Properties

Label 8085.2.a.ci.1.1
Level $8085$
Weight $2$
Character 8085.1
Self dual yes
Analytic conductor $64.559$
Analytic rank $1$
Dimension $10$
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] = [8085,2,Mod(1,8085)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8085, 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("8085.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8085.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: \(64.5590500342\)
Analytic rank: \(1\)
Dimension: \(10\)
Coefficient field: \(\mathbb{Q}[x]/(x^{10} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 104x^{5} + 40x^{4} + 104x^{3} - 48x^{2} - 32x + 14 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(2.64021\) of defining polynomial
Character \(\chi\) \(=\) 8085.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.64021 q^{2} -1.00000 q^{3} +4.97072 q^{4} -1.00000 q^{5} +2.64021 q^{6} -7.84333 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-2.64021 q^{2} -1.00000 q^{3} +4.97072 q^{4} -1.00000 q^{5} +2.64021 q^{6} -7.84333 q^{8} +1.00000 q^{9} +2.64021 q^{10} -1.00000 q^{11} -4.97072 q^{12} +1.46829 q^{13} +1.00000 q^{15} +10.7666 q^{16} -1.32245 q^{17} -2.64021 q^{18} +1.90824 q^{19} -4.97072 q^{20} +2.64021 q^{22} +6.10323 q^{23} +7.84333 q^{24} +1.00000 q^{25} -3.87661 q^{26} -1.00000 q^{27} -5.36654 q^{29} -2.64021 q^{30} +5.25881 q^{31} -12.7395 q^{32} +1.00000 q^{33} +3.49155 q^{34} +4.97072 q^{36} +0.910067 q^{37} -5.03815 q^{38} -1.46829 q^{39} +7.84333 q^{40} -7.64988 q^{41} -10.1646 q^{43} -4.97072 q^{44} -1.00000 q^{45} -16.1138 q^{46} -4.31503 q^{47} -10.7666 q^{48} -2.64021 q^{50} +1.32245 q^{51} +7.29847 q^{52} -3.12495 q^{53} +2.64021 q^{54} +1.00000 q^{55} -1.90824 q^{57} +14.1688 q^{58} +3.76158 q^{59} +4.97072 q^{60} +13.6215 q^{61} -13.8844 q^{62} +12.1017 q^{64} -1.46829 q^{65} -2.64021 q^{66} -10.7458 q^{67} -6.57353 q^{68} -6.10323 q^{69} +7.68712 q^{71} -7.84333 q^{72} +8.62258 q^{73} -2.40277 q^{74} -1.00000 q^{75} +9.48531 q^{76} +3.87661 q^{78} +4.43519 q^{79} -10.7666 q^{80} +1.00000 q^{81} +20.1973 q^{82} -15.3931 q^{83} +1.32245 q^{85} +26.8367 q^{86} +5.36654 q^{87} +7.84333 q^{88} +14.7962 q^{89} +2.64021 q^{90} +30.3374 q^{92} -5.25881 q^{93} +11.3926 q^{94} -1.90824 q^{95} +12.7395 q^{96} -10.5475 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10 q - 4 q^{2} - 10 q^{3} + 8 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 10 q - 4 q^{2} - 10 q^{3} + 8 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} + 10 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 8 q^{13} + 10 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} + 18 q^{19} - 8 q^{20} + 4 q^{22} - 18 q^{23} + 12 q^{24} + 10 q^{25} + 4 q^{26} - 10 q^{27} - 10 q^{29} - 4 q^{30} + 20 q^{31} - 28 q^{32} + 10 q^{33} + 16 q^{34} + 8 q^{36} - 4 q^{37} - 24 q^{38} - 8 q^{39} + 12 q^{40} + 16 q^{41} - 30 q^{43} - 8 q^{44} - 10 q^{45} - 12 q^{46} - 16 q^{47} - 4 q^{48} - 4 q^{50} - 2 q^{51} + 36 q^{52} - 14 q^{53} + 4 q^{54} + 10 q^{55} - 18 q^{57} - 4 q^{58} + 10 q^{59} + 8 q^{60} + 38 q^{61} + 20 q^{62} + 20 q^{64} - 8 q^{65} - 4 q^{66} - 16 q^{67} - 32 q^{68} + 18 q^{69} - 4 q^{71} - 12 q^{72} + 16 q^{73} - 4 q^{74} - 10 q^{75} + 48 q^{76} - 4 q^{78} - 28 q^{79} - 4 q^{80} + 10 q^{81} + 4 q^{82} - 2 q^{83} - 2 q^{85} + 16 q^{86} + 10 q^{87} + 12 q^{88} - 26 q^{89} + 4 q^{90} - 20 q^{93} + 36 q^{94} - 18 q^{95} + 28 q^{96} + 26 q^{97} - 10 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.64021 −1.86691 −0.933456 0.358692i \(-0.883223\pi\)
−0.933456 + 0.358692i \(0.883223\pi\)
\(3\) −1.00000 −0.577350
\(4\) 4.97072 2.48536
\(5\) −1.00000 −0.447214
\(6\) 2.64021 1.07786
\(7\) 0 0
\(8\) −7.84333 −2.77304
\(9\) 1.00000 0.333333
\(10\) 2.64021 0.834908
\(11\) −1.00000 −0.301511
\(12\) −4.97072 −1.43492
\(13\) 1.46829 0.407231 0.203616 0.979051i \(-0.434731\pi\)
0.203616 + 0.979051i \(0.434731\pi\)
\(14\) 0 0
\(15\) 1.00000 0.258199
\(16\) 10.7666 2.69165
\(17\) −1.32245 −0.320741 −0.160371 0.987057i \(-0.551269\pi\)
−0.160371 + 0.987057i \(0.551269\pi\)
\(18\) −2.64021 −0.622304
\(19\) 1.90824 0.437779 0.218890 0.975750i \(-0.429757\pi\)
0.218890 + 0.975750i \(0.429757\pi\)
\(20\) −4.97072 −1.11149
\(21\) 0 0
\(22\) 2.64021 0.562895
\(23\) 6.10323 1.27261 0.636305 0.771437i \(-0.280462\pi\)
0.636305 + 0.771437i \(0.280462\pi\)
\(24\) 7.84333 1.60101
\(25\) 1.00000 0.200000
\(26\) −3.87661 −0.760265
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −5.36654 −0.996542 −0.498271 0.867021i \(-0.666032\pi\)
−0.498271 + 0.867021i \(0.666032\pi\)
\(30\) −2.64021 −0.482035
\(31\) 5.25881 0.944509 0.472255 0.881462i \(-0.343440\pi\)
0.472255 + 0.881462i \(0.343440\pi\)
\(32\) −12.7395 −2.25204
\(33\) 1.00000 0.174078
\(34\) 3.49155 0.598795
\(35\) 0 0
\(36\) 4.97072 0.828453
\(37\) 0.910067 0.149614 0.0748070 0.997198i \(-0.476166\pi\)
0.0748070 + 0.997198i \(0.476166\pi\)
\(38\) −5.03815 −0.817295
\(39\) −1.46829 −0.235115
\(40\) 7.84333 1.24014
\(41\) −7.64988 −1.19471 −0.597355 0.801977i \(-0.703782\pi\)
−0.597355 + 0.801977i \(0.703782\pi\)
\(42\) 0 0
\(43\) −10.1646 −1.55008 −0.775042 0.631909i \(-0.782272\pi\)
−0.775042 + 0.631909i \(0.782272\pi\)
\(44\) −4.97072 −0.749364
\(45\) −1.00000 −0.149071
\(46\) −16.1138 −2.37585
\(47\) −4.31503 −0.629413 −0.314706 0.949189i \(-0.601906\pi\)
−0.314706 + 0.949189i \(0.601906\pi\)
\(48\) −10.7666 −1.55403
\(49\) 0 0
\(50\) −2.64021 −0.373382
\(51\) 1.32245 0.185180
\(52\) 7.29847 1.01212
\(53\) −3.12495 −0.429245 −0.214623 0.976697i \(-0.568852\pi\)
−0.214623 + 0.976697i \(0.568852\pi\)
\(54\) 2.64021 0.359287
\(55\) 1.00000 0.134840
\(56\) 0 0
\(57\) −1.90824 −0.252752
\(58\) 14.1688 1.86046
\(59\) 3.76158 0.489717 0.244858 0.969559i \(-0.421259\pi\)
0.244858 + 0.969559i \(0.421259\pi\)
\(60\) 4.97072 0.641717
\(61\) 13.6215 1.74405 0.872026 0.489460i \(-0.162806\pi\)
0.872026 + 0.489460i \(0.162806\pi\)
\(62\) −13.8844 −1.76332
\(63\) 0 0
\(64\) 12.1017 1.51271
\(65\) −1.46829 −0.182119
\(66\) −2.64021 −0.324988
\(67\) −10.7458 −1.31280 −0.656401 0.754412i \(-0.727922\pi\)
−0.656401 + 0.754412i \(0.727922\pi\)
\(68\) −6.57353 −0.797157
\(69\) −6.10323 −0.734742
\(70\) 0 0
\(71\) 7.68712 0.912294 0.456147 0.889905i \(-0.349229\pi\)
0.456147 + 0.889905i \(0.349229\pi\)
\(72\) −7.84333 −0.924345
\(73\) 8.62258 1.00920 0.504599 0.863354i \(-0.331641\pi\)
0.504599 + 0.863354i \(0.331641\pi\)
\(74\) −2.40277 −0.279316
\(75\) −1.00000 −0.115470
\(76\) 9.48531 1.08804
\(77\) 0 0
\(78\) 3.87661 0.438939
\(79\) 4.43519 0.498998 0.249499 0.968375i \(-0.419734\pi\)
0.249499 + 0.968375i \(0.419734\pi\)
\(80\) −10.7666 −1.20374
\(81\) 1.00000 0.111111
\(82\) 20.1973 2.23042
\(83\) −15.3931 −1.68961 −0.844804 0.535076i \(-0.820283\pi\)
−0.844804 + 0.535076i \(0.820283\pi\)
\(84\) 0 0
\(85\) 1.32245 0.143440
\(86\) 26.8367 2.89387
\(87\) 5.36654 0.575354
\(88\) 7.84333 0.836102
\(89\) 14.7962 1.56839 0.784195 0.620514i \(-0.213076\pi\)
0.784195 + 0.620514i \(0.213076\pi\)
\(90\) 2.64021 0.278303
\(91\) 0 0
\(92\) 30.3374 3.16290
\(93\) −5.25881 −0.545313
\(94\) 11.3926 1.17506
\(95\) −1.90824 −0.195781
\(96\) 12.7395 1.30022
\(97\) −10.5475 −1.07094 −0.535468 0.844555i \(-0.679865\pi\)
−0.535468 + 0.844555i \(0.679865\pi\)
\(98\) 0 0
\(99\) −1.00000 −0.100504
\(100\) 4.97072 0.497072
\(101\) −1.15863 −0.115288 −0.0576441 0.998337i \(-0.518359\pi\)
−0.0576441 + 0.998337i \(0.518359\pi\)
\(102\) −3.49155 −0.345715
\(103\) −5.82710 −0.574161 −0.287081 0.957906i \(-0.592685\pi\)
−0.287081 + 0.957906i \(0.592685\pi\)
\(104\) −11.5163 −1.12927
\(105\) 0 0
\(106\) 8.25053 0.801363
\(107\) −8.62135 −0.833457 −0.416728 0.909031i \(-0.636823\pi\)
−0.416728 + 0.909031i \(0.636823\pi\)
\(108\) −4.97072 −0.478308
\(109\) −0.496925 −0.0475968 −0.0237984 0.999717i \(-0.507576\pi\)
−0.0237984 + 0.999717i \(0.507576\pi\)
\(110\) −2.64021 −0.251734
\(111\) −0.910067 −0.0863797
\(112\) 0 0
\(113\) −3.47631 −0.327024 −0.163512 0.986541i \(-0.552282\pi\)
−0.163512 + 0.986541i \(0.552282\pi\)
\(114\) 5.03815 0.471866
\(115\) −6.10323 −0.569129
\(116\) −26.6756 −2.47677
\(117\) 1.46829 0.135744
\(118\) −9.93138 −0.914258
\(119\) 0 0
\(120\) −7.84333 −0.715995
\(121\) 1.00000 0.0909091
\(122\) −35.9636 −3.25599
\(123\) 7.64988 0.689767
\(124\) 26.1400 2.34745
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 4.99984 0.443664 0.221832 0.975085i \(-0.428796\pi\)
0.221832 + 0.975085i \(0.428796\pi\)
\(128\) −6.47211 −0.572059
\(129\) 10.1646 0.894942
\(130\) 3.87661 0.340001
\(131\) 7.58371 0.662592 0.331296 0.943527i \(-0.392514\pi\)
0.331296 + 0.943527i \(0.392514\pi\)
\(132\) 4.97072 0.432646
\(133\) 0 0
\(134\) 28.3711 2.45089
\(135\) 1.00000 0.0860663
\(136\) 10.3724 0.889427
\(137\) 1.59336 0.136130 0.0680651 0.997681i \(-0.478317\pi\)
0.0680651 + 0.997681i \(0.478317\pi\)
\(138\) 16.1138 1.37170
\(139\) −2.57556 −0.218456 −0.109228 0.994017i \(-0.534838\pi\)
−0.109228 + 0.994017i \(0.534838\pi\)
\(140\) 0 0
\(141\) 4.31503 0.363391
\(142\) −20.2956 −1.70317
\(143\) −1.46829 −0.122785
\(144\) 10.7666 0.897218
\(145\) 5.36654 0.445667
\(146\) −22.7654 −1.88408
\(147\) 0 0
\(148\) 4.52369 0.371845
\(149\) −5.68525 −0.465754 −0.232877 0.972506i \(-0.574814\pi\)
−0.232877 + 0.972506i \(0.574814\pi\)
\(150\) 2.64021 0.215572
\(151\) −17.3701 −1.41356 −0.706778 0.707435i \(-0.749852\pi\)
−0.706778 + 0.707435i \(0.749852\pi\)
\(152\) −14.9669 −1.21398
\(153\) −1.32245 −0.106914
\(154\) 0 0
\(155\) −5.25881 −0.422397
\(156\) −7.29847 −0.584346
\(157\) −3.29676 −0.263110 −0.131555 0.991309i \(-0.541997\pi\)
−0.131555 + 0.991309i \(0.541997\pi\)
\(158\) −11.7098 −0.931585
\(159\) 3.12495 0.247825
\(160\) 12.7395 1.00714
\(161\) 0 0
\(162\) −2.64021 −0.207435
\(163\) 19.2220 1.50559 0.752793 0.658257i \(-0.228706\pi\)
0.752793 + 0.658257i \(0.228706\pi\)
\(164\) −38.0254 −2.96929
\(165\) −1.00000 −0.0778499
\(166\) 40.6410 3.15435
\(167\) 6.40905 0.495947 0.247974 0.968767i \(-0.420235\pi\)
0.247974 + 0.968767i \(0.420235\pi\)
\(168\) 0 0
\(169\) −10.8441 −0.834163
\(170\) −3.49155 −0.267789
\(171\) 1.90824 0.145926
\(172\) −50.5253 −3.85252
\(173\) −7.71736 −0.586740 −0.293370 0.955999i \(-0.594777\pi\)
−0.293370 + 0.955999i \(0.594777\pi\)
\(174\) −14.1688 −1.07414
\(175\) 0 0
\(176\) −10.7666 −0.811564
\(177\) −3.76158 −0.282738
\(178\) −39.0650 −2.92805
\(179\) 12.3294 0.921545 0.460772 0.887518i \(-0.347572\pi\)
0.460772 + 0.887518i \(0.347572\pi\)
\(180\) −4.97072 −0.370496
\(181\) 20.4362 1.51901 0.759504 0.650503i \(-0.225442\pi\)
0.759504 + 0.650503i \(0.225442\pi\)
\(182\) 0 0
\(183\) −13.6215 −1.00693
\(184\) −47.8696 −3.52899
\(185\) −0.910067 −0.0669094
\(186\) 13.8844 1.01805
\(187\) 1.32245 0.0967071
\(188\) −21.4488 −1.56432
\(189\) 0 0
\(190\) 5.03815 0.365506
\(191\) −17.2996 −1.25175 −0.625877 0.779922i \(-0.715259\pi\)
−0.625877 + 0.779922i \(0.715259\pi\)
\(192\) −12.1017 −0.873365
\(193\) 2.99867 0.215849 0.107924 0.994159i \(-0.465580\pi\)
0.107924 + 0.994159i \(0.465580\pi\)
\(194\) 27.8476 1.99934
\(195\) 1.46829 0.105147
\(196\) 0 0
\(197\) −8.31748 −0.592596 −0.296298 0.955096i \(-0.595752\pi\)
−0.296298 + 0.955096i \(0.595752\pi\)
\(198\) 2.64021 0.187632
\(199\) 13.5052 0.957356 0.478678 0.877990i \(-0.341116\pi\)
0.478678 + 0.877990i \(0.341116\pi\)
\(200\) −7.84333 −0.554607
\(201\) 10.7458 0.757947
\(202\) 3.05903 0.215233
\(203\) 0 0
\(204\) 6.57353 0.460239
\(205\) 7.64988 0.534291
\(206\) 15.3848 1.07191
\(207\) 6.10323 0.424204
\(208\) 15.8085 1.09613
\(209\) −1.90824 −0.131995
\(210\) 0 0
\(211\) 3.00583 0.206930 0.103465 0.994633i \(-0.467007\pi\)
0.103465 + 0.994633i \(0.467007\pi\)
\(212\) −15.5333 −1.06683
\(213\) −7.68712 −0.526713
\(214\) 22.7622 1.55599
\(215\) 10.1646 0.693219
\(216\) 7.84333 0.533671
\(217\) 0 0
\(218\) 1.31199 0.0888591
\(219\) −8.62258 −0.582660
\(220\) 4.97072 0.335126
\(221\) −1.94174 −0.130616
\(222\) 2.40277 0.161263
\(223\) 2.06434 0.138238 0.0691192 0.997608i \(-0.477981\pi\)
0.0691192 + 0.997608i \(0.477981\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 9.17820 0.610525
\(227\) 22.7368 1.50909 0.754546 0.656247i \(-0.227857\pi\)
0.754546 + 0.656247i \(0.227857\pi\)
\(228\) −9.48531 −0.628180
\(229\) −14.9902 −0.990584 −0.495292 0.868727i \(-0.664939\pi\)
−0.495292 + 0.868727i \(0.664939\pi\)
\(230\) 16.1138 1.06251
\(231\) 0 0
\(232\) 42.0916 2.76345
\(233\) −13.9089 −0.911202 −0.455601 0.890184i \(-0.650576\pi\)
−0.455601 + 0.890184i \(0.650576\pi\)
\(234\) −3.87661 −0.253422
\(235\) 4.31503 0.281482
\(236\) 18.6978 1.21712
\(237\) −4.43519 −0.288097
\(238\) 0 0
\(239\) −8.09118 −0.523375 −0.261687 0.965153i \(-0.584279\pi\)
−0.261687 + 0.965153i \(0.584279\pi\)
\(240\) 10.7666 0.694982
\(241\) 14.7093 0.947509 0.473755 0.880657i \(-0.342898\pi\)
0.473755 + 0.880657i \(0.342898\pi\)
\(242\) −2.64021 −0.169719
\(243\) −1.00000 −0.0641500
\(244\) 67.7086 4.33460
\(245\) 0 0
\(246\) −20.1973 −1.28773
\(247\) 2.80185 0.178277
\(248\) −41.2465 −2.61916
\(249\) 15.3931 0.975496
\(250\) 2.64021 0.166982
\(251\) 22.1292 1.39678 0.698391 0.715717i \(-0.253900\pi\)
0.698391 + 0.715717i \(0.253900\pi\)
\(252\) 0 0
\(253\) −6.10323 −0.383707
\(254\) −13.2006 −0.828282
\(255\) −1.32245 −0.0828150
\(256\) −7.11568 −0.444730
\(257\) −25.2025 −1.57209 −0.786045 0.618169i \(-0.787875\pi\)
−0.786045 + 0.618169i \(0.787875\pi\)
\(258\) −26.8367 −1.67078
\(259\) 0 0
\(260\) −7.29847 −0.452632
\(261\) −5.36654 −0.332181
\(262\) −20.0226 −1.23700
\(263\) −17.8984 −1.10366 −0.551832 0.833956i \(-0.686071\pi\)
−0.551832 + 0.833956i \(0.686071\pi\)
\(264\) −7.84333 −0.482724
\(265\) 3.12495 0.191964
\(266\) 0 0
\(267\) −14.7962 −0.905511
\(268\) −53.4141 −3.26279
\(269\) −16.2110 −0.988404 −0.494202 0.869347i \(-0.664540\pi\)
−0.494202 + 0.869347i \(0.664540\pi\)
\(270\) −2.64021 −0.160678
\(271\) 6.78977 0.412449 0.206224 0.978505i \(-0.433882\pi\)
0.206224 + 0.978505i \(0.433882\pi\)
\(272\) −14.2383 −0.863324
\(273\) 0 0
\(274\) −4.20681 −0.254143
\(275\) −1.00000 −0.0603023
\(276\) −30.3374 −1.82610
\(277\) −10.9969 −0.660740 −0.330370 0.943851i \(-0.607174\pi\)
−0.330370 + 0.943851i \(0.607174\pi\)
\(278\) 6.80002 0.407838
\(279\) 5.25881 0.314836
\(280\) 0 0
\(281\) 14.4623 0.862746 0.431373 0.902174i \(-0.358029\pi\)
0.431373 + 0.902174i \(0.358029\pi\)
\(282\) −11.3926 −0.678420
\(283\) 13.6634 0.812203 0.406101 0.913828i \(-0.366888\pi\)
0.406101 + 0.913828i \(0.366888\pi\)
\(284\) 38.2105 2.26738
\(285\) 1.90824 0.113034
\(286\) 3.87661 0.229229
\(287\) 0 0
\(288\) −12.7395 −0.750681
\(289\) −15.2511 −0.897125
\(290\) −14.1688 −0.832021
\(291\) 10.5475 0.618305
\(292\) 42.8604 2.50822
\(293\) −18.7269 −1.09404 −0.547020 0.837120i \(-0.684238\pi\)
−0.547020 + 0.837120i \(0.684238\pi\)
\(294\) 0 0
\(295\) −3.76158 −0.219008
\(296\) −7.13795 −0.414885
\(297\) 1.00000 0.0580259
\(298\) 15.0103 0.869522
\(299\) 8.96133 0.518247
\(300\) −4.97072 −0.286985
\(301\) 0 0
\(302\) 45.8607 2.63899
\(303\) 1.15863 0.0665616
\(304\) 20.5452 1.17835
\(305\) −13.6215 −0.779964
\(306\) 3.49155 0.199598
\(307\) −9.11259 −0.520083 −0.260041 0.965597i \(-0.583736\pi\)
−0.260041 + 0.965597i \(0.583736\pi\)
\(308\) 0 0
\(309\) 5.82710 0.331492
\(310\) 13.8844 0.788579
\(311\) 13.2795 0.753010 0.376505 0.926415i \(-0.377126\pi\)
0.376505 + 0.926415i \(0.377126\pi\)
\(312\) 11.5163 0.651983
\(313\) 2.22034 0.125501 0.0627504 0.998029i \(-0.480013\pi\)
0.0627504 + 0.998029i \(0.480013\pi\)
\(314\) 8.70414 0.491203
\(315\) 0 0
\(316\) 22.0461 1.24019
\(317\) 22.2699 1.25080 0.625402 0.780302i \(-0.284935\pi\)
0.625402 + 0.780302i \(0.284935\pi\)
\(318\) −8.25053 −0.462667
\(319\) 5.36654 0.300469
\(320\) −12.1017 −0.676506
\(321\) 8.62135 0.481197
\(322\) 0 0
\(323\) −2.52355 −0.140414
\(324\) 4.97072 0.276151
\(325\) 1.46829 0.0814463
\(326\) −50.7503 −2.81080
\(327\) 0.496925 0.0274800
\(328\) 60.0005 3.31298
\(329\) 0 0
\(330\) 2.64021 0.145339
\(331\) −20.0057 −1.09961 −0.549807 0.835292i \(-0.685299\pi\)
−0.549807 + 0.835292i \(0.685299\pi\)
\(332\) −76.5146 −4.19928
\(333\) 0.910067 0.0498714
\(334\) −16.9213 −0.925890
\(335\) 10.7458 0.587103
\(336\) 0 0
\(337\) 35.4230 1.92961 0.964807 0.262958i \(-0.0846982\pi\)
0.964807 + 0.262958i \(0.0846982\pi\)
\(338\) 28.6308 1.55731
\(339\) 3.47631 0.188807
\(340\) 6.57353 0.356499
\(341\) −5.25881 −0.284780
\(342\) −5.03815 −0.272432
\(343\) 0 0
\(344\) 79.7242 4.29844
\(345\) 6.10323 0.328587
\(346\) 20.3755 1.09539
\(347\) −6.74944 −0.362329 −0.181165 0.983453i \(-0.557987\pi\)
−0.181165 + 0.983453i \(0.557987\pi\)
\(348\) 26.6756 1.42996
\(349\) 2.23091 0.119418 0.0597090 0.998216i \(-0.480983\pi\)
0.0597090 + 0.998216i \(0.480983\pi\)
\(350\) 0 0
\(351\) −1.46829 −0.0783717
\(352\) 12.7395 0.679017
\(353\) 8.24153 0.438652 0.219326 0.975652i \(-0.429614\pi\)
0.219326 + 0.975652i \(0.429614\pi\)
\(354\) 9.93138 0.527847
\(355\) −7.68712 −0.407990
\(356\) 73.5476 3.89802
\(357\) 0 0
\(358\) −32.5523 −1.72044
\(359\) 9.67460 0.510606 0.255303 0.966861i \(-0.417825\pi\)
0.255303 + 0.966861i \(0.417825\pi\)
\(360\) 7.84333 0.413380
\(361\) −15.3586 −0.808349
\(362\) −53.9558 −2.83585
\(363\) −1.00000 −0.0524864
\(364\) 0 0
\(365\) −8.62258 −0.451327
\(366\) 35.9636 1.87985
\(367\) −10.1412 −0.529364 −0.264682 0.964336i \(-0.585267\pi\)
−0.264682 + 0.964336i \(0.585267\pi\)
\(368\) 65.7111 3.42543
\(369\) −7.64988 −0.398237
\(370\) 2.40277 0.124914
\(371\) 0 0
\(372\) −26.1400 −1.35530
\(373\) −24.2646 −1.25637 −0.628186 0.778063i \(-0.716202\pi\)
−0.628186 + 0.778063i \(0.716202\pi\)
\(374\) −3.49155 −0.180544
\(375\) 1.00000 0.0516398
\(376\) 33.8442 1.74538
\(377\) −7.87966 −0.405823
\(378\) 0 0
\(379\) −4.59132 −0.235840 −0.117920 0.993023i \(-0.537623\pi\)
−0.117920 + 0.993023i \(0.537623\pi\)
\(380\) −9.48531 −0.486586
\(381\) −4.99984 −0.256150
\(382\) 45.6746 2.33691
\(383\) 23.2876 1.18994 0.594971 0.803747i \(-0.297163\pi\)
0.594971 + 0.803747i \(0.297163\pi\)
\(384\) 6.47211 0.330278
\(385\) 0 0
\(386\) −7.91712 −0.402971
\(387\) −10.1646 −0.516695
\(388\) −52.4287 −2.66166
\(389\) −32.3443 −1.63992 −0.819960 0.572421i \(-0.806004\pi\)
−0.819960 + 0.572421i \(0.806004\pi\)
\(390\) −3.87661 −0.196300
\(391\) −8.07121 −0.408179
\(392\) 0 0
\(393\) −7.58371 −0.382548
\(394\) 21.9599 1.10632
\(395\) −4.43519 −0.223159
\(396\) −4.97072 −0.249788
\(397\) 12.5036 0.627538 0.313769 0.949499i \(-0.398408\pi\)
0.313769 + 0.949499i \(0.398408\pi\)
\(398\) −35.6565 −1.78730
\(399\) 0 0
\(400\) 10.7666 0.538331
\(401\) 32.9395 1.64492 0.822459 0.568824i \(-0.192602\pi\)
0.822459 + 0.568824i \(0.192602\pi\)
\(402\) −28.3711 −1.41502
\(403\) 7.72147 0.384634
\(404\) −5.75923 −0.286532
\(405\) −1.00000 −0.0496904
\(406\) 0 0
\(407\) −0.910067 −0.0451103
\(408\) −10.3724 −0.513511
\(409\) 5.48449 0.271191 0.135595 0.990764i \(-0.456705\pi\)
0.135595 + 0.990764i \(0.456705\pi\)
\(410\) −20.1973 −0.997474
\(411\) −1.59336 −0.0785948
\(412\) −28.9649 −1.42700
\(413\) 0 0
\(414\) −16.1138 −0.791951
\(415\) 15.3931 0.755616
\(416\) −18.7053 −0.917103
\(417\) 2.57556 0.126126
\(418\) 5.03815 0.246424
\(419\) −5.22081 −0.255053 −0.127527 0.991835i \(-0.540704\pi\)
−0.127527 + 0.991835i \(0.540704\pi\)
\(420\) 0 0
\(421\) −36.1044 −1.75962 −0.879810 0.475326i \(-0.842330\pi\)
−0.879810 + 0.475326i \(0.842330\pi\)
\(422\) −7.93603 −0.386320
\(423\) −4.31503 −0.209804
\(424\) 24.5100 1.19031
\(425\) −1.32245 −0.0641482
\(426\) 20.2956 0.983327
\(427\) 0 0
\(428\) −42.8543 −2.07144
\(429\) 1.46829 0.0708899
\(430\) −26.8367 −1.29418
\(431\) 31.7237 1.52808 0.764039 0.645170i \(-0.223213\pi\)
0.764039 + 0.645170i \(0.223213\pi\)
\(432\) −10.7666 −0.518009
\(433\) 25.9251 1.24588 0.622939 0.782270i \(-0.285938\pi\)
0.622939 + 0.782270i \(0.285938\pi\)
\(434\) 0 0
\(435\) −5.36654 −0.257306
\(436\) −2.47008 −0.118295
\(437\) 11.6464 0.557123
\(438\) 22.7654 1.08778
\(439\) −27.6259 −1.31851 −0.659256 0.751919i \(-0.729129\pi\)
−0.659256 + 0.751919i \(0.729129\pi\)
\(440\) −7.84333 −0.373916
\(441\) 0 0
\(442\) 5.12662 0.243848
\(443\) 40.1305 1.90666 0.953329 0.301932i \(-0.0976316\pi\)
0.953329 + 0.301932i \(0.0976316\pi\)
\(444\) −4.52369 −0.214685
\(445\) −14.7962 −0.701406
\(446\) −5.45030 −0.258079
\(447\) 5.68525 0.268903
\(448\) 0 0
\(449\) 31.6309 1.49275 0.746377 0.665523i \(-0.231791\pi\)
0.746377 + 0.665523i \(0.231791\pi\)
\(450\) −2.64021 −0.124461
\(451\) 7.64988 0.360219
\(452\) −17.2798 −0.812772
\(453\) 17.3701 0.816117
\(454\) −60.0299 −2.81734
\(455\) 0 0
\(456\) 14.9669 0.700890
\(457\) 16.9286 0.791889 0.395944 0.918274i \(-0.370417\pi\)
0.395944 + 0.918274i \(0.370417\pi\)
\(458\) 39.5774 1.84933
\(459\) 1.32245 0.0617267
\(460\) −30.3374 −1.41449
\(461\) 24.8508 1.15742 0.578709 0.815534i \(-0.303557\pi\)
0.578709 + 0.815534i \(0.303557\pi\)
\(462\) 0 0
\(463\) 18.1176 0.841997 0.420999 0.907061i \(-0.361680\pi\)
0.420999 + 0.907061i \(0.361680\pi\)
\(464\) −57.7795 −2.68235
\(465\) 5.25881 0.243871
\(466\) 36.7224 1.70113
\(467\) 21.9464 1.01556 0.507779 0.861487i \(-0.330467\pi\)
0.507779 + 0.861487i \(0.330467\pi\)
\(468\) 7.29847 0.337372
\(469\) 0 0
\(470\) −11.3926 −0.525502
\(471\) 3.29676 0.151907
\(472\) −29.5033 −1.35800
\(473\) 10.1646 0.467368
\(474\) 11.7098 0.537851
\(475\) 1.90824 0.0875559
\(476\) 0 0
\(477\) −3.12495 −0.143082
\(478\) 21.3624 0.977095
\(479\) −22.8628 −1.04463 −0.522315 0.852753i \(-0.674931\pi\)
−0.522315 + 0.852753i \(0.674931\pi\)
\(480\) −12.7395 −0.581475
\(481\) 1.33625 0.0609275
\(482\) −38.8357 −1.76892
\(483\) 0 0
\(484\) 4.97072 0.225942
\(485\) 10.5475 0.478937
\(486\) 2.64021 0.119762
\(487\) 12.3707 0.560569 0.280285 0.959917i \(-0.409571\pi\)
0.280285 + 0.959917i \(0.409571\pi\)
\(488\) −106.838 −4.83632
\(489\) −19.2220 −0.869251
\(490\) 0 0
\(491\) −34.6766 −1.56493 −0.782467 0.622692i \(-0.786039\pi\)
−0.782467 + 0.622692i \(0.786039\pi\)
\(492\) 38.0254 1.71432
\(493\) 7.09698 0.319632
\(494\) −7.39748 −0.332828
\(495\) 1.00000 0.0449467
\(496\) 56.6195 2.54229
\(497\) 0 0
\(498\) −40.6410 −1.82116
\(499\) −31.1455 −1.39426 −0.697131 0.716944i \(-0.745540\pi\)
−0.697131 + 0.716944i \(0.745540\pi\)
\(500\) −4.97072 −0.222297
\(501\) −6.40905 −0.286335
\(502\) −58.4257 −2.60767
\(503\) −31.5669 −1.40750 −0.703749 0.710448i \(-0.748492\pi\)
−0.703749 + 0.710448i \(0.748492\pi\)
\(504\) 0 0
\(505\) 1.15863 0.0515584
\(506\) 16.1138 0.716346
\(507\) 10.8441 0.481604
\(508\) 24.8528 1.10267
\(509\) −10.2180 −0.452904 −0.226452 0.974022i \(-0.572713\pi\)
−0.226452 + 0.974022i \(0.572713\pi\)
\(510\) 3.49155 0.154608
\(511\) 0 0
\(512\) 31.7311 1.40233
\(513\) −1.90824 −0.0842507
\(514\) 66.5400 2.93495
\(515\) 5.82710 0.256773
\(516\) 50.5253 2.22425
\(517\) 4.31503 0.189775
\(518\) 0 0
\(519\) 7.71736 0.338754
\(520\) 11.5163 0.505024
\(521\) −8.95953 −0.392524 −0.196262 0.980551i \(-0.562880\pi\)
−0.196262 + 0.980551i \(0.562880\pi\)
\(522\) 14.1688 0.620152
\(523\) 38.6053 1.68809 0.844046 0.536271i \(-0.180168\pi\)
0.844046 + 0.536271i \(0.180168\pi\)
\(524\) 37.6965 1.64678
\(525\) 0 0
\(526\) 47.2556 2.06044
\(527\) −6.95451 −0.302943
\(528\) 10.7666 0.468557
\(529\) 14.2494 0.619538
\(530\) −8.25053 −0.358380
\(531\) 3.76158 0.163239
\(532\) 0 0
\(533\) −11.2323 −0.486524
\(534\) 39.0650 1.69051
\(535\) 8.62135 0.372733
\(536\) 84.2825 3.64045
\(537\) −12.3294 −0.532054
\(538\) 42.8006 1.84526
\(539\) 0 0
\(540\) 4.97072 0.213906
\(541\) 23.3879 1.00552 0.502762 0.864425i \(-0.332317\pi\)
0.502762 + 0.864425i \(0.332317\pi\)
\(542\) −17.9264 −0.770006
\(543\) −20.4362 −0.876999
\(544\) 16.8473 0.722323
\(545\) 0.496925 0.0212859
\(546\) 0 0
\(547\) 24.2222 1.03567 0.517833 0.855481i \(-0.326739\pi\)
0.517833 + 0.855481i \(0.326739\pi\)
\(548\) 7.92016 0.338332
\(549\) 13.6215 0.581351
\(550\) 2.64021 0.112579
\(551\) −10.2406 −0.436266
\(552\) 47.8696 2.03747
\(553\) 0 0
\(554\) 29.0342 1.23354
\(555\) 0.910067 0.0386302
\(556\) −12.8024 −0.542942
\(557\) −37.4636 −1.58739 −0.793693 0.608319i \(-0.791844\pi\)
−0.793693 + 0.608319i \(0.791844\pi\)
\(558\) −13.8844 −0.587772
\(559\) −14.9246 −0.631243
\(560\) 0 0
\(561\) −1.32245 −0.0558339
\(562\) −38.1834 −1.61067
\(563\) 16.1375 0.680116 0.340058 0.940405i \(-0.389553\pi\)
0.340058 + 0.940405i \(0.389553\pi\)
\(564\) 21.4488 0.903159
\(565\) 3.47631 0.146250
\(566\) −36.0742 −1.51631
\(567\) 0 0
\(568\) −60.2926 −2.52982
\(569\) 23.4149 0.981604 0.490802 0.871271i \(-0.336704\pi\)
0.490802 + 0.871271i \(0.336704\pi\)
\(570\) −5.03815 −0.211025
\(571\) −26.3177 −1.10136 −0.550680 0.834716i \(-0.685632\pi\)
−0.550680 + 0.834716i \(0.685632\pi\)
\(572\) −7.29847 −0.305165
\(573\) 17.2996 0.722701
\(574\) 0 0
\(575\) 6.10323 0.254522
\(576\) 12.1017 0.504238
\(577\) 45.1935 1.88143 0.940716 0.339195i \(-0.110155\pi\)
0.940716 + 0.339195i \(0.110155\pi\)
\(578\) 40.2662 1.67485
\(579\) −2.99867 −0.124620
\(580\) 26.6756 1.10764
\(581\) 0 0
\(582\) −27.8476 −1.15432
\(583\) 3.12495 0.129422
\(584\) −67.6298 −2.79854
\(585\) −1.46829 −0.0607065
\(586\) 49.4431 2.04247
\(587\) −17.1124 −0.706303 −0.353151 0.935566i \(-0.614890\pi\)
−0.353151 + 0.935566i \(0.614890\pi\)
\(588\) 0 0
\(589\) 10.0350 0.413487
\(590\) 9.93138 0.408868
\(591\) 8.31748 0.342135
\(592\) 9.79834 0.402709
\(593\) 15.4135 0.632956 0.316478 0.948600i \(-0.397500\pi\)
0.316478 + 0.948600i \(0.397500\pi\)
\(594\) −2.64021 −0.108329
\(595\) 0 0
\(596\) −28.2598 −1.15757
\(597\) −13.5052 −0.552730
\(598\) −23.6598 −0.967521
\(599\) −0.638573 −0.0260914 −0.0130457 0.999915i \(-0.504153\pi\)
−0.0130457 + 0.999915i \(0.504153\pi\)
\(600\) 7.84333 0.320203
\(601\) −47.0074 −1.91747 −0.958736 0.284298i \(-0.908239\pi\)
−0.958736 + 0.284298i \(0.908239\pi\)
\(602\) 0 0
\(603\) −10.7458 −0.437601
\(604\) −86.3417 −3.51320
\(605\) −1.00000 −0.0406558
\(606\) −3.05903 −0.124265
\(607\) −34.5649 −1.40294 −0.701472 0.712697i \(-0.747474\pi\)
−0.701472 + 0.712697i \(0.747474\pi\)
\(608\) −24.3099 −0.985898
\(609\) 0 0
\(610\) 35.9636 1.45612
\(611\) −6.33574 −0.256317
\(612\) −6.57353 −0.265719
\(613\) −11.4623 −0.462956 −0.231478 0.972840i \(-0.574356\pi\)
−0.231478 + 0.972840i \(0.574356\pi\)
\(614\) 24.0592 0.970949
\(615\) −7.64988 −0.308473
\(616\) 0 0
\(617\) −5.48742 −0.220915 −0.110458 0.993881i \(-0.535232\pi\)
−0.110458 + 0.993881i \(0.535232\pi\)
\(618\) −15.3848 −0.618867
\(619\) −24.6364 −0.990222 −0.495111 0.868830i \(-0.664873\pi\)
−0.495111 + 0.868830i \(0.664873\pi\)
\(620\) −26.1400 −1.04981
\(621\) −6.10323 −0.244914
\(622\) −35.0606 −1.40580
\(623\) 0 0
\(624\) −15.8085 −0.632848
\(625\) 1.00000 0.0400000
\(626\) −5.86216 −0.234299
\(627\) 1.90824 0.0762076
\(628\) −16.3873 −0.653923
\(629\) −1.20352 −0.0479874
\(630\) 0 0
\(631\) −33.7720 −1.34444 −0.672222 0.740350i \(-0.734660\pi\)
−0.672222 + 0.740350i \(0.734660\pi\)
\(632\) −34.7867 −1.38374
\(633\) −3.00583 −0.119471
\(634\) −58.7974 −2.33514
\(635\) −4.99984 −0.198413
\(636\) 15.5333 0.615934
\(637\) 0 0
\(638\) −14.1688 −0.560949
\(639\) 7.68712 0.304098
\(640\) 6.47211 0.255832
\(641\) 12.1006 0.477945 0.238972 0.971026i \(-0.423189\pi\)
0.238972 + 0.971026i \(0.423189\pi\)
\(642\) −22.7622 −0.898352
\(643\) 5.76993 0.227544 0.113772 0.993507i \(-0.463707\pi\)
0.113772 + 0.993507i \(0.463707\pi\)
\(644\) 0 0
\(645\) −10.1646 −0.400230
\(646\) 6.66270 0.262140
\(647\) 45.5459 1.79059 0.895296 0.445471i \(-0.146964\pi\)
0.895296 + 0.445471i \(0.146964\pi\)
\(648\) −7.84333 −0.308115
\(649\) −3.76158 −0.147655
\(650\) −3.87661 −0.152053
\(651\) 0 0
\(652\) 95.5474 3.74192
\(653\) −38.1388 −1.49249 −0.746244 0.665673i \(-0.768145\pi\)
−0.746244 + 0.665673i \(0.768145\pi\)
\(654\) −1.31199 −0.0513028
\(655\) −7.58371 −0.296320
\(656\) −82.3633 −3.21575
\(657\) 8.62258 0.336399
\(658\) 0 0
\(659\) −41.1962 −1.60478 −0.802388 0.596803i \(-0.796437\pi\)
−0.802388 + 0.596803i \(0.796437\pi\)
\(660\) −4.97072 −0.193485
\(661\) −15.8103 −0.614949 −0.307474 0.951556i \(-0.599484\pi\)
−0.307474 + 0.951556i \(0.599484\pi\)
\(662\) 52.8193 2.05288
\(663\) 1.94174 0.0754111
\(664\) 120.733 4.68534
\(665\) 0 0
\(666\) −2.40277 −0.0931054
\(667\) −32.7532 −1.26821
\(668\) 31.8576 1.23261
\(669\) −2.06434 −0.0798120
\(670\) −28.3711 −1.09607
\(671\) −13.6215 −0.525851
\(672\) 0 0
\(673\) 18.7115 0.721275 0.360637 0.932706i \(-0.382559\pi\)
0.360637 + 0.932706i \(0.382559\pi\)
\(674\) −93.5243 −3.60242
\(675\) −1.00000 −0.0384900
\(676\) −53.9030 −2.07319
\(677\) −17.4216 −0.669568 −0.334784 0.942295i \(-0.608663\pi\)
−0.334784 + 0.942295i \(0.608663\pi\)
\(678\) −9.17820 −0.352487
\(679\) 0 0
\(680\) −10.3724 −0.397764
\(681\) −22.7368 −0.871275
\(682\) 13.8844 0.531660
\(683\) 12.8600 0.492074 0.246037 0.969260i \(-0.420872\pi\)
0.246037 + 0.969260i \(0.420872\pi\)
\(684\) 9.48531 0.362680
\(685\) −1.59336 −0.0608792
\(686\) 0 0
\(687\) 14.9902 0.571914
\(688\) −109.438 −4.17229
\(689\) −4.58835 −0.174802
\(690\) −16.1138 −0.613442
\(691\) −34.8830 −1.32701 −0.663505 0.748171i \(-0.730932\pi\)
−0.663505 + 0.748171i \(0.730932\pi\)
\(692\) −38.3608 −1.45826
\(693\) 0 0
\(694\) 17.8200 0.676437
\(695\) 2.57556 0.0976965
\(696\) −42.0916 −1.59548
\(697\) 10.1166 0.383193
\(698\) −5.89008 −0.222943
\(699\) 13.9089 0.526083
\(700\) 0 0
\(701\) −38.6696 −1.46053 −0.730266 0.683163i \(-0.760604\pi\)
−0.730266 + 0.683163i \(0.760604\pi\)
\(702\) 3.87661 0.146313
\(703\) 1.73662 0.0654980
\(704\) −12.1017 −0.456100
\(705\) −4.31503 −0.162514
\(706\) −21.7594 −0.818925
\(707\) 0 0
\(708\) −18.6978 −0.702706
\(709\) 36.9867 1.38906 0.694531 0.719462i \(-0.255612\pi\)
0.694531 + 0.719462i \(0.255612\pi\)
\(710\) 20.2956 0.761682
\(711\) 4.43519 0.166333
\(712\) −116.051 −4.34920
\(713\) 32.0957 1.20199
\(714\) 0 0
\(715\) 1.46829 0.0549111
\(716\) 61.2861 2.29037
\(717\) 8.09118 0.302171
\(718\) −25.5430 −0.953256
\(719\) −11.0403 −0.411734 −0.205867 0.978580i \(-0.566001\pi\)
−0.205867 + 0.978580i \(0.566001\pi\)
\(720\) −10.7666 −0.401248
\(721\) 0 0
\(722\) 40.5501 1.50912
\(723\) −14.7093 −0.547045
\(724\) 101.582 3.77528
\(725\) −5.36654 −0.199308
\(726\) 2.64021 0.0979875
\(727\) −40.2559 −1.49301 −0.746504 0.665381i \(-0.768269\pi\)
−0.746504 + 0.665381i \(0.768269\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 22.7654 0.842587
\(731\) 13.4422 0.497176
\(732\) −67.7086 −2.50258
\(733\) −49.5298 −1.82943 −0.914713 0.404105i \(-0.867583\pi\)
−0.914713 + 0.404105i \(0.867583\pi\)
\(734\) 26.7748 0.988275
\(735\) 0 0
\(736\) −77.7519 −2.86597
\(737\) 10.7458 0.395825
\(738\) 20.1973 0.743473
\(739\) −50.5362 −1.85900 −0.929502 0.368817i \(-0.879763\pi\)
−0.929502 + 0.368817i \(0.879763\pi\)
\(740\) −4.52369 −0.166294
\(741\) −2.80185 −0.102929
\(742\) 0 0
\(743\) −32.3856 −1.18811 −0.594057 0.804423i \(-0.702475\pi\)
−0.594057 + 0.804423i \(0.702475\pi\)
\(744\) 41.2465 1.51217
\(745\) 5.68525 0.208292
\(746\) 64.0636 2.34554
\(747\) −15.3931 −0.563203
\(748\) 6.57353 0.240352
\(749\) 0 0
\(750\) −2.64021 −0.0964069
\(751\) −51.3682 −1.87445 −0.937227 0.348721i \(-0.886616\pi\)
−0.937227 + 0.348721i \(0.886616\pi\)
\(752\) −46.4583 −1.69416
\(753\) −22.1292 −0.806432
\(754\) 20.8040 0.757636
\(755\) 17.3701 0.632162
\(756\) 0 0
\(757\) −12.8641 −0.467555 −0.233778 0.972290i \(-0.575109\pi\)
−0.233778 + 0.972290i \(0.575109\pi\)
\(758\) 12.1221 0.440293
\(759\) 6.10323 0.221533
\(760\) 14.9669 0.542907
\(761\) 2.61077 0.0946404 0.0473202 0.998880i \(-0.484932\pi\)
0.0473202 + 0.998880i \(0.484932\pi\)
\(762\) 13.2006 0.478209
\(763\) 0 0
\(764\) −85.9914 −3.11106
\(765\) 1.32245 0.0478133
\(766\) −61.4843 −2.22152
\(767\) 5.52311 0.199428
\(768\) 7.11568 0.256765
\(769\) −13.4032 −0.483331 −0.241666 0.970360i \(-0.577694\pi\)
−0.241666 + 0.970360i \(0.577694\pi\)
\(770\) 0 0
\(771\) 25.2025 0.907647
\(772\) 14.9055 0.536462
\(773\) −0.424626 −0.0152727 −0.00763637 0.999971i \(-0.502431\pi\)
−0.00763637 + 0.999971i \(0.502431\pi\)
\(774\) 26.8367 0.964624
\(775\) 5.25881 0.188902
\(776\) 82.7275 2.96974
\(777\) 0 0
\(778\) 85.3958 3.06159
\(779\) −14.5978 −0.523020
\(780\) 7.29847 0.261327
\(781\) −7.68712 −0.275067
\(782\) 21.3097 0.762033
\(783\) 5.36654 0.191785
\(784\) 0 0
\(785\) 3.29676 0.117666
\(786\) 20.0226 0.714183
\(787\) −13.0742 −0.466046 −0.233023 0.972471i \(-0.574862\pi\)
−0.233023 + 0.972471i \(0.574862\pi\)
\(788\) −41.3439 −1.47281
\(789\) 17.8984 0.637200
\(790\) 11.7098 0.416617
\(791\) 0 0
\(792\) 7.84333 0.278701
\(793\) 20.0003 0.710233
\(794\) −33.0122 −1.17156
\(795\) −3.12495 −0.110831
\(796\) 67.1304 2.37937
\(797\) −50.9558 −1.80495 −0.902474 0.430744i \(-0.858251\pi\)
−0.902474 + 0.430744i \(0.858251\pi\)
\(798\) 0 0
\(799\) 5.70642 0.201878
\(800\) −12.7395 −0.450409
\(801\) 14.7962 0.522797
\(802\) −86.9672 −3.07092
\(803\) −8.62258 −0.304284
\(804\) 53.4141 1.88377
\(805\) 0 0
\(806\) −20.3863 −0.718077
\(807\) 16.2110 0.570655
\(808\) 9.08753 0.319698
\(809\) 1.27487 0.0448222 0.0224111 0.999749i \(-0.492866\pi\)
0.0224111 + 0.999749i \(0.492866\pi\)
\(810\) 2.64021 0.0927676
\(811\) −28.2548 −0.992159 −0.496080 0.868277i \(-0.665228\pi\)
−0.496080 + 0.868277i \(0.665228\pi\)
\(812\) 0 0
\(813\) −6.78977 −0.238128
\(814\) 2.40277 0.0842170
\(815\) −19.2220 −0.673319
\(816\) 14.2383 0.498440
\(817\) −19.3964 −0.678595
\(818\) −14.4802 −0.506289
\(819\) 0 0
\(820\) 38.0254 1.32791
\(821\) −2.29991 −0.0802674 −0.0401337 0.999194i \(-0.512778\pi\)
−0.0401337 + 0.999194i \(0.512778\pi\)
\(822\) 4.20681 0.146729
\(823\) 23.2401 0.810100 0.405050 0.914295i \(-0.367254\pi\)
0.405050 + 0.914295i \(0.367254\pi\)
\(824\) 45.7039 1.59217
\(825\) 1.00000 0.0348155
\(826\) 0 0
\(827\) −44.6467 −1.55252 −0.776258 0.630415i \(-0.782885\pi\)
−0.776258 + 0.630415i \(0.782885\pi\)
\(828\) 30.3374 1.05430
\(829\) 25.1551 0.873672 0.436836 0.899541i \(-0.356099\pi\)
0.436836 + 0.899541i \(0.356099\pi\)
\(830\) −40.6410 −1.41067
\(831\) 10.9969 0.381479
\(832\) 17.7689 0.616024
\(833\) 0 0
\(834\) −6.80002 −0.235465
\(835\) −6.40905 −0.221794
\(836\) −9.48531 −0.328056
\(837\) −5.25881 −0.181771
\(838\) 13.7840 0.476162
\(839\) −11.4878 −0.396601 −0.198301 0.980141i \(-0.563542\pi\)
−0.198301 + 0.980141i \(0.563542\pi\)
\(840\) 0 0
\(841\) −0.200202 −0.00690350
\(842\) 95.3232 3.28506
\(843\) −14.4623 −0.498107
\(844\) 14.9411 0.514295
\(845\) 10.8441 0.373049
\(846\) 11.3926 0.391686
\(847\) 0 0
\(848\) −33.6451 −1.15538
\(849\) −13.6634 −0.468926
\(850\) 3.49155 0.119759
\(851\) 5.55434 0.190400
\(852\) −38.2105 −1.30907
\(853\) 16.9057 0.578839 0.289419 0.957202i \(-0.406538\pi\)
0.289419 + 0.957202i \(0.406538\pi\)
\(854\) 0 0
\(855\) −1.90824 −0.0652603
\(856\) 67.6201 2.31121
\(857\) −36.8371 −1.25833 −0.629166 0.777271i \(-0.716604\pi\)
−0.629166 + 0.777271i \(0.716604\pi\)
\(858\) −3.87661 −0.132345
\(859\) −6.66817 −0.227515 −0.113757 0.993509i \(-0.536289\pi\)
−0.113757 + 0.993509i \(0.536289\pi\)
\(860\) 50.5253 1.72290
\(861\) 0 0
\(862\) −83.7574 −2.85279
\(863\) −18.7919 −0.639685 −0.319842 0.947471i \(-0.603630\pi\)
−0.319842 + 0.947471i \(0.603630\pi\)
\(864\) 12.7395 0.433406
\(865\) 7.71736 0.262398
\(866\) −68.4477 −2.32595
\(867\) 15.2511 0.517955
\(868\) 0 0
\(869\) −4.43519 −0.150454
\(870\) 14.1688 0.480368
\(871\) −15.7779 −0.534614
\(872\) 3.89755 0.131988
\(873\) −10.5475 −0.356979
\(874\) −30.7490 −1.04010
\(875\) 0 0
\(876\) −42.8604 −1.44812
\(877\) −43.7779 −1.47827 −0.739137 0.673555i \(-0.764766\pi\)
−0.739137 + 0.673555i \(0.764766\pi\)
\(878\) 72.9382 2.46155
\(879\) 18.7269 0.631644
\(880\) 10.7666 0.362942
\(881\) 6.06844 0.204451 0.102226 0.994761i \(-0.467404\pi\)
0.102226 + 0.994761i \(0.467404\pi\)
\(882\) 0 0
\(883\) 18.7996 0.632658 0.316329 0.948649i \(-0.397550\pi\)
0.316329 + 0.948649i \(0.397550\pi\)
\(884\) −9.65187 −0.324627
\(885\) 3.76158 0.126444
\(886\) −105.953 −3.55956
\(887\) 1.46141 0.0490694 0.0245347 0.999699i \(-0.492190\pi\)
0.0245347 + 0.999699i \(0.492190\pi\)
\(888\) 7.13795 0.239534
\(889\) 0 0
\(890\) 39.0650 1.30946
\(891\) −1.00000 −0.0335013
\(892\) 10.2613 0.343572
\(893\) −8.23411 −0.275544
\(894\) −15.0103 −0.502019
\(895\) −12.3294 −0.412127
\(896\) 0 0
\(897\) −8.96133 −0.299210
\(898\) −83.5123 −2.78684
\(899\) −28.2216 −0.941244
\(900\) 4.97072 0.165691
\(901\) 4.13259 0.137677
\(902\) −20.1973 −0.672497
\(903\) 0 0
\(904\) 27.2659 0.906849
\(905\) −20.4362 −0.679321
\(906\) −45.8607 −1.52362
\(907\) −56.5762 −1.87858 −0.939291 0.343122i \(-0.888516\pi\)
−0.939291 + 0.343122i \(0.888516\pi\)
\(908\) 113.018 3.75064
\(909\) −1.15863 −0.0384294
\(910\) 0 0
\(911\) −21.6779 −0.718222 −0.359111 0.933295i \(-0.616920\pi\)
−0.359111 + 0.933295i \(0.616920\pi\)
\(912\) −20.5452 −0.680321
\(913\) 15.3931 0.509436
\(914\) −44.6952 −1.47839
\(915\) 13.6215 0.450312
\(916\) −74.5123 −2.46196
\(917\) 0 0
\(918\) −3.49155 −0.115238
\(919\) −27.0999 −0.893942 −0.446971 0.894549i \(-0.647497\pi\)
−0.446971 + 0.894549i \(0.647497\pi\)
\(920\) 47.8696 1.57821
\(921\) 9.11259 0.300270
\(922\) −65.6114 −2.16080
\(923\) 11.2870 0.371515
\(924\) 0 0
\(925\) 0.910067 0.0299228
\(926\) −47.8344 −1.57193
\(927\) −5.82710 −0.191387
\(928\) 68.3670 2.24426
\(929\) 31.4252 1.03103 0.515513 0.856882i \(-0.327601\pi\)
0.515513 + 0.856882i \(0.327601\pi\)
\(930\) −13.8844 −0.455286
\(931\) 0 0
\(932\) −69.1372 −2.26467
\(933\) −13.2795 −0.434750
\(934\) −57.9432 −1.89596
\(935\) −1.32245 −0.0432487
\(936\) −11.5163 −0.376422
\(937\) −6.06684 −0.198195 −0.0990975 0.995078i \(-0.531596\pi\)
−0.0990975 + 0.995078i \(0.531596\pi\)
\(938\) 0 0
\(939\) −2.22034 −0.0724580
\(940\) 21.4488 0.699584
\(941\) 8.71299 0.284035 0.142018 0.989864i \(-0.454641\pi\)
0.142018 + 0.989864i \(0.454641\pi\)
\(942\) −8.70414 −0.283596
\(943\) −46.6890 −1.52040
\(944\) 40.4995 1.31815
\(945\) 0 0
\(946\) −26.8367 −0.872535
\(947\) −18.0921 −0.587914 −0.293957 0.955819i \(-0.594972\pi\)
−0.293957 + 0.955819i \(0.594972\pi\)
\(948\) −22.0461 −0.716024
\(949\) 12.6605 0.410977
\(950\) −5.03815 −0.163459
\(951\) −22.2699 −0.722152
\(952\) 0 0
\(953\) −2.58983 −0.0838927 −0.0419463 0.999120i \(-0.513356\pi\)
−0.0419463 + 0.999120i \(0.513356\pi\)
\(954\) 8.25053 0.267121
\(955\) 17.2996 0.559802
\(956\) −40.2190 −1.30077
\(957\) −5.36654 −0.173476
\(958\) 60.3627 1.95023
\(959\) 0 0
\(960\) 12.1017 0.390581
\(961\) −3.34496 −0.107902
\(962\) −3.52797 −0.113746
\(963\) −8.62135 −0.277819
\(964\) 73.1158 2.35490
\(965\) −2.99867 −0.0965305
\(966\) 0 0
\(967\) −27.1943 −0.874510 −0.437255 0.899337i \(-0.644049\pi\)
−0.437255 + 0.899337i \(0.644049\pi\)
\(968\) −7.84333 −0.252094
\(969\) 2.52355 0.0810680
\(970\) −27.8476 −0.894134
\(971\) 43.3753 1.39198 0.695990 0.718052i \(-0.254966\pi\)
0.695990 + 0.718052i \(0.254966\pi\)
\(972\) −4.97072 −0.159436
\(973\) 0 0
\(974\) −32.6612 −1.04653
\(975\) −1.46829 −0.0470230
\(976\) 146.657 4.69438
\(977\) −12.0461 −0.385388 −0.192694 0.981259i \(-0.561722\pi\)
−0.192694 + 0.981259i \(0.561722\pi\)
\(978\) 50.7503 1.62281
\(979\) −14.7962 −0.472888
\(980\) 0 0
\(981\) −0.496925 −0.0158656
\(982\) 91.5537 2.92160
\(983\) 25.7593 0.821594 0.410797 0.911727i \(-0.365250\pi\)
0.410797 + 0.911727i \(0.365250\pi\)
\(984\) −60.0005 −1.91275
\(985\) 8.31748 0.265017
\(986\) −18.7375 −0.596725
\(987\) 0 0
\(988\) 13.9272 0.443084
\(989\) −62.0368 −1.97265
\(990\) −2.64021 −0.0839114
\(991\) −23.3082 −0.740409 −0.370205 0.928950i \(-0.620712\pi\)
−0.370205 + 0.928950i \(0.620712\pi\)
\(992\) −66.9945 −2.12708
\(993\) 20.0057 0.634862
\(994\) 0 0
\(995\) −13.5052 −0.428143
\(996\) 76.5146 2.42446
\(997\) 12.0798 0.382570 0.191285 0.981535i \(-0.438735\pi\)
0.191285 + 0.981535i \(0.438735\pi\)
\(998\) 82.2306 2.60296
\(999\) −0.910067 −0.0287932
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 8085.2.a.ci.1.1 10
7.6 odd 2 8085.2.a.cj.1.1 yes 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8085.2.a.ci.1.1 10 1.1 even 1 trivial
8085.2.a.cj.1.1 yes 10 7.6 odd 2