + 0.967337i \(0.581580\pi\)
\(840\) 0 0
\(841\) −27.9487 −0.963747
\(842\) −22.4124 −0.772384
\(843\) 12.9405 0.445693
\(844\) −49.2562 −1.69547
\(845\) 0 0
\(846\) −15.2424 −0.524043
\(847\) −3.61829 −0.124326
\(848\) 0.994441 0.0341493
\(849\) 2.28372 0.0783769
\(850\) 0 0
\(851\) 50.0645 1.71619
\(852\) −36.5594 −1.25250
\(853\) 51.5775 1.76598 0.882990 0.469392i \(-0.155527\pi\)
0.882990 + 0.469392i \(0.155527\pi\)
\(854\) 61.4303 2.10210
\(855\) 0 0
\(856\) −54.0755 −1.84826
\(857\) 46.6355 1.59304 0.796520 0.604612i \(-0.206672\pi\)
0.796520 + 0.604612i \(0.206672\pi\)
\(858\) 4.62125 0.157767
\(859\) −18.6711 −0.637048 −0.318524 0.947915i \(-0.603187\pi\)
−0.318524 + 0.947915i \(0.603187\pi\)
\(860\) 0 0
\(861\) −16.9831 −0.578783
\(862\) 11.1888 0.381091
\(863\) −43.0160 −1.46428 −0.732141 0.681153i \(-0.761479\pi\)
−0.732141 + 0.681153i \(0.761479\pi\)
\(864\) 57.2042 1.94613
\(865\) 0 0
\(866\) −47.5712 −1.61654
\(867\) 7.54300 0.256174
\(868\) −28.8184 −0.978160
\(869\) −13.6725 −0.463809
\(870\) 0 0
\(871\) 5.48533 0.185863
\(872\) −10.6830 −0.361771
\(873\) −21.6464 −0.732619
\(874\) 19.4898 0.659253
\(875\) 0 0
\(876\) −7.95678 −0.268835
\(877\) −56.0429 −1.89243 −0.946217 0.323534i \(-0.895129\pi\)
−0.946217 + 0.323534i \(0.895129\pi\)
\(878\) 76.9466 2.59682
\(879\) 4.34803 0.146655
\(880\) 0 0
\(881\) 17.9947 0.606257 0.303128 0.952950i \(-0.401969\pi\)
0.303128 + 0.952950i \(0.401969\pi\)
\(882\) −24.9887 −0.841412
\(883\) −1.99550 −0.0671540 −0.0335770 0.999436i \(-0.510690\pi\)
−0.0335770 + 0.999436i \(0.510690\pi\)
\(884\) 23.3498 0.785339
\(885\) 0 0
\(886\) 63.6687 2.13899
\(887\) −7.20927 −0.242063 −0.121032 0.992649i \(-0.538620\pi\)
−0.121032 + 0.992649i \(0.538620\pi\)
\(888\) −59.3633 −1.99210
\(889\) −16.9948 −0.569988
\(890\) 0 0
\(891\) 1.82753 0.0612246
\(892\) 1.26867 0.0424782
\(893\) 3.71597 0.124350
\(894\) −5.77909 −0.193282
\(895\) 0 0
\(896\) −0.140902 −0.00470720
\(897\) −13.1883 −0.440344
\(898\) 101.338 3.38168
\(899\) 1.69102 0.0563986
\(900\) 0 0
\(901\) 0.336492 0.0112102
\(902\) 10.2559 0.341485
\(903\) −23.2866 −0.774928
\(904\) 89.0006 2.96012
\(905\) 0 0
\(906\) 47.8774 1.59062
\(907\) 25.7832 0.856116 0.428058 0.903751i \(-0.359198\pi\)
0.428058 + 0.903751i \(0.359198\pi\)
\(908\) −131.965 −4.37942
\(909\) 17.2701 0.572814
\(910\) 0 0
\(911\) 31.1334 1.03149 0.515747 0.856741i \(-0.327514\pi\)
0.515747 + 0.856741i \(0.327514\pi\)
\(912\) −11.5580 −0.382725
\(913\) 5.44061 0.180058
\(914\) 19.5389 0.646291
\(915\) 0 0
\(916\) −26.7146 −0.882676
\(917\) −13.5493 −0.447437
\(918\) 46.7034 1.54144
\(919\) 5.42725 0.179029 0.0895143 0.995986i \(-0.471469\pi\)
0.0895143 + 0.995986i \(0.471469\pi\)
\(920\) 0 0
\(921\) −28.1452 −0.927416
\(922\) 41.7560 1.37516
\(923\) 9.35887 0.308051
\(924\) −20.8988 −0.687520
\(925\) 0 0
\(926\) 15.9469 0.524049
\(927\) −7.83531 −0.257345
\(928\) 10.7323 0.352305
\(929\) −21.6025 −0.708756 −0.354378 0.935102i \(-0.615307\pi\)
−0.354378 + 0.935102i \(0.615307\pi\)
\(930\) 0 0
\(931\) 6.09205 0.199659
\(932\) −132.678 −4.34603
\(933\) 19.1390 0.626583
\(934\) 69.6113 2.27775
\(935\) 0 0
\(936\) −17.1597 −0.560882
\(937\) −31.6840 −1.03507 −0.517536 0.855661i \(-0.673151\pi\)
−0.517536 + 0.855661i \(0.673151\pi\)
\(938\) −35.0796 −1.14539
\(939\) 19.1399 0.624608
\(940\) 0 0
\(941\) −5.63987 −0.183854 −0.0919272 0.995766i \(-0.529303\pi\)
−0.0919272 + 0.995766i \(0.529303\pi\)
\(942\) 77.0843 2.51154
\(943\) −29.2687 −0.953120
\(944\) 128.518 4.18290
\(945\) 0 0
\(946\) 14.0625 0.457212
\(947\) 51.7369 1.68122 0.840611 0.541639i \(-0.182196\pi\)
0.840611 + 0.541639i \(0.182196\pi\)
\(948\) −78.9709 −2.56486
\(949\) 2.03686 0.0661194
\(950\) 0 0
\(951\) −24.9682 −0.809650
\(952\) −87.4850 −2.83540
\(953\) 16.2553 0.526561 0.263281 0.964719i \(-0.415196\pi\)
0.263281 + 0.964719i \(0.415196\pi\)
\(954\) −0.422088 −0.0136656
\(955\) 0 0
\(956\) 6.77750 0.219200
\(957\) 1.22631 0.0396410
\(958\) −42.3601 −1.36859
\(959\) −57.0225 −1.84135
\(960\) 0 0
\(961\) −28.2801 −0.912261
\(962\) 25.9384 0.836289
\(963\) 11.4792 0.369913
\(964\) −100.304 −3.23057
\(965\) 0 0
\(966\) 84.3413 2.71364
\(967\) 54.5004 1.75261 0.876307 0.481754i \(-0.160000\pi\)
0.876307 + 0.481754i \(0.160000\pi\)
\(968\) 7.39397 0.237651
\(969\) −3.91093 −0.125637
\(970\) 0 0
\(971\) −34.2679 −1.09971 −0.549855 0.835260i \(-0.685317\pi\)
−0.549855 + 0.835260i \(0.685317\pi\)
\(972\) −68.6247 −2.20114
\(973\) 9.14783 0.293266
\(974\) 12.6078 0.403981
\(975\) 0 0
\(976\) −62.7834 −2.00965
\(977\) −55.5644 −1.77766 −0.888831 0.458234i \(-0.848482\pi\)
−0.888831 + 0.458234i \(0.848482\pi\)
\(978\) −11.6315 −0.371934
\(979\) −12.1357 −0.387858
\(980\) 0 0
\(981\) 2.26780 0.0724052
\(982\) −22.3066 −0.711832
\(983\) 41.3971 1.32036 0.660181 0.751106i \(-0.270479\pi\)
0.660181 + 0.751106i \(0.270479\pi\)
\(984\) 34.7049 1.10635
\(985\) 0 0
\(986\) 8.76221 0.279046
\(987\) 16.0807 0.511853
\(988\) 7.14054 0.227171
\(989\) −40.1321 −1.27613
\(990\) 0 0
\(991\) 60.8219 1.93207 0.966036 0.258406i \(-0.0831973\pi\)
0.966036 + 0.258406i \(0.0831973\pi\)
\(992\) 17.2623 0.548077
\(993\) −18.0758 −0.573618
\(994\) −59.8515 −1.89837
\(995\) 0 0
\(996\) 31.4242 0.995715
\(997\) −26.0627 −0.825414 −0.412707 0.910864i \(-0.635417\pi\)
−0.412707 + 0.910864i \(0.635417\pi\)
\(998\) −35.1031 −1.11117
\(999\) 36.6876 1.16074
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 5225.2.a.n.1.6 7
5.4 even 2 209.2.a.d.1.2 7
15.14 odd 2 1881.2.a.p.1.6 7
20.19 odd 2 3344.2.a.ba.1.4 7
55.54 odd 2 2299.2.a.q.1.6 7
95.94 odd 2 3971.2.a.i.1.6 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
209.2.a.d.1.2 7 5.4 even 2
1881.2.a.p.1.6 7 15.14 odd 2
2299.2.a.q.1.6 7 55.54 odd 2
3344.2.a.ba.1.4 7 20.19 odd 2
3971.2.a.i.1.6 7 95.94 odd 2
5225.2.a.n.1.6 7 1.1 even 1 trivial