Properties

Label 8015.2.a.k.1.12
Level $8015$
Weight $2$
Character 8015.1
Self dual yes
Analytic conductor $64.000$
Analytic rank $1$
Dimension $49$
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] = [8015,2,Mod(1,8015)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8015, 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("8015.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8015.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: \(64.0000972201\)
Analytic rank: \(1\)
Dimension: \(49\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Character \(\chi\) \(=\) 8015.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.80610 q^{2} +2.35882 q^{3} +1.26200 q^{4} -1.00000 q^{5} -4.26027 q^{6} -1.00000 q^{7} +1.33289 q^{8} +2.56402 q^{9} +O(q^{10})\) \(q-1.80610 q^{2} +2.35882 q^{3} +1.26200 q^{4} -1.00000 q^{5} -4.26027 q^{6} -1.00000 q^{7} +1.33289 q^{8} +2.56402 q^{9} +1.80610 q^{10} -2.69801 q^{11} +2.97684 q^{12} +3.47935 q^{13} +1.80610 q^{14} -2.35882 q^{15} -4.93135 q^{16} +0.778691 q^{17} -4.63089 q^{18} -3.47577 q^{19} -1.26200 q^{20} -2.35882 q^{21} +4.87288 q^{22} -3.41103 q^{23} +3.14406 q^{24} +1.00000 q^{25} -6.28405 q^{26} -1.02839 q^{27} -1.26200 q^{28} +1.67574 q^{29} +4.26027 q^{30} +2.44606 q^{31} +6.24074 q^{32} -6.36412 q^{33} -1.40640 q^{34} +1.00000 q^{35} +3.23581 q^{36} -6.83263 q^{37} +6.27760 q^{38} +8.20714 q^{39} -1.33289 q^{40} +2.85499 q^{41} +4.26027 q^{42} +8.30335 q^{43} -3.40490 q^{44} -2.56402 q^{45} +6.16066 q^{46} +8.26335 q^{47} -11.6322 q^{48} +1.00000 q^{49} -1.80610 q^{50} +1.83679 q^{51} +4.39095 q^{52} +8.82198 q^{53} +1.85737 q^{54} +2.69801 q^{55} -1.33289 q^{56} -8.19872 q^{57} -3.02655 q^{58} +4.26791 q^{59} -2.97684 q^{60} +0.270428 q^{61} -4.41784 q^{62} -2.56402 q^{63} -1.40870 q^{64} -3.47935 q^{65} +11.4943 q^{66} -8.19429 q^{67} +0.982712 q^{68} -8.04599 q^{69} -1.80610 q^{70} -13.5386 q^{71} +3.41757 q^{72} +7.03308 q^{73} +12.3404 q^{74} +2.35882 q^{75} -4.38644 q^{76} +2.69801 q^{77} -14.8229 q^{78} -0.794791 q^{79} +4.93135 q^{80} -10.1179 q^{81} -5.15640 q^{82} -11.2610 q^{83} -2.97684 q^{84} -0.778691 q^{85} -14.9967 q^{86} +3.95276 q^{87} -3.59617 q^{88} +3.24583 q^{89} +4.63089 q^{90} -3.47935 q^{91} -4.30473 q^{92} +5.76982 q^{93} -14.9245 q^{94} +3.47577 q^{95} +14.7208 q^{96} -9.06141 q^{97} -1.80610 q^{98} -6.91777 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 49 q - 3 q^{2} - 10 q^{3} + 49 q^{4} - 49 q^{5} + 10 q^{6} - 49 q^{7} - 6 q^{8} + 39 q^{9} + 3 q^{10} + 16 q^{11} - 26 q^{12} - 31 q^{13} + 3 q^{14} + 10 q^{15} + 49 q^{16} - 18 q^{17} + 4 q^{18} - 16 q^{19} - 49 q^{20} + 10 q^{21} + 10 q^{22} + 10 q^{23} + 2 q^{24} + 49 q^{25} - 22 q^{26} - 58 q^{27} - 49 q^{28} + 31 q^{29} - 10 q^{30} - 35 q^{31} - 5 q^{32} - 82 q^{33} - 41 q^{34} + 49 q^{35} + 49 q^{36} - 24 q^{37} - 20 q^{38} + 41 q^{39} + 6 q^{40} + 30 q^{41} - 10 q^{42} - 19 q^{43} + 27 q^{44} - 39 q^{45} + 15 q^{46} - 39 q^{47} - 51 q^{48} + 49 q^{49} - 3 q^{50} + 46 q^{51} - 94 q^{52} - 17 q^{53} + 9 q^{54} - 16 q^{55} + 6 q^{56} - 23 q^{57} - 46 q^{58} + 11 q^{59} + 26 q^{60} - 9 q^{61} - 49 q^{62} - 39 q^{63} + 10 q^{64} + 31 q^{65} - 10 q^{66} - 2 q^{67} - 73 q^{68} - 47 q^{69} - 3 q^{70} + 26 q^{71} - 39 q^{72} - 100 q^{73} + 8 q^{74} - 10 q^{75} - 71 q^{76} - 16 q^{77} - 51 q^{78} + 50 q^{79} - 49 q^{80} + 61 q^{81} - 36 q^{82} - 67 q^{83} + 26 q^{84} + 18 q^{85} + 33 q^{86} - 45 q^{87} - q^{88} - 19 q^{89} - 4 q^{90} + 31 q^{91} + 7 q^{92} + 9 q^{93} - 33 q^{94} + 16 q^{95} - 8 q^{96} - 85 q^{97} - 3 q^{98} + 27 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.80610 −1.27711 −0.638554 0.769577i \(-0.720467\pi\)
−0.638554 + 0.769577i \(0.720467\pi\)
\(3\) 2.35882 1.36186 0.680932 0.732346i \(-0.261575\pi\)
0.680932 + 0.732346i \(0.261575\pi\)
\(4\) 1.26200 0.631002
\(5\) −1.00000 −0.447214
\(6\) −4.26027 −1.73925
\(7\) −1.00000 −0.377964
\(8\) 1.33289 0.471249
\(9\) 2.56402 0.854675
\(10\) 1.80610 0.571140
\(11\) −2.69801 −0.813481 −0.406741 0.913544i \(-0.633335\pi\)
−0.406741 + 0.913544i \(0.633335\pi\)
\(12\) 2.97684 0.859340
\(13\) 3.47935 0.964997 0.482498 0.875897i \(-0.339729\pi\)
0.482498 + 0.875897i \(0.339729\pi\)
\(14\) 1.80610 0.482701
\(15\) −2.35882 −0.609044
\(16\) −4.93135 −1.23284
\(17\) 0.778691 0.188860 0.0944302 0.995531i \(-0.469897\pi\)
0.0944302 + 0.995531i \(0.469897\pi\)
\(18\) −4.63089 −1.09151
\(19\) −3.47577 −0.797397 −0.398698 0.917082i \(-0.630538\pi\)
−0.398698 + 0.917082i \(0.630538\pi\)
\(20\) −1.26200 −0.282193
\(21\) −2.35882 −0.514736
\(22\) 4.87288 1.03890
\(23\) −3.41103 −0.711248 −0.355624 0.934629i \(-0.615732\pi\)
−0.355624 + 0.934629i \(0.615732\pi\)
\(24\) 3.14406 0.641778
\(25\) 1.00000 0.200000
\(26\) −6.28405 −1.23240
\(27\) −1.02839 −0.197913
\(28\) −1.26200 −0.238496
\(29\) 1.67574 0.311176 0.155588 0.987822i \(-0.450273\pi\)
0.155588 + 0.987822i \(0.450273\pi\)
\(30\) 4.26027 0.777815
\(31\) 2.44606 0.439326 0.219663 0.975576i \(-0.429504\pi\)
0.219663 + 0.975576i \(0.429504\pi\)
\(32\) 6.24074 1.10322
\(33\) −6.36412 −1.10785
\(34\) −1.40640 −0.241195
\(35\) 1.00000 0.169031
\(36\) 3.23581 0.539302
\(37\) −6.83263 −1.12328 −0.561639 0.827383i \(-0.689829\pi\)
−0.561639 + 0.827383i \(0.689829\pi\)
\(38\) 6.27760 1.01836
\(39\) 8.20714 1.31419
\(40\) −1.33289 −0.210749
\(41\) 2.85499 0.445875 0.222937 0.974833i \(-0.428435\pi\)
0.222937 + 0.974833i \(0.428435\pi\)
\(42\) 4.26027 0.657373
\(43\) 8.30335 1.26625 0.633125 0.774050i \(-0.281772\pi\)
0.633125 + 0.774050i \(0.281772\pi\)
\(44\) −3.40490 −0.513309
\(45\) −2.56402 −0.382222
\(46\) 6.16066 0.908340
\(47\) 8.26335 1.20533 0.602667 0.797993i \(-0.294105\pi\)
0.602667 + 0.797993i \(0.294105\pi\)
\(48\) −11.6322 −1.67896
\(49\) 1.00000 0.142857
\(50\) −1.80610 −0.255421
\(51\) 1.83679 0.257202
\(52\) 4.39095 0.608915
\(53\) 8.82198 1.21179 0.605896 0.795544i \(-0.292815\pi\)
0.605896 + 0.795544i \(0.292815\pi\)
\(54\) 1.85737 0.252756
\(55\) 2.69801 0.363800
\(56\) −1.33289 −0.178116
\(57\) −8.19872 −1.08595
\(58\) −3.02655 −0.397406
\(59\) 4.26791 0.555635 0.277817 0.960634i \(-0.410389\pi\)
0.277817 + 0.960634i \(0.410389\pi\)
\(60\) −2.97684 −0.384308
\(61\) 0.270428 0.0346247 0.0173124 0.999850i \(-0.494489\pi\)
0.0173124 + 0.999850i \(0.494489\pi\)
\(62\) −4.41784 −0.561066
\(63\) −2.56402 −0.323037
\(64\) −1.40870 −0.176088
\(65\) −3.47935 −0.431560
\(66\) 11.4943 1.41484
\(67\) −8.19429 −1.00109 −0.500546 0.865710i \(-0.666867\pi\)
−0.500546 + 0.865710i \(0.666867\pi\)
\(68\) 0.982712 0.119171
\(69\) −8.04599 −0.968623
\(70\) −1.80610 −0.215870
\(71\) −13.5386 −1.60673 −0.803366 0.595485i \(-0.796960\pi\)
−0.803366 + 0.595485i \(0.796960\pi\)
\(72\) 3.41757 0.402765
\(73\) 7.03308 0.823159 0.411580 0.911374i \(-0.364977\pi\)
0.411580 + 0.911374i \(0.364977\pi\)
\(74\) 12.3404 1.43455
\(75\) 2.35882 0.272373
\(76\) −4.38644 −0.503159
\(77\) 2.69801 0.307467
\(78\) −14.8229 −1.67837
\(79\) −0.794791 −0.0894210 −0.0447105 0.999000i \(-0.514237\pi\)
−0.0447105 + 0.999000i \(0.514237\pi\)
\(80\) 4.93135 0.551342
\(81\) −10.1179 −1.12421
\(82\) −5.15640 −0.569429
\(83\) −11.2610 −1.23605 −0.618026 0.786158i \(-0.712067\pi\)
−0.618026 + 0.786158i \(0.712067\pi\)
\(84\) −2.97684 −0.324800
\(85\) −0.778691 −0.0844609
\(86\) −14.9967 −1.61714
\(87\) 3.95276 0.423780
\(88\) −3.59617 −0.383353
\(89\) 3.24583 0.344058 0.172029 0.985092i \(-0.444968\pi\)
0.172029 + 0.985092i \(0.444968\pi\)
\(90\) 4.63089 0.488139
\(91\) −3.47935 −0.364734
\(92\) −4.30473 −0.448799
\(93\) 5.76982 0.598302
\(94\) −14.9245 −1.53934
\(95\) 3.47577 0.356607
\(96\) 14.7208 1.50243
\(97\) −9.06141 −0.920047 −0.460023 0.887907i \(-0.652159\pi\)
−0.460023 + 0.887907i \(0.652159\pi\)
\(98\) −1.80610 −0.182444
\(99\) −6.91777 −0.695262
\(100\) 1.26200 0.126200
\(101\) −17.5198 −1.74328 −0.871642 0.490144i \(-0.836944\pi\)
−0.871642 + 0.490144i \(0.836944\pi\)
\(102\) −3.31743 −0.328475
\(103\) 12.4744 1.22914 0.614570 0.788862i \(-0.289330\pi\)
0.614570 + 0.788862i \(0.289330\pi\)
\(104\) 4.63760 0.454754
\(105\) 2.35882 0.230197
\(106\) −15.9334 −1.54759
\(107\) 6.21181 0.600518 0.300259 0.953858i \(-0.402927\pi\)
0.300259 + 0.953858i \(0.402927\pi\)
\(108\) −1.29783 −0.124884
\(109\) −9.79103 −0.937810 −0.468905 0.883249i \(-0.655351\pi\)
−0.468905 + 0.883249i \(0.655351\pi\)
\(110\) −4.87288 −0.464611
\(111\) −16.1169 −1.52975
\(112\) 4.93135 0.465969
\(113\) 5.38244 0.506337 0.253169 0.967422i \(-0.418527\pi\)
0.253169 + 0.967422i \(0.418527\pi\)
\(114\) 14.8077 1.38687
\(115\) 3.41103 0.318080
\(116\) 2.11479 0.196353
\(117\) 8.92113 0.824758
\(118\) −7.70829 −0.709605
\(119\) −0.778691 −0.0713825
\(120\) −3.14406 −0.287012
\(121\) −3.72073 −0.338248
\(122\) −0.488420 −0.0442195
\(123\) 6.73440 0.607221
\(124\) 3.08694 0.277216
\(125\) −1.00000 −0.0894427
\(126\) 4.63089 0.412552
\(127\) −0.808924 −0.0717804 −0.0358902 0.999356i \(-0.511427\pi\)
−0.0358902 + 0.999356i \(0.511427\pi\)
\(128\) −9.93721 −0.878334
\(129\) 19.5861 1.72446
\(130\) 6.28405 0.551148
\(131\) −14.3625 −1.25486 −0.627428 0.778674i \(-0.715892\pi\)
−0.627428 + 0.778674i \(0.715892\pi\)
\(132\) −8.03155 −0.699057
\(133\) 3.47577 0.301388
\(134\) 14.7997 1.27850
\(135\) 1.02839 0.0885095
\(136\) 1.03791 0.0890003
\(137\) 4.04262 0.345384 0.172692 0.984976i \(-0.444753\pi\)
0.172692 + 0.984976i \(0.444753\pi\)
\(138\) 14.5319 1.23704
\(139\) −21.5514 −1.82797 −0.913984 0.405750i \(-0.867010\pi\)
−0.913984 + 0.405750i \(0.867010\pi\)
\(140\) 1.26200 0.106659
\(141\) 19.4918 1.64150
\(142\) 24.4520 2.05197
\(143\) −9.38731 −0.785007
\(144\) −12.6441 −1.05368
\(145\) −1.67574 −0.139162
\(146\) −12.7025 −1.05126
\(147\) 2.35882 0.194552
\(148\) −8.62281 −0.708791
\(149\) −8.47320 −0.694152 −0.347076 0.937837i \(-0.612825\pi\)
−0.347076 + 0.937837i \(0.612825\pi\)
\(150\) −4.26027 −0.347849
\(151\) −16.5614 −1.34774 −0.673872 0.738848i \(-0.735370\pi\)
−0.673872 + 0.738848i \(0.735370\pi\)
\(152\) −4.63284 −0.375773
\(153\) 1.99658 0.161414
\(154\) −4.87288 −0.392668
\(155\) −2.44606 −0.196472
\(156\) 10.3575 0.829260
\(157\) −3.08498 −0.246208 −0.123104 0.992394i \(-0.539285\pi\)
−0.123104 + 0.992394i \(0.539285\pi\)
\(158\) 1.43547 0.114200
\(159\) 20.8095 1.65030
\(160\) −6.24074 −0.493374
\(161\) 3.41103 0.268826
\(162\) 18.2739 1.43573
\(163\) −1.59303 −0.124775 −0.0623877 0.998052i \(-0.519872\pi\)
−0.0623877 + 0.998052i \(0.519872\pi\)
\(164\) 3.60301 0.281348
\(165\) 6.36412 0.495446
\(166\) 20.3385 1.57857
\(167\) 9.79861 0.758239 0.379120 0.925348i \(-0.376227\pi\)
0.379120 + 0.925348i \(0.376227\pi\)
\(168\) −3.14406 −0.242569
\(169\) −0.894157 −0.0687813
\(170\) 1.40640 0.107866
\(171\) −8.91197 −0.681515
\(172\) 10.4789 0.799006
\(173\) −3.00346 −0.228349 −0.114175 0.993461i \(-0.536422\pi\)
−0.114175 + 0.993461i \(0.536422\pi\)
\(174\) −7.13908 −0.541213
\(175\) −1.00000 −0.0755929
\(176\) 13.3048 1.00289
\(177\) 10.0672 0.756700
\(178\) −5.86231 −0.439399
\(179\) 16.2014 1.21095 0.605473 0.795866i \(-0.292984\pi\)
0.605473 + 0.795866i \(0.292984\pi\)
\(180\) −3.23581 −0.241183
\(181\) −7.32365 −0.544362 −0.272181 0.962246i \(-0.587745\pi\)
−0.272181 + 0.962246i \(0.587745\pi\)
\(182\) 6.28405 0.465805
\(183\) 0.637890 0.0471542
\(184\) −4.54654 −0.335175
\(185\) 6.83263 0.502345
\(186\) −10.4209 −0.764096
\(187\) −2.10092 −0.153634
\(188\) 10.4284 0.760569
\(189\) 1.02839 0.0748041
\(190\) −6.27760 −0.455425
\(191\) −20.0713 −1.45231 −0.726155 0.687531i \(-0.758694\pi\)
−0.726155 + 0.687531i \(0.758694\pi\)
\(192\) −3.32288 −0.239808
\(193\) −0.770165 −0.0554377 −0.0277188 0.999616i \(-0.508824\pi\)
−0.0277188 + 0.999616i \(0.508824\pi\)
\(194\) 16.3658 1.17500
\(195\) −8.20714 −0.587726
\(196\) 1.26200 0.0901432
\(197\) 7.98403 0.568838 0.284419 0.958700i \(-0.408199\pi\)
0.284419 + 0.958700i \(0.408199\pi\)
\(198\) 12.4942 0.887924
\(199\) 1.63400 0.115831 0.0579157 0.998321i \(-0.481555\pi\)
0.0579157 + 0.998321i \(0.481555\pi\)
\(200\) 1.33289 0.0942499
\(201\) −19.3289 −1.36335
\(202\) 31.6425 2.22636
\(203\) −1.67574 −0.117614
\(204\) 2.31804 0.162295
\(205\) −2.85499 −0.199401
\(206\) −22.5301 −1.56974
\(207\) −8.74595 −0.607886
\(208\) −17.1579 −1.18969
\(209\) 9.37767 0.648667
\(210\) −4.26027 −0.293986
\(211\) 10.6926 0.736109 0.368055 0.929804i \(-0.380024\pi\)
0.368055 + 0.929804i \(0.380024\pi\)
\(212\) 11.1334 0.764644
\(213\) −31.9350 −2.18815
\(214\) −11.2192 −0.766926
\(215\) −8.30335 −0.566284
\(216\) −1.37073 −0.0932665
\(217\) −2.44606 −0.166050
\(218\) 17.6836 1.19768
\(219\) 16.5897 1.12103
\(220\) 3.40490 0.229559
\(221\) 2.70933 0.182250
\(222\) 29.1088 1.95366
\(223\) −9.65827 −0.646766 −0.323383 0.946268i \(-0.604820\pi\)
−0.323383 + 0.946268i \(0.604820\pi\)
\(224\) −6.24074 −0.416977
\(225\) 2.56402 0.170935
\(226\) −9.72123 −0.646647
\(227\) 13.7845 0.914912 0.457456 0.889232i \(-0.348761\pi\)
0.457456 + 0.889232i \(0.348761\pi\)
\(228\) −10.3468 −0.685235
\(229\) −1.00000 −0.0660819
\(230\) −6.16066 −0.406222
\(231\) 6.36412 0.418728
\(232\) 2.23358 0.146642
\(233\) −23.3690 −1.53095 −0.765476 0.643465i \(-0.777496\pi\)
−0.765476 + 0.643465i \(0.777496\pi\)
\(234\) −16.1125 −1.05330
\(235\) −8.26335 −0.539042
\(236\) 5.38613 0.350607
\(237\) −1.87477 −0.121779
\(238\) 1.40640 0.0911631
\(239\) −7.31814 −0.473371 −0.236686 0.971586i \(-0.576061\pi\)
−0.236686 + 0.971586i \(0.576061\pi\)
\(240\) 11.6322 0.750853
\(241\) 27.2092 1.75270 0.876351 0.481673i \(-0.159971\pi\)
0.876351 + 0.481673i \(0.159971\pi\)
\(242\) 6.72002 0.431979
\(243\) −20.7810 −1.33310
\(244\) 0.341281 0.0218483
\(245\) −1.00000 −0.0638877
\(246\) −12.1630 −0.775486
\(247\) −12.0934 −0.769485
\(248\) 3.26034 0.207032
\(249\) −26.5626 −1.68333
\(250\) 1.80610 0.114228
\(251\) 30.1833 1.90515 0.952575 0.304303i \(-0.0984234\pi\)
0.952575 + 0.304303i \(0.0984234\pi\)
\(252\) −3.23581 −0.203837
\(253\) 9.20299 0.578587
\(254\) 1.46100 0.0916713
\(255\) −1.83679 −0.115024
\(256\) 20.7650 1.29781
\(257\) 11.1732 0.696963 0.348482 0.937316i \(-0.386697\pi\)
0.348482 + 0.937316i \(0.386697\pi\)
\(258\) −35.3745 −2.20232
\(259\) 6.83263 0.424559
\(260\) −4.39095 −0.272315
\(261\) 4.29663 0.265955
\(262\) 25.9401 1.60259
\(263\) 21.0183 1.29604 0.648020 0.761623i \(-0.275597\pi\)
0.648020 + 0.761623i \(0.275597\pi\)
\(264\) −8.48270 −0.522074
\(265\) −8.82198 −0.541930
\(266\) −6.27760 −0.384904
\(267\) 7.65633 0.468560
\(268\) −10.3412 −0.631692
\(269\) 19.1959 1.17040 0.585198 0.810891i \(-0.301017\pi\)
0.585198 + 0.810891i \(0.301017\pi\)
\(270\) −1.85737 −0.113036
\(271\) −19.0389 −1.15653 −0.578264 0.815850i \(-0.696270\pi\)
−0.578264 + 0.815850i \(0.696270\pi\)
\(272\) −3.84000 −0.232834
\(273\) −8.20714 −0.496719
\(274\) −7.30138 −0.441092
\(275\) −2.69801 −0.162696
\(276\) −10.1541 −0.611204
\(277\) −17.6164 −1.05846 −0.529232 0.848477i \(-0.677520\pi\)
−0.529232 + 0.848477i \(0.677520\pi\)
\(278\) 38.9241 2.33451
\(279\) 6.27176 0.375481
\(280\) 1.33289 0.0796557
\(281\) −31.8274 −1.89867 −0.949333 0.314273i \(-0.898239\pi\)
−0.949333 + 0.314273i \(0.898239\pi\)
\(282\) −35.2041 −2.09637
\(283\) 13.6244 0.809885 0.404942 0.914342i \(-0.367292\pi\)
0.404942 + 0.914342i \(0.367292\pi\)
\(284\) −17.0857 −1.01385
\(285\) 8.19872 0.485650
\(286\) 16.9544 1.00254
\(287\) −2.85499 −0.168525
\(288\) 16.0014 0.942892
\(289\) −16.3936 −0.964332
\(290\) 3.02655 0.177725
\(291\) −21.3742 −1.25298
\(292\) 8.87577 0.519415
\(293\) −16.1345 −0.942586 −0.471293 0.881977i \(-0.656212\pi\)
−0.471293 + 0.881977i \(0.656212\pi\)
\(294\) −4.26027 −0.248464
\(295\) −4.26791 −0.248488
\(296\) −9.10718 −0.529344
\(297\) 2.77460 0.160999
\(298\) 15.3035 0.886506
\(299\) −11.8681 −0.686352
\(300\) 2.97684 0.171868
\(301\) −8.30335 −0.478597
\(302\) 29.9115 1.72121
\(303\) −41.3260 −2.37412
\(304\) 17.1403 0.983061
\(305\) −0.270428 −0.0154847
\(306\) −3.60603 −0.206143
\(307\) −23.4666 −1.33931 −0.669654 0.742674i \(-0.733557\pi\)
−0.669654 + 0.742674i \(0.733557\pi\)
\(308\) 3.40490 0.194012
\(309\) 29.4249 1.67392
\(310\) 4.41784 0.250916
\(311\) 28.4374 1.61254 0.806269 0.591550i \(-0.201484\pi\)
0.806269 + 0.591550i \(0.201484\pi\)
\(312\) 10.9393 0.619314
\(313\) −14.2227 −0.803917 −0.401958 0.915658i \(-0.631670\pi\)
−0.401958 + 0.915658i \(0.631670\pi\)
\(314\) 5.57178 0.314434
\(315\) 2.56402 0.144466
\(316\) −1.00303 −0.0564249
\(317\) −1.76366 −0.0990572 −0.0495286 0.998773i \(-0.515772\pi\)
−0.0495286 + 0.998773i \(0.515772\pi\)
\(318\) −37.5840 −2.10761
\(319\) −4.52116 −0.253136
\(320\) 1.40870 0.0787489
\(321\) 14.6525 0.817824
\(322\) −6.16066 −0.343320
\(323\) −2.70655 −0.150597
\(324\) −12.7688 −0.709376
\(325\) 3.47935 0.192999
\(326\) 2.87717 0.159352
\(327\) −23.0953 −1.27717
\(328\) 3.80540 0.210118
\(329\) −8.26335 −0.455573
\(330\) −11.4943 −0.632738
\(331\) −13.6892 −0.752427 −0.376214 0.926533i \(-0.622774\pi\)
−0.376214 + 0.926533i \(0.622774\pi\)
\(332\) −14.2114 −0.779951
\(333\) −17.5190 −0.960037
\(334\) −17.6973 −0.968352
\(335\) 8.19429 0.447702
\(336\) 11.6322 0.634587
\(337\) −26.8521 −1.46273 −0.731364 0.681988i \(-0.761116\pi\)
−0.731364 + 0.681988i \(0.761116\pi\)
\(338\) 1.61494 0.0878411
\(339\) 12.6962 0.689562
\(340\) −0.982712 −0.0532950
\(341\) −6.59950 −0.357383
\(342\) 16.0959 0.870368
\(343\) −1.00000 −0.0539949
\(344\) 11.0675 0.596719
\(345\) 8.04599 0.433181
\(346\) 5.42456 0.291626
\(347\) −9.72411 −0.522018 −0.261009 0.965336i \(-0.584055\pi\)
−0.261009 + 0.965336i \(0.584055\pi\)
\(348\) 4.98840 0.267406
\(349\) 3.37643 0.180736 0.0903681 0.995908i \(-0.471196\pi\)
0.0903681 + 0.995908i \(0.471196\pi\)
\(350\) 1.80610 0.0965402
\(351\) −3.57811 −0.190986
\(352\) −16.8376 −0.897446
\(353\) −35.2945 −1.87853 −0.939267 0.343186i \(-0.888494\pi\)
−0.939267 + 0.343186i \(0.888494\pi\)
\(354\) −18.1824 −0.966386
\(355\) 13.5386 0.718553
\(356\) 4.09626 0.217101
\(357\) −1.83679 −0.0972133
\(358\) −29.2613 −1.54651
\(359\) −1.87438 −0.0989257 −0.0494629 0.998776i \(-0.515751\pi\)
−0.0494629 + 0.998776i \(0.515751\pi\)
\(360\) −3.41757 −0.180122
\(361\) −6.91901 −0.364158
\(362\) 13.2273 0.695209
\(363\) −8.77653 −0.460649
\(364\) −4.39095 −0.230148
\(365\) −7.03308 −0.368128
\(366\) −1.15209 −0.0602210
\(367\) −5.01404 −0.261731 −0.130865 0.991400i \(-0.541776\pi\)
−0.130865 + 0.991400i \(0.541776\pi\)
\(368\) 16.8210 0.876854
\(369\) 7.32026 0.381078
\(370\) −12.3404 −0.641548
\(371\) −8.82198 −0.458014
\(372\) 7.28154 0.377530
\(373\) −7.12713 −0.369029 −0.184514 0.982830i \(-0.559071\pi\)
−0.184514 + 0.982830i \(0.559071\pi\)
\(374\) 3.79447 0.196207
\(375\) −2.35882 −0.121809
\(376\) 11.0142 0.568013
\(377\) 5.83047 0.300284
\(378\) −1.85737 −0.0955329
\(379\) −1.47600 −0.0758173 −0.0379086 0.999281i \(-0.512070\pi\)
−0.0379086 + 0.999281i \(0.512070\pi\)
\(380\) 4.38644 0.225020
\(381\) −1.90810 −0.0977552
\(382\) 36.2508 1.85475
\(383\) −10.8848 −0.556187 −0.278093 0.960554i \(-0.589702\pi\)
−0.278093 + 0.960554i \(0.589702\pi\)
\(384\) −23.4401 −1.19617
\(385\) −2.69801 −0.137503
\(386\) 1.39100 0.0707999
\(387\) 21.2900 1.08223
\(388\) −11.4355 −0.580552
\(389\) −10.7866 −0.546904 −0.273452 0.961886i \(-0.588166\pi\)
−0.273452 + 0.961886i \(0.588166\pi\)
\(390\) 14.8229 0.750589
\(391\) −2.65613 −0.134326
\(392\) 1.33289 0.0673214
\(393\) −33.8785 −1.70894
\(394\) −14.4200 −0.726467
\(395\) 0.794791 0.0399903
\(396\) −8.73026 −0.438712
\(397\) 12.9324 0.649059 0.324529 0.945876i \(-0.394794\pi\)
0.324529 + 0.945876i \(0.394794\pi\)
\(398\) −2.95118 −0.147929
\(399\) 8.19872 0.410449
\(400\) −4.93135 −0.246568
\(401\) 19.7263 0.985086 0.492543 0.870288i \(-0.336068\pi\)
0.492543 + 0.870288i \(0.336068\pi\)
\(402\) 34.9099 1.74115
\(403\) 8.51070 0.423948
\(404\) −22.1100 −1.10002
\(405\) 10.1179 0.502760
\(406\) 3.02655 0.150205
\(407\) 18.4345 0.913765
\(408\) 2.44825 0.121206
\(409\) −18.0336 −0.891703 −0.445852 0.895107i \(-0.647099\pi\)
−0.445852 + 0.895107i \(0.647099\pi\)
\(410\) 5.15640 0.254657
\(411\) 9.53580 0.470366
\(412\) 15.7428 0.775590
\(413\) −4.26791 −0.210010
\(414\) 15.7961 0.776335
\(415\) 11.2610 0.552779
\(416\) 21.7137 1.06460
\(417\) −50.8359 −2.48944
\(418\) −16.9370 −0.828418
\(419\) 1.30530 0.0637681 0.0318841 0.999492i \(-0.489849\pi\)
0.0318841 + 0.999492i \(0.489849\pi\)
\(420\) 2.97684 0.145255
\(421\) −7.25636 −0.353654 −0.176827 0.984242i \(-0.556583\pi\)
−0.176827 + 0.984242i \(0.556583\pi\)
\(422\) −19.3119 −0.940090
\(423\) 21.1874 1.03017
\(424\) 11.7588 0.571057
\(425\) 0.778691 0.0377721
\(426\) 57.6779 2.79450
\(427\) −0.270428 −0.0130869
\(428\) 7.83933 0.378928
\(429\) −22.1430 −1.06907
\(430\) 14.9967 0.723205
\(431\) 23.2032 1.11766 0.558830 0.829283i \(-0.311251\pi\)
0.558830 + 0.829283i \(0.311251\pi\)
\(432\) 5.07134 0.243995
\(433\) −25.4114 −1.22119 −0.610596 0.791942i \(-0.709070\pi\)
−0.610596 + 0.791942i \(0.709070\pi\)
\(434\) 4.41784 0.212063
\(435\) −3.95276 −0.189520
\(436\) −12.3563 −0.591761
\(437\) 11.8559 0.567147
\(438\) −29.9628 −1.43168
\(439\) −18.0990 −0.863817 −0.431909 0.901917i \(-0.642160\pi\)
−0.431909 + 0.901917i \(0.642160\pi\)
\(440\) 3.59617 0.171440
\(441\) 2.56402 0.122096
\(442\) −4.89334 −0.232752
\(443\) −28.7398 −1.36547 −0.682735 0.730666i \(-0.739210\pi\)
−0.682735 + 0.730666i \(0.739210\pi\)
\(444\) −20.3396 −0.965277
\(445\) −3.24583 −0.153867
\(446\) 17.4438 0.825989
\(447\) −19.9867 −0.945340
\(448\) 1.40870 0.0665550
\(449\) −23.8604 −1.12604 −0.563021 0.826443i \(-0.690361\pi\)
−0.563021 + 0.826443i \(0.690361\pi\)
\(450\) −4.63089 −0.218302
\(451\) −7.70280 −0.362711
\(452\) 6.79266 0.319500
\(453\) −39.0652 −1.83545
\(454\) −24.8963 −1.16844
\(455\) 3.47935 0.163114
\(456\) −10.9280 −0.511752
\(457\) −11.9053 −0.556906 −0.278453 0.960450i \(-0.589822\pi\)
−0.278453 + 0.960450i \(0.589822\pi\)
\(458\) 1.80610 0.0843936
\(459\) −0.800796 −0.0373779
\(460\) 4.30473 0.200709
\(461\) 24.0076 1.11814 0.559072 0.829119i \(-0.311157\pi\)
0.559072 + 0.829119i \(0.311157\pi\)
\(462\) −11.4943 −0.534761
\(463\) −13.3775 −0.621704 −0.310852 0.950458i \(-0.600614\pi\)
−0.310852 + 0.950458i \(0.600614\pi\)
\(464\) −8.26365 −0.383630
\(465\) −5.76982 −0.267569
\(466\) 42.2067 1.95519
\(467\) −16.8470 −0.779586 −0.389793 0.920902i \(-0.627453\pi\)
−0.389793 + 0.920902i \(0.627453\pi\)
\(468\) 11.2585 0.520425
\(469\) 8.19429 0.378377
\(470\) 14.9245 0.688414
\(471\) −7.27690 −0.335302
\(472\) 5.68868 0.261843
\(473\) −22.4025 −1.03007
\(474\) 3.38602 0.155525
\(475\) −3.47577 −0.159479
\(476\) −0.982712 −0.0450425
\(477\) 22.6198 1.03569
\(478\) 13.2173 0.604546
\(479\) 9.77482 0.446623 0.223312 0.974747i \(-0.428313\pi\)
0.223312 + 0.974747i \(0.428313\pi\)
\(480\) −14.7208 −0.671908
\(481\) −23.7731 −1.08396
\(482\) −49.1427 −2.23839
\(483\) 8.04599 0.366105
\(484\) −4.69558 −0.213436
\(485\) 9.06141 0.411457
\(486\) 37.5326 1.70251
\(487\) 3.93867 0.178478 0.0892390 0.996010i \(-0.471557\pi\)
0.0892390 + 0.996010i \(0.471557\pi\)
\(488\) 0.360452 0.0163169
\(489\) −3.75766 −0.169927
\(490\) 1.80610 0.0815914
\(491\) 13.5362 0.610879 0.305439 0.952212i \(-0.401197\pi\)
0.305439 + 0.952212i \(0.401197\pi\)
\(492\) 8.49885 0.383158
\(493\) 1.30488 0.0587689
\(494\) 21.8419 0.982715
\(495\) 6.91777 0.310931
\(496\) −12.0624 −0.541618
\(497\) 13.5386 0.607288
\(498\) 47.9747 2.14980
\(499\) 40.2323 1.80104 0.900522 0.434810i \(-0.143184\pi\)
0.900522 + 0.434810i \(0.143184\pi\)
\(500\) −1.26200 −0.0564386
\(501\) 23.1131 1.03262
\(502\) −54.5141 −2.43308
\(503\) 24.1807 1.07816 0.539082 0.842253i \(-0.318771\pi\)
0.539082 + 0.842253i \(0.318771\pi\)
\(504\) −3.41757 −0.152231
\(505\) 17.5198 0.779620
\(506\) −16.6215 −0.738917
\(507\) −2.10915 −0.0936708
\(508\) −1.02087 −0.0452936
\(509\) −28.1881 −1.24941 −0.624707 0.780859i \(-0.714781\pi\)
−0.624707 + 0.780859i \(0.714781\pi\)
\(510\) 3.31743 0.146898
\(511\) −7.03308 −0.311125
\(512\) −17.6293 −0.779114
\(513\) 3.57444 0.157815
\(514\) −20.1799 −0.890097
\(515\) −12.4744 −0.549688
\(516\) 24.7178 1.08814
\(517\) −22.2946 −0.980516
\(518\) −12.3404 −0.542207
\(519\) −7.08462 −0.310980
\(520\) −4.63760 −0.203372
\(521\) −14.7648 −0.646856 −0.323428 0.946253i \(-0.604835\pi\)
−0.323428 + 0.946253i \(0.604835\pi\)
\(522\) −7.76015 −0.339653
\(523\) 13.1768 0.576182 0.288091 0.957603i \(-0.406979\pi\)
0.288091 + 0.957603i \(0.406979\pi\)
\(524\) −18.1255 −0.791817
\(525\) −2.35882 −0.102947
\(526\) −37.9611 −1.65518
\(527\) 1.90473 0.0829712
\(528\) 31.3837 1.36580
\(529\) −11.3649 −0.494126
\(530\) 15.9334 0.692103
\(531\) 10.9430 0.474887
\(532\) 4.38644 0.190176
\(533\) 9.93350 0.430267
\(534\) −13.8281 −0.598401
\(535\) −6.21181 −0.268560
\(536\) −10.9221 −0.471764
\(537\) 38.2161 1.64915
\(538\) −34.6698 −1.49472
\(539\) −2.69801 −0.116212
\(540\) 1.29783 0.0558497
\(541\) −8.13954 −0.349946 −0.174973 0.984573i \(-0.555984\pi\)
−0.174973 + 0.984573i \(0.555984\pi\)
\(542\) 34.3861 1.47701
\(543\) −17.2752 −0.741348
\(544\) 4.85961 0.208354
\(545\) 9.79103 0.419402
\(546\) 14.8229 0.634363
\(547\) 36.1200 1.54438 0.772190 0.635392i \(-0.219161\pi\)
0.772190 + 0.635392i \(0.219161\pi\)
\(548\) 5.10180 0.217938
\(549\) 0.693384 0.0295929
\(550\) 4.87288 0.207780
\(551\) −5.82448 −0.248131
\(552\) −10.7245 −0.456463
\(553\) 0.794791 0.0337980
\(554\) 31.8169 1.35177
\(555\) 16.1169 0.684126
\(556\) −27.1980 −1.15345
\(557\) −43.1603 −1.82876 −0.914380 0.404856i \(-0.867322\pi\)
−0.914380 + 0.404856i \(0.867322\pi\)
\(558\) −11.3274 −0.479529
\(559\) 28.8902 1.22193
\(560\) −4.93135 −0.208388
\(561\) −4.95568 −0.209229
\(562\) 57.4836 2.42480
\(563\) 29.7682 1.25458 0.627291 0.778785i \(-0.284164\pi\)
0.627291 + 0.778785i \(0.284164\pi\)
\(564\) 24.5987 1.03579
\(565\) −5.38244 −0.226441
\(566\) −24.6070 −1.03431
\(567\) 10.1179 0.424910
\(568\) −18.0455 −0.757172
\(569\) 15.1312 0.634333 0.317167 0.948370i \(-0.397269\pi\)
0.317167 + 0.948370i \(0.397269\pi\)
\(570\) −14.8077 −0.620227
\(571\) −8.76823 −0.366939 −0.183470 0.983025i \(-0.558733\pi\)
−0.183470 + 0.983025i \(0.558733\pi\)
\(572\) −11.8468 −0.495341
\(573\) −47.3446 −1.97785
\(574\) 5.15640 0.215224
\(575\) −3.41103 −0.142250
\(576\) −3.61195 −0.150498
\(577\) 46.7565 1.94650 0.973248 0.229755i \(-0.0737925\pi\)
0.973248 + 0.229755i \(0.0737925\pi\)
\(578\) 29.6086 1.23155
\(579\) −1.81668 −0.0754986
\(580\) −2.11479 −0.0878118
\(581\) 11.2610 0.467184
\(582\) 38.6040 1.60019
\(583\) −23.8018 −0.985770
\(584\) 9.37435 0.387913
\(585\) −8.92113 −0.368843
\(586\) 29.1405 1.20378
\(587\) −14.2095 −0.586491 −0.293245 0.956037i \(-0.594735\pi\)
−0.293245 + 0.956037i \(0.594735\pi\)
\(588\) 2.97684 0.122763
\(589\) −8.50196 −0.350317
\(590\) 7.70829 0.317345
\(591\) 18.8329 0.774681
\(592\) 33.6941 1.38482
\(593\) −7.50225 −0.308081 −0.154040 0.988065i \(-0.549229\pi\)
−0.154040 + 0.988065i \(0.549229\pi\)
\(594\) −5.01121 −0.205612
\(595\) 0.778691 0.0319232
\(596\) −10.6932 −0.438011
\(597\) 3.85432 0.157747
\(598\) 21.4351 0.876545
\(599\) 1.90564 0.0778622 0.0389311 0.999242i \(-0.487605\pi\)
0.0389311 + 0.999242i \(0.487605\pi\)
\(600\) 3.14406 0.128356
\(601\) −21.3548 −0.871079 −0.435539 0.900170i \(-0.643442\pi\)
−0.435539 + 0.900170i \(0.643442\pi\)
\(602\) 14.9967 0.611220
\(603\) −21.0104 −0.855609
\(604\) −20.9005 −0.850430
\(605\) 3.72073 0.151269
\(606\) 74.6389 3.03200
\(607\) 3.74074 0.151832 0.0759159 0.997114i \(-0.475812\pi\)
0.0759159 + 0.997114i \(0.475812\pi\)
\(608\) −21.6914 −0.879702
\(609\) −3.95276 −0.160174
\(610\) 0.488420 0.0197756
\(611\) 28.7511 1.16314
\(612\) 2.51970 0.101853
\(613\) 7.27475 0.293824 0.146912 0.989150i \(-0.453067\pi\)
0.146912 + 0.989150i \(0.453067\pi\)
\(614\) 42.3830 1.71044
\(615\) −6.73440 −0.271557
\(616\) 3.59617 0.144894
\(617\) −10.0873 −0.406100 −0.203050 0.979168i \(-0.565085\pi\)
−0.203050 + 0.979168i \(0.565085\pi\)
\(618\) −53.1443 −2.13778
\(619\) 21.0990 0.848039 0.424019 0.905653i \(-0.360619\pi\)
0.424019 + 0.905653i \(0.360619\pi\)
\(620\) −3.08694 −0.123975
\(621\) 3.50785 0.140765
\(622\) −51.3609 −2.05938
\(623\) −3.24583 −0.130042
\(624\) −40.4723 −1.62019
\(625\) 1.00000 0.0400000
\(626\) 25.6877 1.02669
\(627\) 22.1202 0.883397
\(628\) −3.89325 −0.155358
\(629\) −5.32051 −0.212143
\(630\) −4.63089 −0.184499
\(631\) 38.0104 1.51317 0.756586 0.653895i \(-0.226866\pi\)
0.756586 + 0.653895i \(0.226866\pi\)
\(632\) −1.05937 −0.0421396
\(633\) 25.2219 1.00248
\(634\) 3.18536 0.126507
\(635\) 0.808924 0.0321012
\(636\) 26.2616 1.04134
\(637\) 3.47935 0.137857
\(638\) 8.16567 0.323282
\(639\) −34.7132 −1.37323
\(640\) 9.93721 0.392803
\(641\) −15.1214 −0.597258 −0.298629 0.954369i \(-0.596529\pi\)
−0.298629 + 0.954369i \(0.596529\pi\)
\(642\) −26.4640 −1.04445
\(643\) −19.9404 −0.786372 −0.393186 0.919459i \(-0.628627\pi\)
−0.393186 + 0.919459i \(0.628627\pi\)
\(644\) 4.30473 0.169630
\(645\) −19.5861 −0.771202
\(646\) 4.88831 0.192328
\(647\) −6.11764 −0.240509 −0.120255 0.992743i \(-0.538371\pi\)
−0.120255 + 0.992743i \(0.538371\pi\)
\(648\) −13.4860 −0.529781
\(649\) −11.5149 −0.451999
\(650\) −6.28405 −0.246481
\(651\) −5.76982 −0.226137
\(652\) −2.01041 −0.0787336
\(653\) −24.6273 −0.963743 −0.481871 0.876242i \(-0.660043\pi\)
−0.481871 + 0.876242i \(0.660043\pi\)
\(654\) 41.7124 1.63108
\(655\) 14.3625 0.561189
\(656\) −14.0790 −0.549691
\(657\) 18.0330 0.703533
\(658\) 14.9245 0.581816
\(659\) 47.6673 1.85685 0.928427 0.371514i \(-0.121161\pi\)
0.928427 + 0.371514i \(0.121161\pi\)
\(660\) 8.03155 0.312628
\(661\) −38.2695 −1.48851 −0.744255 0.667895i \(-0.767195\pi\)
−0.744255 + 0.667895i \(0.767195\pi\)
\(662\) 24.7241 0.960930
\(663\) 6.39083 0.248199
\(664\) −15.0097 −0.582489
\(665\) −3.47577 −0.134785
\(666\) 31.6412 1.22607
\(667\) −5.71598 −0.221324
\(668\) 12.3659 0.478451
\(669\) −22.7821 −0.880807
\(670\) −14.7997 −0.571764
\(671\) −0.729617 −0.0281666
\(672\) −14.7208 −0.567866
\(673\) 38.9282 1.50057 0.750286 0.661113i \(-0.229916\pi\)
0.750286 + 0.661113i \(0.229916\pi\)
\(674\) 48.4976 1.86806
\(675\) −1.02839 −0.0395826
\(676\) −1.12843 −0.0434012
\(677\) −9.47715 −0.364236 −0.182118 0.983277i \(-0.558295\pi\)
−0.182118 + 0.983277i \(0.558295\pi\)
\(678\) −22.9306 −0.880645
\(679\) 9.06141 0.347745
\(680\) −1.03791 −0.0398022
\(681\) 32.5152 1.24599
\(682\) 11.9194 0.456417
\(683\) 28.6025 1.09444 0.547222 0.836987i \(-0.315685\pi\)
0.547222 + 0.836987i \(0.315685\pi\)
\(684\) −11.2469 −0.430038
\(685\) −4.04262 −0.154460
\(686\) 1.80610 0.0689573
\(687\) −2.35882 −0.0899945
\(688\) −40.9468 −1.56108
\(689\) 30.6947 1.16938
\(690\) −14.5319 −0.553219
\(691\) −24.4699 −0.930879 −0.465440 0.885080i \(-0.654104\pi\)
−0.465440 + 0.885080i \(0.654104\pi\)
\(692\) −3.79038 −0.144089
\(693\) 6.91777 0.262784
\(694\) 17.5627 0.666672
\(695\) 21.5514 0.817492
\(696\) 5.26861 0.199706
\(697\) 2.22315 0.0842080
\(698\) −6.09818 −0.230819
\(699\) −55.1231 −2.08495
\(700\) −1.26200 −0.0476993
\(701\) 0.880539 0.0332575 0.0166288 0.999862i \(-0.494707\pi\)
0.0166288 + 0.999862i \(0.494707\pi\)
\(702\) 6.46244 0.243909
\(703\) 23.7487 0.895698
\(704\) 3.80070 0.143244
\(705\) −19.4918 −0.734102
\(706\) 63.7454 2.39909
\(707\) 17.5198 0.658899
\(708\) 12.7049 0.477479
\(709\) 6.81673 0.256008 0.128004 0.991774i \(-0.459143\pi\)
0.128004 + 0.991774i \(0.459143\pi\)
\(710\) −24.4520 −0.917669
\(711\) −2.03786 −0.0764259
\(712\) 4.32636 0.162137
\(713\) −8.34358 −0.312470
\(714\) 3.31743 0.124152
\(715\) 9.38731 0.351066
\(716\) 20.4462 0.764110
\(717\) −17.2622 −0.644667
\(718\) 3.38531 0.126339
\(719\) 17.9723 0.670254 0.335127 0.942173i \(-0.391221\pi\)
0.335127 + 0.942173i \(0.391221\pi\)
\(720\) 12.6441 0.471218
\(721\) −12.4744 −0.464571
\(722\) 12.4964 0.465069
\(723\) 64.1817 2.38694
\(724\) −9.24248 −0.343494
\(725\) 1.67574 0.0622353
\(726\) 15.8513 0.588297
\(727\) 6.94947 0.257742 0.128871 0.991661i \(-0.458865\pi\)
0.128871 + 0.991661i \(0.458865\pi\)
\(728\) −4.63760 −0.171881
\(729\) −18.6651 −0.691299
\(730\) 12.7025 0.470139
\(731\) 6.46575 0.239144
\(732\) 0.805020 0.0297544
\(733\) −30.7773 −1.13678 −0.568392 0.822758i \(-0.692434\pi\)
−0.568392 + 0.822758i \(0.692434\pi\)
\(734\) 9.05588 0.334258
\(735\) −2.35882 −0.0870063
\(736\) −21.2873 −0.784661
\(737\) 22.1083 0.814370
\(738\) −13.2211 −0.486677
\(739\) −43.8253 −1.61214 −0.806070 0.591820i \(-0.798409\pi\)
−0.806070 + 0.591820i \(0.798409\pi\)
\(740\) 8.62281 0.316981
\(741\) −28.5262 −1.04793
\(742\) 15.9334 0.584934
\(743\) −19.9002 −0.730069 −0.365034 0.930994i \(-0.618943\pi\)
−0.365034 + 0.930994i \(0.618943\pi\)
\(744\) 7.69056 0.281950
\(745\) 8.47320 0.310434
\(746\) 12.8723 0.471289
\(747\) −28.8734 −1.05642
\(748\) −2.65137 −0.0969436
\(749\) −6.21181 −0.226974
\(750\) 4.26027 0.155563
\(751\) −34.5488 −1.26071 −0.630353 0.776309i \(-0.717090\pi\)
−0.630353 + 0.776309i \(0.717090\pi\)
\(752\) −40.7495 −1.48598
\(753\) 71.1968 2.59456
\(754\) −10.5304 −0.383495
\(755\) 16.5614 0.602730
\(756\) 1.29783 0.0472016
\(757\) −6.66275 −0.242162 −0.121081 0.992643i \(-0.538636\pi\)
−0.121081 + 0.992643i \(0.538636\pi\)
\(758\) 2.66582 0.0968268
\(759\) 21.7082 0.787957
\(760\) 4.63284 0.168051
\(761\) 13.7146 0.497153 0.248576 0.968612i \(-0.420037\pi\)
0.248576 + 0.968612i \(0.420037\pi\)
\(762\) 3.44623 0.124844
\(763\) 9.79103 0.354459
\(764\) −25.3301 −0.916411
\(765\) −1.99658 −0.0721866
\(766\) 19.6590 0.710310
\(767\) 14.8495 0.536186
\(768\) 48.9809 1.76745
\(769\) 39.1739 1.41265 0.706323 0.707889i \(-0.250352\pi\)
0.706323 + 0.707889i \(0.250352\pi\)
\(770\) 4.87288 0.175607
\(771\) 26.3555 0.949169
\(772\) −0.971952 −0.0349813
\(773\) −0.100450 −0.00361295 −0.00180648 0.999998i \(-0.500575\pi\)
−0.00180648 + 0.999998i \(0.500575\pi\)
\(774\) −38.4519 −1.38213
\(775\) 2.44606 0.0878652
\(776\) −12.0779 −0.433571
\(777\) 16.1169 0.578192
\(778\) 19.4818 0.698455
\(779\) −9.92330 −0.355539
\(780\) −10.3575 −0.370856
\(781\) 36.5272 1.30705
\(782\) 4.79725 0.171549
\(783\) −1.72331 −0.0615859
\(784\) −4.93135 −0.176120
\(785\) 3.08498 0.110108
\(786\) 61.1880 2.18250
\(787\) −12.7518 −0.454553 −0.227277 0.973830i \(-0.572982\pi\)
−0.227277 + 0.973830i \(0.572982\pi\)
\(788\) 10.0759 0.358938
\(789\) 49.5782 1.76503
\(790\) −1.43547 −0.0510719
\(791\) −5.38244 −0.191377
\(792\) −9.22066 −0.327642
\(793\) 0.940912 0.0334128
\(794\) −23.3572 −0.828918
\(795\) −20.8095 −0.738035
\(796\) 2.06212 0.0730899
\(797\) 1.82432 0.0646209 0.0323104 0.999478i \(-0.489713\pi\)
0.0323104 + 0.999478i \(0.489713\pi\)
\(798\) −14.8077 −0.524188
\(799\) 6.43460 0.227640
\(800\) 6.24074 0.220643
\(801\) 8.32240 0.294057
\(802\) −35.6278 −1.25806
\(803\) −18.9753 −0.669625
\(804\) −24.3931 −0.860278
\(805\) −3.41103 −0.120223
\(806\) −15.3712 −0.541427
\(807\) 45.2797 1.59392
\(808\) −23.3520 −0.821521
\(809\) −46.3515 −1.62963 −0.814816 0.579719i \(-0.803162\pi\)
−0.814816 + 0.579719i \(0.803162\pi\)
\(810\) −18.2739 −0.642078
\(811\) 7.34056 0.257762 0.128881 0.991660i \(-0.458862\pi\)
0.128881 + 0.991660i \(0.458862\pi\)
\(812\) −2.11479 −0.0742145
\(813\) −44.9092 −1.57503
\(814\) −33.2946 −1.16698
\(815\) 1.59303 0.0558013
\(816\) −9.05786 −0.317089
\(817\) −28.8606 −1.00970
\(818\) 32.5705 1.13880
\(819\) −8.92113 −0.311729
\(820\) −3.60301 −0.125823
\(821\) 46.8176 1.63395 0.816973 0.576676i \(-0.195650\pi\)
0.816973 + 0.576676i \(0.195650\pi\)
\(822\) −17.2226 −0.600708
\(823\) 54.0930 1.88556 0.942782 0.333410i \(-0.108199\pi\)
0.942782 + 0.333410i \(0.108199\pi\)
\(824\) 16.6271 0.579232
\(825\) −6.36412 −0.221570
\(826\) 7.70829 0.268206
\(827\) 18.0070 0.626166 0.313083 0.949726i \(-0.398638\pi\)
0.313083 + 0.949726i \(0.398638\pi\)
\(828\) −11.0374 −0.383577
\(829\) 7.38649 0.256544 0.128272 0.991739i \(-0.459057\pi\)
0.128272 + 0.991739i \(0.459057\pi\)
\(830\) −20.3385 −0.705958
\(831\) −41.5538 −1.44149
\(832\) −4.90137 −0.169924
\(833\) 0.778691 0.0269800
\(834\) 91.8148 3.17929
\(835\) −9.79861 −0.339095
\(836\) 11.8347 0.409311
\(837\) −2.51550 −0.0869483
\(838\) −2.35751 −0.0814387
\(839\) 2.41776 0.0834704 0.0417352 0.999129i \(-0.486711\pi\)
0.0417352 + 0.999129i \(0.486711\pi\)
\(840\) 3.14406 0.108480
\(841\) −26.1919 −0.903169
\(842\) 13.1057 0.451653
\(843\) −75.0751 −2.58572
\(844\) 13.4941 0.464487
\(845\) 0.894157 0.0307599
\(846\) −38.2667 −1.31564
\(847\) 3.72073 0.127846
\(848\) −43.5043 −1.49394
\(849\) 32.1374 1.10295
\(850\) −1.40640 −0.0482390
\(851\) 23.3063 0.798929
\(852\) −40.3022 −1.38073
\(853\) −42.1871 −1.44446 −0.722229 0.691654i \(-0.756882\pi\)
−0.722229 + 0.691654i \(0.756882\pi\)
\(854\) 0.488420 0.0167134
\(855\) 8.91197 0.304783
\(856\) 8.27968 0.282994
\(857\) −48.2645 −1.64868 −0.824342 0.566092i \(-0.808455\pi\)
−0.824342 + 0.566092i \(0.808455\pi\)
\(858\) 39.9925 1.36532
\(859\) −16.9361 −0.577851 −0.288926 0.957352i \(-0.593298\pi\)
−0.288926 + 0.957352i \(0.593298\pi\)
\(860\) −10.4789 −0.357327
\(861\) −6.73440 −0.229508
\(862\) −41.9074 −1.42737
\(863\) −36.7487 −1.25094 −0.625470 0.780248i \(-0.715093\pi\)
−0.625470 + 0.780248i \(0.715093\pi\)
\(864\) −6.41789 −0.218341
\(865\) 3.00346 0.102121
\(866\) 45.8955 1.55959
\(867\) −38.6696 −1.31329
\(868\) −3.08694 −0.104778
\(869\) 2.14436 0.0727423
\(870\) 7.13908 0.242038
\(871\) −28.5108 −0.966051
\(872\) −13.0504 −0.441943
\(873\) −23.2337 −0.786341
\(874\) −21.4130 −0.724307
\(875\) 1.00000 0.0338062
\(876\) 20.9363 0.707373
\(877\) −42.2279 −1.42593 −0.712967 0.701197i \(-0.752649\pi\)
−0.712967 + 0.701197i \(0.752649\pi\)
\(878\) 32.6886 1.10319
\(879\) −38.0583 −1.28367
\(880\) −13.3048 −0.448506
\(881\) −21.2963 −0.717489 −0.358745 0.933436i \(-0.616795\pi\)
−0.358745 + 0.933436i \(0.616795\pi\)
\(882\) −4.63089 −0.155930
\(883\) −49.0025 −1.64907 −0.824533 0.565814i \(-0.808562\pi\)
−0.824533 + 0.565814i \(0.808562\pi\)
\(884\) 3.41919 0.115000
\(885\) −10.0672 −0.338406
\(886\) 51.9071 1.74385
\(887\) 11.9802 0.402257 0.201128 0.979565i \(-0.435539\pi\)
0.201128 + 0.979565i \(0.435539\pi\)
\(888\) −21.4822 −0.720895
\(889\) 0.808924 0.0271304
\(890\) 5.86231 0.196505
\(891\) 27.2981 0.914520
\(892\) −12.1888 −0.408111
\(893\) −28.7215 −0.961130
\(894\) 36.0981 1.20730
\(895\) −16.2014 −0.541552
\(896\) 9.93721 0.331979
\(897\) −27.9948 −0.934718
\(898\) 43.0943 1.43808
\(899\) 4.09896 0.136708
\(900\) 3.23581 0.107860
\(901\) 6.86960 0.228859
\(902\) 13.9120 0.463220
\(903\) −19.5861 −0.651785
\(904\) 7.17422 0.238611
\(905\) 7.32365 0.243446
\(906\) 70.5558 2.34406
\(907\) −33.1736 −1.10151 −0.550755 0.834667i \(-0.685660\pi\)
−0.550755 + 0.834667i \(0.685660\pi\)
\(908\) 17.3962 0.577312
\(909\) −44.9211 −1.48994
\(910\) −6.28405 −0.208314
\(911\) −22.2094 −0.735830 −0.367915 0.929859i \(-0.619928\pi\)
−0.367915 + 0.929859i \(0.619928\pi\)
\(912\) 40.4308 1.33880
\(913\) 30.3822 1.00550
\(914\) 21.5022 0.711228
\(915\) −0.637890 −0.0210880
\(916\) −1.26200 −0.0416978
\(917\) 14.3625 0.474291
\(918\) 1.44632 0.0477356
\(919\) 3.58678 0.118317 0.0591585 0.998249i \(-0.481158\pi\)
0.0591585 + 0.998249i \(0.481158\pi\)
\(920\) 4.54654 0.149895
\(921\) −55.3533 −1.82395
\(922\) −43.3601 −1.42799
\(923\) −47.1054 −1.55049
\(924\) 8.03155 0.264219
\(925\) −6.83263 −0.224656
\(926\) 24.1611 0.793983
\(927\) 31.9847 1.05052
\(928\) 10.4578 0.343295
\(929\) 9.67444 0.317408 0.158704 0.987326i \(-0.449268\pi\)
0.158704 + 0.987326i \(0.449268\pi\)
\(930\) 10.4209 0.341714
\(931\) −3.47577 −0.113914
\(932\) −29.4917 −0.966034
\(933\) 67.0787 2.19606
\(934\) 30.4274 0.995615
\(935\) 2.10092 0.0687073
\(936\) 11.8909 0.388667
\(937\) 22.9093 0.748413 0.374207 0.927345i \(-0.377915\pi\)
0.374207 + 0.927345i \(0.377915\pi\)
\(938\) −14.7997 −0.483228
\(939\) −33.5488 −1.09483
\(940\) −10.4284 −0.340137
\(941\) 0.817156 0.0266385 0.0133193 0.999911i \(-0.495760\pi\)
0.0133193 + 0.999911i \(0.495760\pi\)
\(942\) 13.1428 0.428216
\(943\) −9.73844 −0.317127
\(944\) −21.0466 −0.685008
\(945\) −1.02839 −0.0334534
\(946\) 40.4613 1.31551
\(947\) 45.3299 1.47302 0.736512 0.676425i \(-0.236472\pi\)
0.736512 + 0.676425i \(0.236472\pi\)
\(948\) −2.36597 −0.0768430
\(949\) 24.4705 0.794346
\(950\) 6.27760 0.203672
\(951\) −4.16016 −0.134903
\(952\) −1.03791 −0.0336390
\(953\) 20.6996 0.670527 0.335264 0.942124i \(-0.391175\pi\)
0.335264 + 0.942124i \(0.391175\pi\)
\(954\) −40.8536 −1.32269
\(955\) 20.0713 0.649493
\(956\) −9.23553 −0.298698
\(957\) −10.6646 −0.344737
\(958\) −17.6543 −0.570386
\(959\) −4.04262 −0.130543
\(960\) 3.32288 0.107245
\(961\) −25.0168 −0.806993
\(962\) 42.9366 1.38433
\(963\) 15.9272 0.513248
\(964\) 34.3382 1.10596
\(965\) 0.770165 0.0247925
\(966\) −14.5319 −0.467555
\(967\) −60.6689 −1.95098 −0.975491 0.220041i \(-0.929381\pi\)
−0.975491 + 0.220041i \(0.929381\pi\)
\(968\) −4.95935 −0.159399
\(969\) −6.38427 −0.205092
\(970\) −16.3658 −0.525475
\(971\) 34.0480 1.09265 0.546325 0.837573i \(-0.316026\pi\)
0.546325 + 0.837573i \(0.316026\pi\)
\(972\) −26.2257 −0.841191
\(973\) 21.5514 0.690907
\(974\) −7.11363 −0.227936
\(975\) 8.20714 0.262839
\(976\) −1.33358 −0.0426867
\(977\) 4.97338 0.159112 0.0795562 0.996830i \(-0.474650\pi\)
0.0795562 + 0.996830i \(0.474650\pi\)
\(978\) 6.78672 0.217015
\(979\) −8.75730 −0.279884
\(980\) −1.26200 −0.0403133
\(981\) −25.1044 −0.801523
\(982\) −24.4477 −0.780157
\(983\) −0.482965 −0.0154042 −0.00770210 0.999970i \(-0.502452\pi\)
−0.00770210 + 0.999970i \(0.502452\pi\)
\(984\) 8.97625 0.286152
\(985\) −7.98403 −0.254392
\(986\) −2.35675 −0.0750541
\(987\) −19.4918 −0.620429
\(988\) −15.2619 −0.485547
\(989\) −28.3229 −0.900617
\(990\) −12.4942 −0.397092
\(991\) 1.01037 0.0320956 0.0160478 0.999871i \(-0.494892\pi\)
0.0160478 + 0.999871i \(0.494892\pi\)
\(992\) 15.2652 0.484672
\(993\) −32.2904 −1.02470
\(994\) −24.4520 −0.775572
\(995\) −1.63400 −0.0518014
\(996\) −33.5221 −1.06219
\(997\) 18.8767 0.597832 0.298916 0.954279i \(-0.403375\pi\)
0.298916 + 0.954279i \(0.403375\pi\)
\(998\) −72.6636 −2.30013
\(999\) 7.02659 0.222311
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 8015.2.a.k.1.12 49
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8015.2.a.k.1.12 49 1.1 even 1 trivial