Properties

Label 8025.2.a.bb.1.5
Level $8025$
Weight $2$
Character 8025.1
Self dual yes
Analytic conductor $64.080$
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] = [8025,2,Mod(1,8025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8025, 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("8025.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8025 = 3 \cdot 5^{2} \cdot 107 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8025.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: \(64.0799476221\)
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: \( x^{7} - 3x^{6} - 9x^{5} + 24x^{4} + 13x^{3} - 47x^{2} + 19x - 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 321)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-1.83986\) of defining polynomial
Character \(\chi\) \(=\) 8025.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.726480 q^{2} +1.00000 q^{3} -1.47223 q^{4} +0.726480 q^{6} -3.04775 q^{7} -2.52250 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+0.726480 q^{2} +1.00000 q^{3} -1.47223 q^{4} +0.726480 q^{6} -3.04775 q^{7} -2.52250 q^{8} +1.00000 q^{9} -4.61409 q^{11} -1.47223 q^{12} +0.527054 q^{13} -2.21413 q^{14} +1.11190 q^{16} -5.95072 q^{17} +0.726480 q^{18} +3.68708 q^{19} -3.04775 q^{21} -3.35205 q^{22} -7.43002 q^{23} -2.52250 q^{24} +0.382895 q^{26} +1.00000 q^{27} +4.48698 q^{28} +1.45296 q^{29} -3.38618 q^{31} +5.85278 q^{32} -4.61409 q^{33} -4.32308 q^{34} -1.47223 q^{36} -5.96860 q^{37} +2.67859 q^{38} +0.527054 q^{39} -4.67325 q^{41} -2.21413 q^{42} -5.43062 q^{43} +6.79299 q^{44} -5.39776 q^{46} +11.1597 q^{47} +1.11190 q^{48} +2.28878 q^{49} -5.95072 q^{51} -0.775943 q^{52} -0.271205 q^{53} +0.726480 q^{54} +7.68796 q^{56} +3.68708 q^{57} +1.05555 q^{58} +7.51794 q^{59} +5.61419 q^{61} -2.45999 q^{62} -3.04775 q^{63} +2.02813 q^{64} -3.35205 q^{66} +10.5410 q^{67} +8.76080 q^{68} -7.43002 q^{69} +15.4009 q^{71} -2.52250 q^{72} +1.83822 q^{73} -4.33607 q^{74} -5.42821 q^{76} +14.0626 q^{77} +0.382895 q^{78} +7.04158 q^{79} +1.00000 q^{81} -3.39502 q^{82} -8.68125 q^{83} +4.48698 q^{84} -3.94524 q^{86} +1.45296 q^{87} +11.6391 q^{88} +0.0613646 q^{89} -1.60633 q^{91} +10.9387 q^{92} -3.38618 q^{93} +8.10730 q^{94} +5.85278 q^{96} -4.65646 q^{97} +1.66275 q^{98} -4.61409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 7 q + 7 q^{3} + 14 q^{4} - 6 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 7 q + 7 q^{3} + 14 q^{4} - 6 q^{7} - 3 q^{8} + 7 q^{9} + 4 q^{11} + 14 q^{12} - 6 q^{13} + 12 q^{14} + 32 q^{16} + 10 q^{17} + 8 q^{19} - 6 q^{21} - 10 q^{22} - 6 q^{23} - 3 q^{24} + 7 q^{26} + 7 q^{27} - 8 q^{28} + 16 q^{31} - 6 q^{32} + 4 q^{33} - 11 q^{34} + 14 q^{36} - 10 q^{37} + 13 q^{38} - 6 q^{39} - 2 q^{41} + 12 q^{42} - 2 q^{43} + 2 q^{44} - 30 q^{46} - 16 q^{47} + 32 q^{48} + 17 q^{49} + 10 q^{51} + 23 q^{52} + 16 q^{53} + 30 q^{56} + 8 q^{57} + 56 q^{58} + 20 q^{59} + 2 q^{61} + 52 q^{62} - 6 q^{63} + 43 q^{64} - 10 q^{66} - 30 q^{67} + 61 q^{68} - 6 q^{69} + 32 q^{71} - 3 q^{72} + 12 q^{73} - q^{74} - 49 q^{76} + 46 q^{77} + 7 q^{78} + 36 q^{79} + 7 q^{81} - 2 q^{82} + 10 q^{83} - 8 q^{84} - 20 q^{86} + 14 q^{88} - 4 q^{89} + 12 q^{91} - 10 q^{92} + 16 q^{93} - 26 q^{94} - 6 q^{96} - 24 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.726480 0.513699 0.256850 0.966451i \(-0.417316\pi\)
0.256850 + 0.966451i \(0.417316\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.47223 −0.736113
\(5\) 0 0
\(6\) 0.726480 0.296584
\(7\) −3.04775 −1.15194 −0.575971 0.817470i \(-0.695376\pi\)
−0.575971 + 0.817470i \(0.695376\pi\)
\(8\) −2.52250 −0.891840
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −4.61409 −1.39120 −0.695601 0.718429i \(-0.744862\pi\)
−0.695601 + 0.718429i \(0.744862\pi\)
\(12\) −1.47223 −0.424995
\(13\) 0.527054 0.146179 0.0730893 0.997325i \(-0.476714\pi\)
0.0730893 + 0.997325i \(0.476714\pi\)
\(14\) −2.21413 −0.591751
\(15\) 0 0
\(16\) 1.11190 0.277976
\(17\) −5.95072 −1.44326 −0.721630 0.692279i \(-0.756607\pi\)
−0.721630 + 0.692279i \(0.756607\pi\)
\(18\) 0.726480 0.171233
\(19\) 3.68708 0.845873 0.422937 0.906159i \(-0.360999\pi\)
0.422937 + 0.906159i \(0.360999\pi\)
\(20\) 0 0
\(21\) −3.04775 −0.665074
\(22\) −3.35205 −0.714659
\(23\) −7.43002 −1.54927 −0.774633 0.632411i \(-0.782065\pi\)
−0.774633 + 0.632411i \(0.782065\pi\)
\(24\) −2.52250 −0.514904
\(25\) 0 0
\(26\) 0.382895 0.0750918
\(27\) 1.00000 0.192450
\(28\) 4.48698 0.847959
\(29\) 1.45296 0.269808 0.134904 0.990859i \(-0.456927\pi\)
0.134904 + 0.990859i \(0.456927\pi\)
\(30\) 0 0
\(31\) −3.38618 −0.608176 −0.304088 0.952644i \(-0.598352\pi\)
−0.304088 + 0.952644i \(0.598352\pi\)
\(32\) 5.85278 1.03464
\(33\) −4.61409 −0.803210
\(34\) −4.32308 −0.741402
\(35\) 0 0
\(36\) −1.47223 −0.245371
\(37\) −5.96860 −0.981232 −0.490616 0.871376i \(-0.663228\pi\)
−0.490616 + 0.871376i \(0.663228\pi\)
\(38\) 2.67859 0.434524
\(39\) 0.527054 0.0843962
\(40\) 0 0
\(41\) −4.67325 −0.729839 −0.364919 0.931039i \(-0.618903\pi\)
−0.364919 + 0.931039i \(0.618903\pi\)
\(42\) −2.21413 −0.341648
\(43\) −5.43062 −0.828162 −0.414081 0.910240i \(-0.635897\pi\)
−0.414081 + 0.910240i \(0.635897\pi\)
\(44\) 6.79299 1.02408
\(45\) 0 0
\(46\) −5.39776 −0.795857
\(47\) 11.1597 1.62781 0.813904 0.580999i \(-0.197338\pi\)
0.813904 + 0.580999i \(0.197338\pi\)
\(48\) 1.11190 0.160489
\(49\) 2.28878 0.326968
\(50\) 0 0
\(51\) −5.95072 −0.833267
\(52\) −0.775943 −0.107604
\(53\) −0.271205 −0.0372529 −0.0186265 0.999827i \(-0.505929\pi\)
−0.0186265 + 0.999827i \(0.505929\pi\)
\(54\) 0.726480 0.0988615
\(55\) 0 0
\(56\) 7.68796 1.02735
\(57\) 3.68708 0.488365
\(58\) 1.05555 0.138600
\(59\) 7.51794 0.978753 0.489376 0.872073i \(-0.337224\pi\)
0.489376 + 0.872073i \(0.337224\pi\)
\(60\) 0 0
\(61\) 5.61419 0.718823 0.359412 0.933179i \(-0.382977\pi\)
0.359412 + 0.933179i \(0.382977\pi\)
\(62\) −2.45999 −0.312420
\(63\) −3.04775 −0.383980
\(64\) 2.02813 0.253516
\(65\) 0 0
\(66\) −3.35205 −0.412608
\(67\) 10.5410 1.28778 0.643892 0.765116i \(-0.277318\pi\)
0.643892 + 0.765116i \(0.277318\pi\)
\(68\) 8.76080 1.06240
\(69\) −7.43002 −0.894469
\(70\) 0 0
\(71\) 15.4009 1.82775 0.913877 0.405990i \(-0.133073\pi\)
0.913877 + 0.405990i \(0.133073\pi\)
\(72\) −2.52250 −0.297280
\(73\) 1.83822 0.215147 0.107574 0.994197i \(-0.465692\pi\)
0.107574 + 0.994197i \(0.465692\pi\)
\(74\) −4.33607 −0.504058
\(75\) 0 0
\(76\) −5.42821 −0.622658
\(77\) 14.0626 1.60258
\(78\) 0.382895 0.0433543
\(79\) 7.04158 0.792240 0.396120 0.918199i \(-0.370356\pi\)
0.396120 + 0.918199i \(0.370356\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) −3.39502 −0.374917
\(83\) −8.68125 −0.952891 −0.476446 0.879204i \(-0.658075\pi\)
−0.476446 + 0.879204i \(0.658075\pi\)
\(84\) 4.48698 0.489569
\(85\) 0 0
\(86\) −3.94524 −0.425426
\(87\) 1.45296 0.155774
\(88\) 11.6391 1.24073
\(89\) 0.0613646 0.00650464 0.00325232 0.999995i \(-0.498965\pi\)
0.00325232 + 0.999995i \(0.498965\pi\)
\(90\) 0 0
\(91\) −1.60633 −0.168389
\(92\) 10.9387 1.14044
\(93\) −3.38618 −0.351131
\(94\) 8.10730 0.836204
\(95\) 0 0
\(96\) 5.85278 0.597347
\(97\) −4.65646 −0.472792 −0.236396 0.971657i \(-0.575966\pi\)
−0.236396 + 0.971657i \(0.575966\pi\)
\(98\) 1.66275 0.167963
\(99\) −4.61409 −0.463734
\(100\) 0 0
\(101\) 9.40708 0.936039 0.468020 0.883718i \(-0.344968\pi\)
0.468020 + 0.883718i \(0.344968\pi\)
\(102\) −4.32308 −0.428049
\(103\) −15.4272 −1.52008 −0.760042 0.649874i \(-0.774822\pi\)
−0.760042 + 0.649874i \(0.774822\pi\)
\(104\) −1.32950 −0.130368
\(105\) 0 0
\(106\) −0.197025 −0.0191368
\(107\) −1.00000 −0.0966736
\(108\) −1.47223 −0.141665
\(109\) −9.22379 −0.883479 −0.441739 0.897143i \(-0.645638\pi\)
−0.441739 + 0.897143i \(0.645638\pi\)
\(110\) 0 0
\(111\) −5.96860 −0.566514
\(112\) −3.38880 −0.320212
\(113\) −7.81945 −0.735592 −0.367796 0.929906i \(-0.619888\pi\)
−0.367796 + 0.929906i \(0.619888\pi\)
\(114\) 2.67859 0.250873
\(115\) 0 0
\(116\) −2.13909 −0.198609
\(117\) 0.527054 0.0487262
\(118\) 5.46164 0.502784
\(119\) 18.1363 1.66255
\(120\) 0 0
\(121\) 10.2898 0.935441
\(122\) 4.07860 0.369259
\(123\) −4.67325 −0.421373
\(124\) 4.98523 0.447687
\(125\) 0 0
\(126\) −2.21413 −0.197250
\(127\) −20.5133 −1.82026 −0.910131 0.414320i \(-0.864019\pi\)
−0.910131 + 0.414320i \(0.864019\pi\)
\(128\) −10.2322 −0.904405
\(129\) −5.43062 −0.478140
\(130\) 0 0
\(131\) 7.77818 0.679583 0.339791 0.940501i \(-0.389644\pi\)
0.339791 + 0.940501i \(0.389644\pi\)
\(132\) 6.79299 0.591254
\(133\) −11.2373 −0.974396
\(134\) 7.65781 0.661534
\(135\) 0 0
\(136\) 15.0107 1.28716
\(137\) 17.7918 1.52005 0.760027 0.649891i \(-0.225186\pi\)
0.760027 + 0.649891i \(0.225186\pi\)
\(138\) −5.39776 −0.459488
\(139\) 2.45851 0.208528 0.104264 0.994550i \(-0.466751\pi\)
0.104264 + 0.994550i \(0.466751\pi\)
\(140\) 0 0
\(141\) 11.1597 0.939816
\(142\) 11.1885 0.938916
\(143\) −2.43188 −0.203364
\(144\) 1.11190 0.0926586
\(145\) 0 0
\(146\) 1.33543 0.110521
\(147\) 2.28878 0.188775
\(148\) 8.78713 0.722297
\(149\) 12.4010 1.01593 0.507966 0.861377i \(-0.330398\pi\)
0.507966 + 0.861377i \(0.330398\pi\)
\(150\) 0 0
\(151\) −17.2238 −1.40165 −0.700826 0.713332i \(-0.747185\pi\)
−0.700826 + 0.713332i \(0.747185\pi\)
\(152\) −9.30066 −0.754383
\(153\) −5.95072 −0.481087
\(154\) 10.2162 0.823245
\(155\) 0 0
\(156\) −0.775943 −0.0621252
\(157\) 22.3958 1.78738 0.893689 0.448687i \(-0.148108\pi\)
0.893689 + 0.448687i \(0.148108\pi\)
\(158\) 5.11557 0.406973
\(159\) −0.271205 −0.0215080
\(160\) 0 0
\(161\) 22.6448 1.78466
\(162\) 0.726480 0.0570777
\(163\) 7.34210 0.575078 0.287539 0.957769i \(-0.407163\pi\)
0.287539 + 0.957769i \(0.407163\pi\)
\(164\) 6.88008 0.537244
\(165\) 0 0
\(166\) −6.30676 −0.489499
\(167\) −0.0802501 −0.00620994 −0.00310497 0.999995i \(-0.500988\pi\)
−0.00310497 + 0.999995i \(0.500988\pi\)
\(168\) 7.68796 0.593139
\(169\) −12.7222 −0.978632
\(170\) 0 0
\(171\) 3.68708 0.281958
\(172\) 7.99511 0.609621
\(173\) 0.445106 0.0338408 0.0169204 0.999857i \(-0.494614\pi\)
0.0169204 + 0.999857i \(0.494614\pi\)
\(174\) 1.05555 0.0800208
\(175\) 0 0
\(176\) −5.13042 −0.386720
\(177\) 7.51794 0.565083
\(178\) 0.0445802 0.00334143
\(179\) 16.6475 1.24430 0.622148 0.782900i \(-0.286260\pi\)
0.622148 + 0.782900i \(0.286260\pi\)
\(180\) 0 0
\(181\) −19.5686 −1.45452 −0.727262 0.686360i \(-0.759208\pi\)
−0.727262 + 0.686360i \(0.759208\pi\)
\(182\) −1.16697 −0.0865013
\(183\) 5.61419 0.415013
\(184\) 18.7423 1.38170
\(185\) 0 0
\(186\) −2.45999 −0.180376
\(187\) 27.4572 2.00787
\(188\) −16.4296 −1.19825
\(189\) −3.04775 −0.221691
\(190\) 0 0
\(191\) 7.03205 0.508821 0.254411 0.967096i \(-0.418119\pi\)
0.254411 + 0.967096i \(0.418119\pi\)
\(192\) 2.02813 0.146367
\(193\) −9.41610 −0.677785 −0.338893 0.940825i \(-0.610052\pi\)
−0.338893 + 0.940825i \(0.610052\pi\)
\(194\) −3.38283 −0.242873
\(195\) 0 0
\(196\) −3.36960 −0.240686
\(197\) 17.5470 1.25017 0.625087 0.780555i \(-0.285064\pi\)
0.625087 + 0.780555i \(0.285064\pi\)
\(198\) −3.35205 −0.238220
\(199\) −11.0431 −0.782824 −0.391412 0.920215i \(-0.628013\pi\)
−0.391412 + 0.920215i \(0.628013\pi\)
\(200\) 0 0
\(201\) 10.5410 0.743503
\(202\) 6.83406 0.480843
\(203\) −4.42826 −0.310803
\(204\) 8.76080 0.613379
\(205\) 0 0
\(206\) −11.2075 −0.780866
\(207\) −7.43002 −0.516422
\(208\) 0.586033 0.0406341
\(209\) −17.0125 −1.17678
\(210\) 0 0
\(211\) 15.8907 1.09396 0.546980 0.837146i \(-0.315778\pi\)
0.546980 + 0.837146i \(0.315778\pi\)
\(212\) 0.399276 0.0274224
\(213\) 15.4009 1.05525
\(214\) −0.726480 −0.0496612
\(215\) 0 0
\(216\) −2.52250 −0.171635
\(217\) 10.3202 0.700583
\(218\) −6.70090 −0.453842
\(219\) 1.83822 0.124215
\(220\) 0 0
\(221\) −3.13635 −0.210974
\(222\) −4.33607 −0.291018
\(223\) 14.8139 0.992009 0.496004 0.868320i \(-0.334800\pi\)
0.496004 + 0.868320i \(0.334800\pi\)
\(224\) −17.8378 −1.19184
\(225\) 0 0
\(226\) −5.68068 −0.377873
\(227\) −27.3563 −1.81570 −0.907849 0.419297i \(-0.862277\pi\)
−0.907849 + 0.419297i \(0.862277\pi\)
\(228\) −5.42821 −0.359492
\(229\) 22.7405 1.50273 0.751367 0.659884i \(-0.229395\pi\)
0.751367 + 0.659884i \(0.229395\pi\)
\(230\) 0 0
\(231\) 14.0626 0.925251
\(232\) −3.66510 −0.240626
\(233\) 14.0156 0.918191 0.459096 0.888387i \(-0.348174\pi\)
0.459096 + 0.888387i \(0.348174\pi\)
\(234\) 0.382895 0.0250306
\(235\) 0 0
\(236\) −11.0681 −0.720473
\(237\) 7.04158 0.457400
\(238\) 13.1757 0.854051
\(239\) 23.8481 1.54260 0.771302 0.636470i \(-0.219606\pi\)
0.771302 + 0.636470i \(0.219606\pi\)
\(240\) 0 0
\(241\) −8.16373 −0.525872 −0.262936 0.964813i \(-0.584691\pi\)
−0.262936 + 0.964813i \(0.584691\pi\)
\(242\) 7.47537 0.480535
\(243\) 1.00000 0.0641500
\(244\) −8.26536 −0.529135
\(245\) 0 0
\(246\) −3.39502 −0.216459
\(247\) 1.94329 0.123649
\(248\) 8.54166 0.542396
\(249\) −8.68125 −0.550152
\(250\) 0 0
\(251\) 8.33147 0.525878 0.262939 0.964812i \(-0.415308\pi\)
0.262939 + 0.964812i \(0.415308\pi\)
\(252\) 4.48698 0.282653
\(253\) 34.2828 2.15534
\(254\) −14.9025 −0.935067
\(255\) 0 0
\(256\) −11.4897 −0.718108
\(257\) 21.9193 1.36729 0.683643 0.729817i \(-0.260395\pi\)
0.683643 + 0.729817i \(0.260395\pi\)
\(258\) −3.94524 −0.245620
\(259\) 18.1908 1.13032
\(260\) 0 0
\(261\) 1.45296 0.0899360
\(262\) 5.65069 0.349101
\(263\) −22.0210 −1.35787 −0.678936 0.734198i \(-0.737559\pi\)
−0.678936 + 0.734198i \(0.737559\pi\)
\(264\) 11.6391 0.716335
\(265\) 0 0
\(266\) −8.16367 −0.500547
\(267\) 0.0613646 0.00375545
\(268\) −15.5187 −0.947955
\(269\) −20.8237 −1.26965 −0.634823 0.772658i \(-0.718927\pi\)
−0.634823 + 0.772658i \(0.718927\pi\)
\(270\) 0 0
\(271\) 13.4274 0.815656 0.407828 0.913059i \(-0.366286\pi\)
0.407828 + 0.913059i \(0.366286\pi\)
\(272\) −6.61662 −0.401191
\(273\) −1.60633 −0.0972195
\(274\) 12.9254 0.780850
\(275\) 0 0
\(276\) 10.9387 0.658431
\(277\) −30.2875 −1.81980 −0.909901 0.414826i \(-0.863842\pi\)
−0.909901 + 0.414826i \(0.863842\pi\)
\(278\) 1.78606 0.107121
\(279\) −3.38618 −0.202725
\(280\) 0 0
\(281\) −1.98260 −0.118272 −0.0591361 0.998250i \(-0.518835\pi\)
−0.0591361 + 0.998250i \(0.518835\pi\)
\(282\) 8.10730 0.482783
\(283\) 16.9481 1.00746 0.503730 0.863861i \(-0.331961\pi\)
0.503730 + 0.863861i \(0.331961\pi\)
\(284\) −22.6737 −1.34543
\(285\) 0 0
\(286\) −1.76671 −0.104468
\(287\) 14.2429 0.840731
\(288\) 5.85278 0.344879
\(289\) 18.4110 1.08300
\(290\) 0 0
\(291\) −4.65646 −0.272967
\(292\) −2.70627 −0.158373
\(293\) −1.05078 −0.0613872 −0.0306936 0.999529i \(-0.509772\pi\)
−0.0306936 + 0.999529i \(0.509772\pi\)
\(294\) 1.66275 0.0969737
\(295\) 0 0
\(296\) 15.0558 0.875101
\(297\) −4.61409 −0.267737
\(298\) 9.00910 0.521883
\(299\) −3.91602 −0.226470
\(300\) 0 0
\(301\) 16.5512 0.953994
\(302\) −12.5127 −0.720028
\(303\) 9.40708 0.540423
\(304\) 4.09967 0.235132
\(305\) 0 0
\(306\) −4.32308 −0.247134
\(307\) 28.4381 1.62305 0.811525 0.584317i \(-0.198638\pi\)
0.811525 + 0.584317i \(0.198638\pi\)
\(308\) −20.7033 −1.17968
\(309\) −15.4272 −0.877621
\(310\) 0 0
\(311\) −24.3839 −1.38268 −0.691342 0.722528i \(-0.742980\pi\)
−0.691342 + 0.722528i \(0.742980\pi\)
\(312\) −1.32950 −0.0752679
\(313\) 13.6663 0.772466 0.386233 0.922401i \(-0.373776\pi\)
0.386233 + 0.922401i \(0.373776\pi\)
\(314\) 16.2701 0.918175
\(315\) 0 0
\(316\) −10.3668 −0.583178
\(317\) 16.5706 0.930698 0.465349 0.885127i \(-0.345929\pi\)
0.465349 + 0.885127i \(0.345929\pi\)
\(318\) −0.197025 −0.0110486
\(319\) −6.70409 −0.375357
\(320\) 0 0
\(321\) −1.00000 −0.0558146
\(322\) 16.4510 0.916780
\(323\) −21.9407 −1.22082
\(324\) −1.47223 −0.0817904
\(325\) 0 0
\(326\) 5.33389 0.295417
\(327\) −9.22379 −0.510077
\(328\) 11.7883 0.650899
\(329\) −34.0120 −1.87514
\(330\) 0 0
\(331\) −1.89673 −0.104253 −0.0521267 0.998640i \(-0.516600\pi\)
−0.0521267 + 0.998640i \(0.516600\pi\)
\(332\) 12.7808 0.701436
\(333\) −5.96860 −0.327077
\(334\) −0.0583001 −0.00319004
\(335\) 0 0
\(336\) −3.38880 −0.184874
\(337\) −13.9796 −0.761517 −0.380759 0.924674i \(-0.624337\pi\)
−0.380759 + 0.924674i \(0.624337\pi\)
\(338\) −9.24244 −0.502722
\(339\) −7.81945 −0.424694
\(340\) 0 0
\(341\) 15.6242 0.846096
\(342\) 2.67859 0.144841
\(343\) 14.3586 0.775293
\(344\) 13.6988 0.738588
\(345\) 0 0
\(346\) 0.323361 0.0173840
\(347\) 4.94636 0.265534 0.132767 0.991147i \(-0.457614\pi\)
0.132767 + 0.991147i \(0.457614\pi\)
\(348\) −2.13909 −0.114667
\(349\) 21.4602 1.14874 0.574369 0.818596i \(-0.305247\pi\)
0.574369 + 0.818596i \(0.305247\pi\)
\(350\) 0 0
\(351\) 0.527054 0.0281321
\(352\) −27.0053 −1.43939
\(353\) 12.6360 0.672547 0.336274 0.941764i \(-0.390833\pi\)
0.336274 + 0.941764i \(0.390833\pi\)
\(354\) 5.46164 0.290283
\(355\) 0 0
\(356\) −0.0903426 −0.00478815
\(357\) 18.1363 0.959874
\(358\) 12.0941 0.639193
\(359\) 20.5962 1.08703 0.543513 0.839401i \(-0.317094\pi\)
0.543513 + 0.839401i \(0.317094\pi\)
\(360\) 0 0
\(361\) −5.40547 −0.284498
\(362\) −14.2162 −0.747188
\(363\) 10.2898 0.540077
\(364\) 2.36488 0.123953
\(365\) 0 0
\(366\) 4.07860 0.213192
\(367\) 12.3694 0.645677 0.322839 0.946454i \(-0.395363\pi\)
0.322839 + 0.946454i \(0.395363\pi\)
\(368\) −8.26146 −0.430658
\(369\) −4.67325 −0.243280
\(370\) 0 0
\(371\) 0.826566 0.0429132
\(372\) 4.98523 0.258472
\(373\) −22.5057 −1.16530 −0.582650 0.812724i \(-0.697984\pi\)
−0.582650 + 0.812724i \(0.697984\pi\)
\(374\) 19.9471 1.03144
\(375\) 0 0
\(376\) −28.1504 −1.45174
\(377\) 0.765789 0.0394401
\(378\) −2.21413 −0.113883
\(379\) −8.34910 −0.428864 −0.214432 0.976739i \(-0.568790\pi\)
−0.214432 + 0.976739i \(0.568790\pi\)
\(380\) 0 0
\(381\) −20.5133 −1.05093
\(382\) 5.10865 0.261381
\(383\) −26.5509 −1.35669 −0.678344 0.734744i \(-0.737302\pi\)
−0.678344 + 0.734744i \(0.737302\pi\)
\(384\) −10.2322 −0.522158
\(385\) 0 0
\(386\) −6.84061 −0.348178
\(387\) −5.43062 −0.276054
\(388\) 6.85537 0.348029
\(389\) 10.9539 0.555385 0.277693 0.960670i \(-0.410430\pi\)
0.277693 + 0.960670i \(0.410430\pi\)
\(390\) 0 0
\(391\) 44.2139 2.23600
\(392\) −5.77345 −0.291603
\(393\) 7.77818 0.392357
\(394\) 12.7476 0.642213
\(395\) 0 0
\(396\) 6.79299 0.341360
\(397\) 12.5411 0.629419 0.314709 0.949188i \(-0.398093\pi\)
0.314709 + 0.949188i \(0.398093\pi\)
\(398\) −8.02259 −0.402136
\(399\) −11.2373 −0.562568
\(400\) 0 0
\(401\) −25.7276 −1.28478 −0.642389 0.766379i \(-0.722056\pi\)
−0.642389 + 0.766379i \(0.722056\pi\)
\(402\) 7.65781 0.381937
\(403\) −1.78470 −0.0889023
\(404\) −13.8494 −0.689031
\(405\) 0 0
\(406\) −3.21704 −0.159659
\(407\) 27.5397 1.36509
\(408\) 15.0107 0.743141
\(409\) 7.58380 0.374995 0.187497 0.982265i \(-0.439962\pi\)
0.187497 + 0.982265i \(0.439962\pi\)
\(410\) 0 0
\(411\) 17.7918 0.877604
\(412\) 22.7123 1.11895
\(413\) −22.9128 −1.12747
\(414\) −5.39776 −0.265286
\(415\) 0 0
\(416\) 3.08473 0.151242
\(417\) 2.45851 0.120394
\(418\) −12.3593 −0.604511
\(419\) −25.1281 −1.22759 −0.613794 0.789466i \(-0.710357\pi\)
−0.613794 + 0.789466i \(0.710357\pi\)
\(420\) 0 0
\(421\) 10.8460 0.528604 0.264302 0.964440i \(-0.414859\pi\)
0.264302 + 0.964440i \(0.414859\pi\)
\(422\) 11.5443 0.561966
\(423\) 11.1597 0.542603
\(424\) 0.684116 0.0332236
\(425\) 0 0
\(426\) 11.1885 0.542083
\(427\) −17.1106 −0.828042
\(428\) 1.47223 0.0711627
\(429\) −2.43188 −0.117412
\(430\) 0 0
\(431\) 17.2467 0.830746 0.415373 0.909651i \(-0.363651\pi\)
0.415373 + 0.909651i \(0.363651\pi\)
\(432\) 1.11190 0.0534965
\(433\) 8.40039 0.403697 0.201849 0.979417i \(-0.435305\pi\)
0.201849 + 0.979417i \(0.435305\pi\)
\(434\) 7.49745 0.359889
\(435\) 0 0
\(436\) 13.5795 0.650340
\(437\) −27.3950 −1.31048
\(438\) 1.33543 0.0638093
\(439\) −20.5888 −0.982652 −0.491326 0.870976i \(-0.663488\pi\)
−0.491326 + 0.870976i \(0.663488\pi\)
\(440\) 0 0
\(441\) 2.28878 0.108989
\(442\) −2.27850 −0.108377
\(443\) 24.5763 1.16766 0.583828 0.811877i \(-0.301554\pi\)
0.583828 + 0.811877i \(0.301554\pi\)
\(444\) 8.78713 0.417019
\(445\) 0 0
\(446\) 10.7620 0.509594
\(447\) 12.4010 0.586549
\(448\) −6.18122 −0.292035
\(449\) 12.4259 0.586414 0.293207 0.956049i \(-0.405277\pi\)
0.293207 + 0.956049i \(0.405277\pi\)
\(450\) 0 0
\(451\) 21.5628 1.01535
\(452\) 11.5120 0.541479
\(453\) −17.2238 −0.809244
\(454\) −19.8738 −0.932723
\(455\) 0 0
\(456\) −9.30066 −0.435544
\(457\) −14.9004 −0.697012 −0.348506 0.937307i \(-0.613311\pi\)
−0.348506 + 0.937307i \(0.613311\pi\)
\(458\) 16.5205 0.771954
\(459\) −5.95072 −0.277756
\(460\) 0 0
\(461\) 14.0000 0.652043 0.326022 0.945362i \(-0.394292\pi\)
0.326022 + 0.945362i \(0.394292\pi\)
\(462\) 10.2162 0.475301
\(463\) −33.9468 −1.57764 −0.788822 0.614622i \(-0.789309\pi\)
−0.788822 + 0.614622i \(0.789309\pi\)
\(464\) 1.61555 0.0750001
\(465\) 0 0
\(466\) 10.1820 0.471674
\(467\) 13.8914 0.642817 0.321409 0.946941i \(-0.395844\pi\)
0.321409 + 0.946941i \(0.395844\pi\)
\(468\) −0.775943 −0.0358680
\(469\) −32.1262 −1.48345
\(470\) 0 0
\(471\) 22.3958 1.03194
\(472\) −18.9640 −0.872891
\(473\) 25.0574 1.15214
\(474\) 5.11557 0.234966
\(475\) 0 0
\(476\) −26.7007 −1.22383
\(477\) −0.271205 −0.0124176
\(478\) 17.3252 0.792434
\(479\) −11.7271 −0.535824 −0.267912 0.963443i \(-0.586334\pi\)
−0.267912 + 0.963443i \(0.586334\pi\)
\(480\) 0 0
\(481\) −3.14578 −0.143435
\(482\) −5.93079 −0.270140
\(483\) 22.6448 1.03038
\(484\) −15.1490 −0.688590
\(485\) 0 0
\(486\) 0.726480 0.0329538
\(487\) −9.82435 −0.445184 −0.222592 0.974912i \(-0.571452\pi\)
−0.222592 + 0.974912i \(0.571452\pi\)
\(488\) −14.1618 −0.641075
\(489\) 7.34210 0.332021
\(490\) 0 0
\(491\) −18.6602 −0.842121 −0.421061 0.907033i \(-0.638342\pi\)
−0.421061 + 0.907033i \(0.638342\pi\)
\(492\) 6.88008 0.310178
\(493\) −8.64616 −0.389403
\(494\) 1.41176 0.0635181
\(495\) 0 0
\(496\) −3.76511 −0.169058
\(497\) −46.9382 −2.10547
\(498\) −6.30676 −0.282613
\(499\) 19.9825 0.894540 0.447270 0.894399i \(-0.352396\pi\)
0.447270 + 0.894399i \(0.352396\pi\)
\(500\) 0 0
\(501\) −0.0802501 −0.00358531
\(502\) 6.05265 0.270143
\(503\) 4.02993 0.179686 0.0898428 0.995956i \(-0.471364\pi\)
0.0898428 + 0.995956i \(0.471364\pi\)
\(504\) 7.68796 0.342449
\(505\) 0 0
\(506\) 24.9058 1.10720
\(507\) −12.7222 −0.565013
\(508\) 30.2002 1.33992
\(509\) 1.34049 0.0594160 0.0297080 0.999559i \(-0.490542\pi\)
0.0297080 + 0.999559i \(0.490542\pi\)
\(510\) 0 0
\(511\) −5.60243 −0.247837
\(512\) 12.1173 0.535514
\(513\) 3.68708 0.162788
\(514\) 15.9239 0.702373
\(515\) 0 0
\(516\) 7.99511 0.351965
\(517\) −51.4919 −2.26461
\(518\) 13.2153 0.580645
\(519\) 0.445106 0.0195380
\(520\) 0 0
\(521\) −6.45034 −0.282594 −0.141297 0.989967i \(-0.545127\pi\)
−0.141297 + 0.989967i \(0.545127\pi\)
\(522\) 1.05555 0.0462001
\(523\) −15.7561 −0.688968 −0.344484 0.938792i \(-0.611946\pi\)
−0.344484 + 0.938792i \(0.611946\pi\)
\(524\) −11.4512 −0.500250
\(525\) 0 0
\(526\) −15.9978 −0.697538
\(527\) 20.1502 0.877757
\(528\) −5.13042 −0.223273
\(529\) 32.2052 1.40023
\(530\) 0 0
\(531\) 7.51794 0.326251
\(532\) 16.5438 0.717266
\(533\) −2.46306 −0.106687
\(534\) 0.0445802 0.00192917
\(535\) 0 0
\(536\) −26.5896 −1.14850
\(537\) 16.6475 0.718394
\(538\) −15.1280 −0.652216
\(539\) −10.5606 −0.454879
\(540\) 0 0
\(541\) −19.5027 −0.838485 −0.419242 0.907874i \(-0.637704\pi\)
−0.419242 + 0.907874i \(0.637704\pi\)
\(542\) 9.75473 0.419002
\(543\) −19.5686 −0.839770
\(544\) −34.8283 −1.49325
\(545\) 0 0
\(546\) −1.16697 −0.0499416
\(547\) −0.313021 −0.0133838 −0.00669192 0.999978i \(-0.502130\pi\)
−0.00669192 + 0.999978i \(0.502130\pi\)
\(548\) −26.1935 −1.11893
\(549\) 5.61419 0.239608
\(550\) 0 0
\(551\) 5.35718 0.228223
\(552\) 18.7423 0.797723
\(553\) −21.4610 −0.912614
\(554\) −22.0033 −0.934830
\(555\) 0 0
\(556\) −3.61949 −0.153501
\(557\) −26.0269 −1.10280 −0.551398 0.834243i \(-0.685905\pi\)
−0.551398 + 0.834243i \(0.685905\pi\)
\(558\) −2.45999 −0.104140
\(559\) −2.86223 −0.121060
\(560\) 0 0
\(561\) 27.4572 1.15924
\(562\) −1.44032 −0.0607563
\(563\) −26.1472 −1.10197 −0.550986 0.834515i \(-0.685748\pi\)
−0.550986 + 0.834515i \(0.685748\pi\)
\(564\) −16.4296 −0.691811
\(565\) 0 0
\(566\) 12.3125 0.517532
\(567\) −3.04775 −0.127993
\(568\) −38.8489 −1.63006
\(569\) −5.83479 −0.244607 −0.122304 0.992493i \(-0.539028\pi\)
−0.122304 + 0.992493i \(0.539028\pi\)
\(570\) 0 0
\(571\) 4.62287 0.193461 0.0967306 0.995311i \(-0.469161\pi\)
0.0967306 + 0.995311i \(0.469161\pi\)
\(572\) 3.58027 0.149699
\(573\) 7.03205 0.293768
\(574\) 10.3472 0.431883
\(575\) 0 0
\(576\) 2.02813 0.0845053
\(577\) −36.5940 −1.52343 −0.761713 0.647914i \(-0.775642\pi\)
−0.761713 + 0.647914i \(0.775642\pi\)
\(578\) 13.3752 0.556337
\(579\) −9.41610 −0.391320
\(580\) 0 0
\(581\) 26.4583 1.09767
\(582\) −3.38283 −0.140223
\(583\) 1.25137 0.0518263
\(584\) −4.63691 −0.191877
\(585\) 0 0
\(586\) −0.763371 −0.0315346
\(587\) 6.69597 0.276372 0.138186 0.990406i \(-0.455873\pi\)
0.138186 + 0.990406i \(0.455873\pi\)
\(588\) −3.36960 −0.138960
\(589\) −12.4851 −0.514440
\(590\) 0 0
\(591\) 17.5470 0.721788
\(592\) −6.63650 −0.272759
\(593\) 44.9423 1.84556 0.922780 0.385328i \(-0.125912\pi\)
0.922780 + 0.385328i \(0.125912\pi\)
\(594\) −3.35205 −0.137536
\(595\) 0 0
\(596\) −18.2571 −0.747841
\(597\) −11.0431 −0.451964
\(598\) −2.84491 −0.116337
\(599\) 41.6016 1.69979 0.849897 0.526948i \(-0.176664\pi\)
0.849897 + 0.526948i \(0.176664\pi\)
\(600\) 0 0
\(601\) −19.9505 −0.813796 −0.406898 0.913474i \(-0.633390\pi\)
−0.406898 + 0.913474i \(0.633390\pi\)
\(602\) 12.0241 0.490066
\(603\) 10.5410 0.429262
\(604\) 25.3573 1.03177
\(605\) 0 0
\(606\) 6.83406 0.277615
\(607\) 38.5437 1.56444 0.782220 0.623003i \(-0.214088\pi\)
0.782220 + 0.623003i \(0.214088\pi\)
\(608\) 21.5797 0.875171
\(609\) −4.42826 −0.179442
\(610\) 0 0
\(611\) 5.88176 0.237951
\(612\) 8.76080 0.354134
\(613\) −21.0071 −0.848471 −0.424235 0.905552i \(-0.639457\pi\)
−0.424235 + 0.905552i \(0.639457\pi\)
\(614\) 20.6598 0.833760
\(615\) 0 0
\(616\) −35.4730 −1.42925
\(617\) −10.1623 −0.409118 −0.204559 0.978854i \(-0.565576\pi\)
−0.204559 + 0.978854i \(0.565576\pi\)
\(618\) −11.2075 −0.450833
\(619\) 38.9227 1.56444 0.782218 0.623004i \(-0.214088\pi\)
0.782218 + 0.623004i \(0.214088\pi\)
\(620\) 0 0
\(621\) −7.43002 −0.298156
\(622\) −17.7144 −0.710284
\(623\) −0.187024 −0.00749296
\(624\) 0.586033 0.0234601
\(625\) 0 0
\(626\) 9.92831 0.396815
\(627\) −17.0125 −0.679414
\(628\) −32.9717 −1.31571
\(629\) 35.5174 1.41617
\(630\) 0 0
\(631\) −32.1333 −1.27921 −0.639603 0.768706i \(-0.720901\pi\)
−0.639603 + 0.768706i \(0.720901\pi\)
\(632\) −17.7624 −0.706551
\(633\) 15.8907 0.631598
\(634\) 12.0382 0.478099
\(635\) 0 0
\(636\) 0.399276 0.0158323
\(637\) 1.20631 0.0477958
\(638\) −4.87039 −0.192821
\(639\) 15.4009 0.609252
\(640\) 0 0
\(641\) −22.7046 −0.896776 −0.448388 0.893839i \(-0.648002\pi\)
−0.448388 + 0.893839i \(0.648002\pi\)
\(642\) −0.726480 −0.0286719
\(643\) 8.23270 0.324666 0.162333 0.986736i \(-0.448098\pi\)
0.162333 + 0.986736i \(0.448098\pi\)
\(644\) −33.3383 −1.31371
\(645\) 0 0
\(646\) −15.9395 −0.627132
\(647\) 47.5899 1.87095 0.935477 0.353388i \(-0.114970\pi\)
0.935477 + 0.353388i \(0.114970\pi\)
\(648\) −2.52250 −0.0990933
\(649\) −34.6885 −1.36164
\(650\) 0 0
\(651\) 10.3202 0.404482
\(652\) −10.8092 −0.423322
\(653\) −36.9870 −1.44741 −0.723707 0.690107i \(-0.757563\pi\)
−0.723707 + 0.690107i \(0.757563\pi\)
\(654\) −6.70090 −0.262026
\(655\) 0 0
\(656\) −5.19620 −0.202877
\(657\) 1.83822 0.0717157
\(658\) −24.7090 −0.963258
\(659\) 9.74467 0.379598 0.189799 0.981823i \(-0.439216\pi\)
0.189799 + 0.981823i \(0.439216\pi\)
\(660\) 0 0
\(661\) 15.1768 0.590308 0.295154 0.955450i \(-0.404629\pi\)
0.295154 + 0.955450i \(0.404629\pi\)
\(662\) −1.37793 −0.0535549
\(663\) −3.13635 −0.121806
\(664\) 21.8985 0.849826
\(665\) 0 0
\(666\) −4.33607 −0.168019
\(667\) −10.7955 −0.418004
\(668\) 0.118146 0.00457122
\(669\) 14.8139 0.572737
\(670\) 0 0
\(671\) −25.9044 −1.00003
\(672\) −17.8378 −0.688109
\(673\) 24.9994 0.963657 0.481828 0.876266i \(-0.339973\pi\)
0.481828 + 0.876266i \(0.339973\pi\)
\(674\) −10.1559 −0.391191
\(675\) 0 0
\(676\) 18.7300 0.720384
\(677\) −14.2024 −0.545842 −0.272921 0.962037i \(-0.587990\pi\)
−0.272921 + 0.962037i \(0.587990\pi\)
\(678\) −5.68068 −0.218165
\(679\) 14.1917 0.544629
\(680\) 0 0
\(681\) −27.3563 −1.04829
\(682\) 11.3506 0.434639
\(683\) 12.7506 0.487888 0.243944 0.969789i \(-0.421559\pi\)
0.243944 + 0.969789i \(0.421559\pi\)
\(684\) −5.42821 −0.207553
\(685\) 0 0
\(686\) 10.4313 0.398267
\(687\) 22.7405 0.867604
\(688\) −6.03833 −0.230209
\(689\) −0.142940 −0.00544558
\(690\) 0 0
\(691\) −31.1546 −1.18517 −0.592587 0.805506i \(-0.701894\pi\)
−0.592587 + 0.805506i \(0.701894\pi\)
\(692\) −0.655297 −0.0249106
\(693\) 14.0626 0.534194
\(694\) 3.59343 0.136405
\(695\) 0 0
\(696\) −3.66510 −0.138925
\(697\) 27.8092 1.05335
\(698\) 15.5904 0.590106
\(699\) 14.0156 0.530118
\(700\) 0 0
\(701\) 21.2223 0.801556 0.400778 0.916175i \(-0.368740\pi\)
0.400778 + 0.916175i \(0.368740\pi\)
\(702\) 0.382895 0.0144514
\(703\) −22.0067 −0.829997
\(704\) −9.35796 −0.352691
\(705\) 0 0
\(706\) 9.17982 0.345487
\(707\) −28.6704 −1.07826
\(708\) −11.0681 −0.415965
\(709\) −3.65794 −0.137377 −0.0686883 0.997638i \(-0.521881\pi\)
−0.0686883 + 0.997638i \(0.521881\pi\)
\(710\) 0 0
\(711\) 7.04158 0.264080
\(712\) −0.154792 −0.00580109
\(713\) 25.1594 0.942227
\(714\) 13.1757 0.493087
\(715\) 0 0
\(716\) −24.5089 −0.915942
\(717\) 23.8481 0.890623
\(718\) 14.9627 0.558404
\(719\) 0.812002 0.0302826 0.0151413 0.999885i \(-0.495180\pi\)
0.0151413 + 0.999885i \(0.495180\pi\)
\(720\) 0 0
\(721\) 47.0182 1.75105
\(722\) −3.92697 −0.146147
\(723\) −8.16373 −0.303613
\(724\) 28.8095 1.07069
\(725\) 0 0
\(726\) 7.47537 0.277437
\(727\) −24.0101 −0.890485 −0.445242 0.895410i \(-0.646882\pi\)
−0.445242 + 0.895410i \(0.646882\pi\)
\(728\) 4.05197 0.150176
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 32.3161 1.19525
\(732\) −8.26536 −0.305496
\(733\) −21.7704 −0.804108 −0.402054 0.915616i \(-0.631704\pi\)
−0.402054 + 0.915616i \(0.631704\pi\)
\(734\) 8.98612 0.331684
\(735\) 0 0
\(736\) −43.4863 −1.60293
\(737\) −48.6370 −1.79157
\(738\) −3.39502 −0.124972
\(739\) 27.0058 0.993423 0.496711 0.867916i \(-0.334541\pi\)
0.496711 + 0.867916i \(0.334541\pi\)
\(740\) 0 0
\(741\) 1.94329 0.0713885
\(742\) 0.600484 0.0220445
\(743\) 16.2017 0.594383 0.297192 0.954818i \(-0.403950\pi\)
0.297192 + 0.954818i \(0.403950\pi\)
\(744\) 8.54166 0.313152
\(745\) 0 0
\(746\) −16.3499 −0.598613
\(747\) −8.68125 −0.317630
\(748\) −40.4231 −1.47802
\(749\) 3.04775 0.111362
\(750\) 0 0
\(751\) 10.3599 0.378039 0.189019 0.981973i \(-0.439469\pi\)
0.189019 + 0.981973i \(0.439469\pi\)
\(752\) 12.4085 0.452491
\(753\) 8.33147 0.303616
\(754\) 0.556331 0.0202604
\(755\) 0 0
\(756\) 4.48698 0.163190
\(757\) 31.1950 1.13380 0.566901 0.823786i \(-0.308142\pi\)
0.566901 + 0.823786i \(0.308142\pi\)
\(758\) −6.06545 −0.220307
\(759\) 34.2828 1.24439
\(760\) 0 0
\(761\) 0.0943888 0.00342159 0.00171079 0.999999i \(-0.499455\pi\)
0.00171079 + 0.999999i \(0.499455\pi\)
\(762\) −14.9025 −0.539861
\(763\) 28.1118 1.01772
\(764\) −10.3528 −0.374550
\(765\) 0 0
\(766\) −19.2887 −0.696930
\(767\) 3.96236 0.143073
\(768\) −11.4897 −0.414600
\(769\) −38.6683 −1.39441 −0.697207 0.716870i \(-0.745574\pi\)
−0.697207 + 0.716870i \(0.745574\pi\)
\(770\) 0 0
\(771\) 21.9193 0.789403
\(772\) 13.8626 0.498927
\(773\) 24.3242 0.874879 0.437439 0.899248i \(-0.355885\pi\)
0.437439 + 0.899248i \(0.355885\pi\)
\(774\) −3.94524 −0.141809
\(775\) 0 0
\(776\) 11.7459 0.421655
\(777\) 18.1908 0.652591
\(778\) 7.95780 0.285301
\(779\) −17.2306 −0.617351
\(780\) 0 0
\(781\) −71.0613 −2.54277
\(782\) 32.1206 1.14863
\(783\) 1.45296 0.0519246
\(784\) 2.54490 0.0908893
\(785\) 0 0
\(786\) 5.65069 0.201554
\(787\) 27.6147 0.984358 0.492179 0.870494i \(-0.336201\pi\)
0.492179 + 0.870494i \(0.336201\pi\)
\(788\) −25.8332 −0.920269
\(789\) −22.0210 −0.783968
\(790\) 0 0
\(791\) 23.8317 0.847359
\(792\) 11.6391 0.413576
\(793\) 2.95898 0.105077
\(794\) 9.11085 0.323332
\(795\) 0 0
\(796\) 16.2579 0.576247
\(797\) 37.4117 1.32519 0.662594 0.748978i \(-0.269455\pi\)
0.662594 + 0.748978i \(0.269455\pi\)
\(798\) −8.16367 −0.288991
\(799\) −66.4082 −2.34935
\(800\) 0 0
\(801\) 0.0613646 0.00216821
\(802\) −18.6906 −0.659989
\(803\) −8.48171 −0.299313
\(804\) −15.5187 −0.547302
\(805\) 0 0
\(806\) −1.29655 −0.0456691
\(807\) −20.8237 −0.733030
\(808\) −23.7294 −0.834797
\(809\) 15.3385 0.539273 0.269636 0.962962i \(-0.413097\pi\)
0.269636 + 0.962962i \(0.413097\pi\)
\(810\) 0 0
\(811\) 4.81264 0.168995 0.0844974 0.996424i \(-0.473072\pi\)
0.0844974 + 0.996424i \(0.473072\pi\)
\(812\) 6.51940 0.228786
\(813\) 13.4274 0.470919
\(814\) 20.0070 0.701246
\(815\) 0 0
\(816\) −6.61662 −0.231628
\(817\) −20.0231 −0.700520
\(818\) 5.50948 0.192634
\(819\) −1.60633 −0.0561297
\(820\) 0 0
\(821\) −54.7554 −1.91098 −0.955489 0.295027i \(-0.904671\pi\)
−0.955489 + 0.295027i \(0.904671\pi\)
\(822\) 12.9254 0.450824
\(823\) −15.9383 −0.555573 −0.277787 0.960643i \(-0.589601\pi\)
−0.277787 + 0.960643i \(0.589601\pi\)
\(824\) 38.9151 1.35567
\(825\) 0 0
\(826\) −16.6457 −0.579178
\(827\) 25.3608 0.881882 0.440941 0.897536i \(-0.354645\pi\)
0.440941 + 0.897536i \(0.354645\pi\)
\(828\) 10.9387 0.380145
\(829\) 42.9249 1.49084 0.745422 0.666593i \(-0.232248\pi\)
0.745422 + 0.666593i \(0.232248\pi\)
\(830\) 0 0
\(831\) −30.2875 −1.05066
\(832\) 1.06893 0.0370586
\(833\) −13.6199 −0.471901
\(834\) 1.78606 0.0618463
\(835\) 0 0
\(836\) 25.0463 0.866243
\(837\) −3.38618 −0.117044
\(838\) −18.2551 −0.630611
\(839\) 33.1819 1.14557 0.572783 0.819707i \(-0.305864\pi\)
0.572783 + 0.819707i \(0.305864\pi\)
\(840\) 0 0
\(841\) −26.8889 −0.927204
\(842\) 7.87943 0.271543
\(843\) −1.98260 −0.0682845
\(844\) −23.3947 −0.805278
\(845\) 0 0
\(846\) 8.10730 0.278735
\(847\) −31.3609 −1.07757
\(848\) −0.301554 −0.0103554
\(849\) 16.9481 0.581658
\(850\) 0 0
\(851\) 44.3468 1.52019
\(852\) −22.6737 −0.776787
\(853\) −36.0092 −1.23293 −0.616466 0.787381i \(-0.711436\pi\)
−0.616466 + 0.787381i \(0.711436\pi\)
\(854\) −12.4305 −0.425364
\(855\) 0 0
\(856\) 2.52250 0.0862174
\(857\) 31.0229 1.05972 0.529861 0.848085i \(-0.322244\pi\)
0.529861 + 0.848085i \(0.322244\pi\)
\(858\) −1.76671 −0.0603145
\(859\) 1.54856 0.0528362 0.0264181 0.999651i \(-0.491590\pi\)
0.0264181 + 0.999651i \(0.491590\pi\)
\(860\) 0 0
\(861\) 14.2429 0.485396
\(862\) 12.5294 0.426754
\(863\) −3.60559 −0.122736 −0.0613679 0.998115i \(-0.519546\pi\)
−0.0613679 + 0.998115i \(0.519546\pi\)
\(864\) 5.85278 0.199116
\(865\) 0 0
\(866\) 6.10272 0.207379
\(867\) 18.4110 0.625271
\(868\) −15.1937 −0.515709
\(869\) −32.4905 −1.10217
\(870\) 0 0
\(871\) 5.55566 0.188247
\(872\) 23.2670 0.787922
\(873\) −4.65646 −0.157597
\(874\) −19.9020 −0.673194
\(875\) 0 0
\(876\) −2.70627 −0.0914365
\(877\) 40.2200 1.35813 0.679066 0.734077i \(-0.262385\pi\)
0.679066 + 0.734077i \(0.262385\pi\)
\(878\) −14.9574 −0.504787
\(879\) −1.05078 −0.0354419
\(880\) 0 0
\(881\) −25.2869 −0.851937 −0.425968 0.904738i \(-0.640067\pi\)
−0.425968 + 0.904738i \(0.640067\pi\)
\(882\) 1.66275 0.0559878
\(883\) −25.1997 −0.848038 −0.424019 0.905653i \(-0.639381\pi\)
−0.424019 + 0.905653i \(0.639381\pi\)
\(884\) 4.61742 0.155301
\(885\) 0 0
\(886\) 17.8542 0.599824
\(887\) −10.8673 −0.364887 −0.182443 0.983216i \(-0.558401\pi\)
−0.182443 + 0.983216i \(0.558401\pi\)
\(888\) 15.0558 0.505240
\(889\) 62.5194 2.09684
\(890\) 0 0
\(891\) −4.61409 −0.154578
\(892\) −21.8093 −0.730231
\(893\) 41.1466 1.37692
\(894\) 9.00910 0.301310
\(895\) 0 0
\(896\) 31.1851 1.04182
\(897\) −3.91602 −0.130752
\(898\) 9.02717 0.301241
\(899\) −4.91999 −0.164091
\(900\) 0 0
\(901\) 1.61387 0.0537657
\(902\) 15.6649 0.521586
\(903\) 16.5512 0.550789
\(904\) 19.7246 0.656030
\(905\) 0 0
\(906\) −12.5127 −0.415708
\(907\) −7.18720 −0.238647 −0.119324 0.992855i \(-0.538073\pi\)
−0.119324 + 0.992855i \(0.538073\pi\)
\(908\) 40.2746 1.33656
\(909\) 9.40708 0.312013
\(910\) 0 0
\(911\) −36.7220 −1.21665 −0.608327 0.793686i \(-0.708159\pi\)
−0.608327 + 0.793686i \(0.708159\pi\)
\(912\) 4.09967 0.135754
\(913\) 40.0561 1.32566
\(914\) −10.8249 −0.358054
\(915\) 0 0
\(916\) −33.4792 −1.10618
\(917\) −23.7059 −0.782839
\(918\) −4.32308 −0.142683
\(919\) 23.6711 0.780837 0.390418 0.920638i \(-0.372330\pi\)
0.390418 + 0.920638i \(0.372330\pi\)
\(920\) 0 0
\(921\) 28.4381 0.937069
\(922\) 10.1707 0.334954
\(923\) 8.11713 0.267179
\(924\) −20.7033 −0.681089
\(925\) 0 0
\(926\) −24.6617 −0.810434
\(927\) −15.4272 −0.506695
\(928\) 8.50386 0.279153
\(929\) −14.8209 −0.486258 −0.243129 0.969994i \(-0.578174\pi\)
−0.243129 + 0.969994i \(0.578174\pi\)
\(930\) 0 0
\(931\) 8.43890 0.276574
\(932\) −20.6341 −0.675893
\(933\) −24.3839 −0.798293
\(934\) 10.0918 0.330215
\(935\) 0 0
\(936\) −1.32950 −0.0434560
\(937\) −31.5111 −1.02942 −0.514712 0.857363i \(-0.672101\pi\)
−0.514712 + 0.857363i \(0.672101\pi\)
\(938\) −23.3391 −0.762048
\(939\) 13.6663 0.445983
\(940\) 0 0
\(941\) 22.9429 0.747916 0.373958 0.927446i \(-0.378000\pi\)
0.373958 + 0.927446i \(0.378000\pi\)
\(942\) 16.2701 0.530108
\(943\) 34.7223 1.13071
\(944\) 8.35922 0.272070
\(945\) 0 0
\(946\) 18.2037 0.591854
\(947\) −3.38995 −0.110158 −0.0550792 0.998482i \(-0.517541\pi\)
−0.0550792 + 0.998482i \(0.517541\pi\)
\(948\) −10.3668 −0.336698
\(949\) 0.968841 0.0314499
\(950\) 0 0
\(951\) 16.5706 0.537339
\(952\) −45.7489 −1.48273
\(953\) −33.1747 −1.07463 −0.537317 0.843380i \(-0.680562\pi\)
−0.537317 + 0.843380i \(0.680562\pi\)
\(954\) −0.197025 −0.00637893
\(955\) 0 0
\(956\) −35.1098 −1.13553
\(957\) −6.70409 −0.216713
\(958\) −8.51949 −0.275252
\(959\) −54.2249 −1.75101
\(960\) 0 0
\(961\) −19.5338 −0.630122
\(962\) −2.28534 −0.0736824
\(963\) −1.00000 −0.0322245
\(964\) 12.0189 0.387102
\(965\) 0 0
\(966\) 16.4510 0.529303
\(967\) −30.1127 −0.968359 −0.484179 0.874969i \(-0.660882\pi\)
−0.484179 + 0.874969i \(0.660882\pi\)
\(968\) −25.9562 −0.834263
\(969\) −21.9407 −0.704838
\(970\) 0 0
\(971\) 30.5503 0.980407 0.490203 0.871608i \(-0.336923\pi\)
0.490203 + 0.871608i \(0.336923\pi\)
\(972\) −1.47223 −0.0472217
\(973\) −7.49294 −0.240212
\(974\) −7.13719 −0.228690
\(975\) 0 0
\(976\) 6.24243 0.199815
\(977\) −39.0056 −1.24790 −0.623949 0.781465i \(-0.714473\pi\)
−0.623949 + 0.781465i \(0.714473\pi\)
\(978\) 5.33389 0.170559
\(979\) −0.283142 −0.00904926
\(980\) 0 0
\(981\) −9.22379 −0.294493
\(982\) −13.5562 −0.432597
\(983\) −18.6052 −0.593412 −0.296706 0.954969i \(-0.595888\pi\)
−0.296706 + 0.954969i \(0.595888\pi\)
\(984\) 11.7883 0.375797
\(985\) 0 0
\(986\) −6.28126 −0.200036
\(987\) −34.0120 −1.08261
\(988\) −2.86096 −0.0910193
\(989\) 40.3496 1.28304
\(990\) 0 0
\(991\) 42.5712 1.35232 0.676159 0.736755i \(-0.263643\pi\)
0.676159 + 0.736755i \(0.263643\pi\)
\(992\) −19.8186 −0.629241
\(993\) −1.89673 −0.0601908
\(994\) −34.0997 −1.08158
\(995\) 0 0
\(996\) 12.7808 0.404974
\(997\) −21.4879 −0.680528 −0.340264 0.940330i \(-0.610516\pi\)
−0.340264 + 0.940330i \(0.610516\pi\)
\(998\) 14.5169 0.459525
\(999\) −5.96860 −0.188838
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 8025.2.a.bb.1.5 7
5.4 even 2 321.2.a.d.1.3 7
15.14 odd 2 963.2.a.e.1.5 7
20.19 odd 2 5136.2.a.bi.1.2 7
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
321.2.a.d.1.3 7 5.4 even 2
963.2.a.e.1.5 7 15.14 odd 2
5136.2.a.bi.1.2 7 20.19 odd 2
8025.2.a.bb.1.5 7 1.1 even 1 trivial