Properties

Label 8015.2.a.h.1.2
Level $8015$
Weight $2$
Character 8015.1
Self dual yes
Analytic conductor $64.000$
Analytic rank $1$
Dimension $38$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

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: \(38\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
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)
 
\(f(q)\) \(=\) \(q-2.59504 q^{2} +0.990389 q^{3} +4.73422 q^{4} +1.00000 q^{5} -2.57010 q^{6} +1.00000 q^{7} -7.09539 q^{8} -2.01913 q^{9} +O(q^{10})\) \(q-2.59504 q^{2} +0.990389 q^{3} +4.73422 q^{4} +1.00000 q^{5} -2.57010 q^{6} +1.00000 q^{7} -7.09539 q^{8} -2.01913 q^{9} -2.59504 q^{10} +2.69347 q^{11} +4.68871 q^{12} -1.27929 q^{13} -2.59504 q^{14} +0.990389 q^{15} +8.94437 q^{16} +3.50266 q^{17} +5.23972 q^{18} -2.44770 q^{19} +4.73422 q^{20} +0.990389 q^{21} -6.98966 q^{22} +2.80389 q^{23} -7.02720 q^{24} +1.00000 q^{25} +3.31980 q^{26} -4.97089 q^{27} +4.73422 q^{28} -4.34420 q^{29} -2.57010 q^{30} +4.94069 q^{31} -9.02018 q^{32} +2.66759 q^{33} -9.08952 q^{34} +1.00000 q^{35} -9.55899 q^{36} -7.74705 q^{37} +6.35188 q^{38} -1.26699 q^{39} -7.09539 q^{40} -10.0194 q^{41} -2.57010 q^{42} +9.00403 q^{43} +12.7515 q^{44} -2.01913 q^{45} -7.27620 q^{46} -5.38153 q^{47} +8.85840 q^{48} +1.00000 q^{49} -2.59504 q^{50} +3.46899 q^{51} -6.05643 q^{52} -2.10468 q^{53} +12.8996 q^{54} +2.69347 q^{55} -7.09539 q^{56} -2.42418 q^{57} +11.2734 q^{58} -0.734590 q^{59} +4.68871 q^{60} -0.871332 q^{61} -12.8213 q^{62} -2.01913 q^{63} +5.51896 q^{64} -1.27929 q^{65} -6.92249 q^{66} -15.4637 q^{67} +16.5823 q^{68} +2.77694 q^{69} -2.59504 q^{70} -7.70039 q^{71} +14.3265 q^{72} -14.7551 q^{73} +20.1039 q^{74} +0.990389 q^{75} -11.5880 q^{76} +2.69347 q^{77} +3.28790 q^{78} -4.33339 q^{79} +8.94437 q^{80} +1.13427 q^{81} +26.0007 q^{82} -9.19097 q^{83} +4.68871 q^{84} +3.50266 q^{85} -23.3658 q^{86} -4.30245 q^{87} -19.1112 q^{88} +0.0533003 q^{89} +5.23972 q^{90} -1.27929 q^{91} +13.2742 q^{92} +4.89320 q^{93} +13.9653 q^{94} -2.44770 q^{95} -8.93348 q^{96} +4.71499 q^{97} -2.59504 q^{98} -5.43847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 38 q - 6 q^{2} - 9 q^{3} + 24 q^{4} + 38 q^{5} - 10 q^{6} + 38 q^{7} - 21 q^{8} + 13 q^{9} - 6 q^{10} - 18 q^{11} - 20 q^{12} - 25 q^{13} - 6 q^{14} - 9 q^{15} - 21 q^{17} - 7 q^{18} - 14 q^{19} + 24 q^{20} - 9 q^{21} - 11 q^{22} - 16 q^{23} - 10 q^{24} + 38 q^{25} - 21 q^{26} - 15 q^{27} + 24 q^{28} - 52 q^{29} - 10 q^{30} - 30 q^{31} - 8 q^{32} - 13 q^{33} - 9 q^{34} + 38 q^{35} - 16 q^{36} - 47 q^{37} - 10 q^{38} - 50 q^{39} - 21 q^{40} - 35 q^{41} - 10 q^{42} - 18 q^{43} - 22 q^{44} + 13 q^{45} - 17 q^{46} - 23 q^{47} - 13 q^{48} + 38 q^{49} - 6 q^{50} - 5 q^{51} - 41 q^{52} - 12 q^{53} + 35 q^{54} - 18 q^{55} - 21 q^{56} - 3 q^{57} - 16 q^{58} - 16 q^{59} - 20 q^{60} - 47 q^{61} + 14 q^{62} + 13 q^{63} - 55 q^{64} - 25 q^{65} - 6 q^{66} - 54 q^{67} + 31 q^{68} - 95 q^{69} - 6 q^{70} - 41 q^{71} - 59 q^{73} - q^{74} - 9 q^{75} - 23 q^{76} - 18 q^{77} + 19 q^{78} - 117 q^{79} - 38 q^{81} + 19 q^{82} - 21 q^{83} - 20 q^{84} - 21 q^{85} - 12 q^{86} - 14 q^{87} - 40 q^{88} - 96 q^{89} - 7 q^{90} - 25 q^{91} + 53 q^{92} - 53 q^{93} - 28 q^{94} - 14 q^{95} + 40 q^{96} - 70 q^{97} - 6 q^{98} - 52 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59504 −1.83497 −0.917484 0.397773i \(-0.869783\pi\)
−0.917484 + 0.397773i \(0.869783\pi\)
\(3\) 0.990389 0.571801 0.285901 0.958259i \(-0.407707\pi\)
0.285901 + 0.958259i \(0.407707\pi\)
\(4\) 4.73422 2.36711
\(5\) 1.00000 0.447214
\(6\) −2.57010 −1.04924
\(7\) 1.00000 0.377964
\(8\) −7.09539 −2.50860
\(9\) −2.01913 −0.673043
\(10\) −2.59504 −0.820623
\(11\) 2.69347 0.812113 0.406056 0.913848i \(-0.366904\pi\)
0.406056 + 0.913848i \(0.366904\pi\)
\(12\) 4.68871 1.35352
\(13\) −1.27929 −0.354811 −0.177405 0.984138i \(-0.556770\pi\)
−0.177405 + 0.984138i \(0.556770\pi\)
\(14\) −2.59504 −0.693553
\(15\) 0.990389 0.255717
\(16\) 8.94437 2.23609
\(17\) 3.50266 0.849519 0.424759 0.905306i \(-0.360359\pi\)
0.424759 + 0.905306i \(0.360359\pi\)
\(18\) 5.23972 1.23501
\(19\) −2.44770 −0.561542 −0.280771 0.959775i \(-0.590590\pi\)
−0.280771 + 0.959775i \(0.590590\pi\)
\(20\) 4.73422 1.05860
\(21\) 0.990389 0.216121
\(22\) −6.98966 −1.49020
\(23\) 2.80389 0.584652 0.292326 0.956319i \(-0.405571\pi\)
0.292326 + 0.956319i \(0.405571\pi\)
\(24\) −7.02720 −1.43442
\(25\) 1.00000 0.200000
\(26\) 3.31980 0.651067
\(27\) −4.97089 −0.956648
\(28\) 4.73422 0.894683
\(29\) −4.34420 −0.806698 −0.403349 0.915046i \(-0.632154\pi\)
−0.403349 + 0.915046i \(0.632154\pi\)
\(30\) −2.57010 −0.469233
\(31\) 4.94069 0.887374 0.443687 0.896182i \(-0.353670\pi\)
0.443687 + 0.896182i \(0.353670\pi\)
\(32\) −9.02018 −1.59456
\(33\) 2.66759 0.464367
\(34\) −9.08952 −1.55884
\(35\) 1.00000 0.169031
\(36\) −9.55899 −1.59317
\(37\) −7.74705 −1.27361 −0.636803 0.771026i \(-0.719744\pi\)
−0.636803 + 0.771026i \(0.719744\pi\)
\(38\) 6.35188 1.03041
\(39\) −1.26699 −0.202881
\(40\) −7.09539 −1.12188
\(41\) −10.0194 −1.56476 −0.782382 0.622799i \(-0.785995\pi\)
−0.782382 + 0.622799i \(0.785995\pi\)
\(42\) −2.57010 −0.396574
\(43\) 9.00403 1.37310 0.686551 0.727082i \(-0.259124\pi\)
0.686551 + 0.727082i \(0.259124\pi\)
\(44\) 12.7515 1.92236
\(45\) −2.01913 −0.300994
\(46\) −7.27620 −1.07282
\(47\) −5.38153 −0.784977 −0.392489 0.919757i \(-0.628386\pi\)
−0.392489 + 0.919757i \(0.628386\pi\)
\(48\) 8.85840 1.27860
\(49\) 1.00000 0.142857
\(50\) −2.59504 −0.366994
\(51\) 3.46899 0.485756
\(52\) −6.05643 −0.839876
\(53\) −2.10468 −0.289101 −0.144550 0.989497i \(-0.546174\pi\)
−0.144550 + 0.989497i \(0.546174\pi\)
\(54\) 12.8996 1.75542
\(55\) 2.69347 0.363188
\(56\) −7.09539 −0.948161
\(57\) −2.42418 −0.321090
\(58\) 11.2734 1.48026
\(59\) −0.734590 −0.0956355 −0.0478178 0.998856i \(-0.515227\pi\)
−0.0478178 + 0.998856i \(0.515227\pi\)
\(60\) 4.68871 0.605310
\(61\) −0.871332 −0.111563 −0.0557813 0.998443i \(-0.517765\pi\)
−0.0557813 + 0.998443i \(0.517765\pi\)
\(62\) −12.8213 −1.62830
\(63\) −2.01913 −0.254386
\(64\) 5.51896 0.689870
\(65\) −1.27929 −0.158676
\(66\) −6.92249 −0.852099
\(67\) −15.4637 −1.88919 −0.944595 0.328239i \(-0.893545\pi\)
−0.944595 + 0.328239i \(0.893545\pi\)
\(68\) 16.5823 2.01090
\(69\) 2.77694 0.334305
\(70\) −2.59504 −0.310166
\(71\) −7.70039 −0.913869 −0.456934 0.889500i \(-0.651053\pi\)
−0.456934 + 0.889500i \(0.651053\pi\)
\(72\) 14.3265 1.68840
\(73\) −14.7551 −1.72696 −0.863478 0.504386i \(-0.831719\pi\)
−0.863478 + 0.504386i \(0.831719\pi\)
\(74\) 20.1039 2.33703
\(75\) 0.990389 0.114360
\(76\) −11.5880 −1.32923
\(77\) 2.69347 0.306950
\(78\) 3.28790 0.372281
\(79\) −4.33339 −0.487545 −0.243772 0.969832i \(-0.578385\pi\)
−0.243772 + 0.969832i \(0.578385\pi\)
\(80\) 8.94437 1.00001
\(81\) 1.13427 0.126030
\(82\) 26.0007 2.87129
\(83\) −9.19097 −1.00884 −0.504420 0.863458i \(-0.668294\pi\)
−0.504420 + 0.863458i \(0.668294\pi\)
\(84\) 4.68871 0.511581
\(85\) 3.50266 0.379916
\(86\) −23.3658 −2.51960
\(87\) −4.30245 −0.461271
\(88\) −19.1112 −2.03727
\(89\) 0.0533003 0.00564982 0.00282491 0.999996i \(-0.499101\pi\)
0.00282491 + 0.999996i \(0.499101\pi\)
\(90\) 5.23972 0.552315
\(91\) −1.27929 −0.134106
\(92\) 13.2742 1.38393
\(93\) 4.89320 0.507401
\(94\) 13.9653 1.44041
\(95\) −2.44770 −0.251129
\(96\) −8.93348 −0.911770
\(97\) 4.71499 0.478735 0.239368 0.970929i \(-0.423060\pi\)
0.239368 + 0.970929i \(0.423060\pi\)
\(98\) −2.59504 −0.262138
\(99\) −5.43847 −0.546587
\(100\) 4.73422 0.473422
\(101\) 13.4649 1.33981 0.669906 0.742446i \(-0.266335\pi\)
0.669906 + 0.742446i \(0.266335\pi\)
\(102\) −9.00216 −0.891347
\(103\) 6.68061 0.658260 0.329130 0.944285i \(-0.393245\pi\)
0.329130 + 0.944285i \(0.393245\pi\)
\(104\) 9.07706 0.890079
\(105\) 0.990389 0.0966521
\(106\) 5.46173 0.530491
\(107\) 13.6633 1.32088 0.660440 0.750878i \(-0.270370\pi\)
0.660440 + 0.750878i \(0.270370\pi\)
\(108\) −23.5333 −2.26449
\(109\) 2.71867 0.260401 0.130201 0.991488i \(-0.458438\pi\)
0.130201 + 0.991488i \(0.458438\pi\)
\(110\) −6.98966 −0.666438
\(111\) −7.67259 −0.728250
\(112\) 8.94437 0.845163
\(113\) 9.85764 0.927329 0.463664 0.886011i \(-0.346534\pi\)
0.463664 + 0.886011i \(0.346534\pi\)
\(114\) 6.29083 0.589190
\(115\) 2.80389 0.261464
\(116\) −20.5664 −1.90954
\(117\) 2.58305 0.238803
\(118\) 1.90629 0.175488
\(119\) 3.50266 0.321088
\(120\) −7.02720 −0.641492
\(121\) −3.74520 −0.340473
\(122\) 2.26114 0.204714
\(123\) −9.92308 −0.894734
\(124\) 23.3903 2.10051
\(125\) 1.00000 0.0894427
\(126\) 5.23972 0.466791
\(127\) 2.26909 0.201349 0.100674 0.994919i \(-0.467900\pi\)
0.100674 + 0.994919i \(0.467900\pi\)
\(128\) 3.71845 0.328668
\(129\) 8.91750 0.785142
\(130\) 3.31980 0.291166
\(131\) 2.95094 0.257825 0.128912 0.991656i \(-0.458851\pi\)
0.128912 + 0.991656i \(0.458851\pi\)
\(132\) 12.6289 1.09921
\(133\) −2.44770 −0.212243
\(134\) 40.1288 3.46660
\(135\) −4.97089 −0.427826
\(136\) −24.8527 −2.13110
\(137\) 1.57986 0.134976 0.0674881 0.997720i \(-0.478502\pi\)
0.0674881 + 0.997720i \(0.478502\pi\)
\(138\) −7.20627 −0.613438
\(139\) −14.5723 −1.23601 −0.618003 0.786175i \(-0.712058\pi\)
−0.618003 + 0.786175i \(0.712058\pi\)
\(140\) 4.73422 0.400114
\(141\) −5.32981 −0.448851
\(142\) 19.9828 1.67692
\(143\) −3.44573 −0.288147
\(144\) −18.0598 −1.50499
\(145\) −4.34420 −0.360766
\(146\) 38.2901 3.16891
\(147\) 0.990389 0.0816859
\(148\) −36.6762 −3.01476
\(149\) −21.6462 −1.77333 −0.886663 0.462417i \(-0.846982\pi\)
−0.886663 + 0.462417i \(0.846982\pi\)
\(150\) −2.57010 −0.209847
\(151\) −9.71070 −0.790246 −0.395123 0.918628i \(-0.629298\pi\)
−0.395123 + 0.918628i \(0.629298\pi\)
\(152\) 17.3674 1.40868
\(153\) −7.07232 −0.571763
\(154\) −6.98966 −0.563243
\(155\) 4.94069 0.396846
\(156\) −5.99822 −0.480242
\(157\) 5.13219 0.409593 0.204797 0.978805i \(-0.434347\pi\)
0.204797 + 0.978805i \(0.434347\pi\)
\(158\) 11.2453 0.894629
\(159\) −2.08446 −0.165308
\(160\) −9.02018 −0.713108
\(161\) 2.80389 0.220978
\(162\) −2.94348 −0.231262
\(163\) 1.57000 0.122972 0.0614861 0.998108i \(-0.480416\pi\)
0.0614861 + 0.998108i \(0.480416\pi\)
\(164\) −47.4339 −3.70396
\(165\) 2.66759 0.207671
\(166\) 23.8509 1.85119
\(167\) −13.0052 −1.00637 −0.503185 0.864179i \(-0.667838\pi\)
−0.503185 + 0.864179i \(0.667838\pi\)
\(168\) −7.02720 −0.542160
\(169\) −11.3634 −0.874109
\(170\) −9.08952 −0.697134
\(171\) 4.94223 0.377942
\(172\) 42.6270 3.25028
\(173\) 19.0672 1.44965 0.724826 0.688932i \(-0.241920\pi\)
0.724826 + 0.688932i \(0.241920\pi\)
\(174\) 11.1650 0.846417
\(175\) 1.00000 0.0755929
\(176\) 24.0914 1.81596
\(177\) −0.727530 −0.0546845
\(178\) −0.138316 −0.0103672
\(179\) −10.3762 −0.775550 −0.387775 0.921754i \(-0.626756\pi\)
−0.387775 + 0.921754i \(0.626756\pi\)
\(180\) −9.55899 −0.712485
\(181\) −11.4462 −0.850787 −0.425393 0.905009i \(-0.639864\pi\)
−0.425393 + 0.905009i \(0.639864\pi\)
\(182\) 3.31980 0.246080
\(183\) −0.862957 −0.0637916
\(184\) −19.8947 −1.46666
\(185\) −7.74705 −0.569574
\(186\) −12.6980 −0.931065
\(187\) 9.43431 0.689905
\(188\) −25.4773 −1.85813
\(189\) −4.97089 −0.361579
\(190\) 6.35188 0.460814
\(191\) −1.08598 −0.0785788 −0.0392894 0.999228i \(-0.512509\pi\)
−0.0392894 + 0.999228i \(0.512509\pi\)
\(192\) 5.46592 0.394469
\(193\) 14.5804 1.04952 0.524759 0.851251i \(-0.324155\pi\)
0.524759 + 0.851251i \(0.324155\pi\)
\(194\) −12.2356 −0.878464
\(195\) −1.26699 −0.0907313
\(196\) 4.73422 0.338158
\(197\) 0.866434 0.0617309 0.0308654 0.999524i \(-0.490174\pi\)
0.0308654 + 0.999524i \(0.490174\pi\)
\(198\) 14.1130 1.00297
\(199\) −14.5659 −1.03255 −0.516273 0.856424i \(-0.672681\pi\)
−0.516273 + 0.856424i \(0.672681\pi\)
\(200\) −7.09539 −0.501720
\(201\) −15.3151 −1.08024
\(202\) −34.9420 −2.45851
\(203\) −4.34420 −0.304903
\(204\) 16.4230 1.14984
\(205\) −10.0194 −0.699784
\(206\) −17.3364 −1.20789
\(207\) −5.66142 −0.393496
\(208\) −11.4424 −0.793390
\(209\) −6.59282 −0.456035
\(210\) −2.57010 −0.177353
\(211\) −22.9950 −1.58304 −0.791519 0.611144i \(-0.790710\pi\)
−0.791519 + 0.611144i \(0.790710\pi\)
\(212\) −9.96403 −0.684333
\(213\) −7.62639 −0.522551
\(214\) −35.4568 −2.42377
\(215\) 9.00403 0.614070
\(216\) 35.2704 2.39985
\(217\) 4.94069 0.335396
\(218\) −7.05505 −0.477828
\(219\) −14.6133 −0.987476
\(220\) 12.7515 0.859705
\(221\) −4.48091 −0.301419
\(222\) 19.9107 1.33632
\(223\) −15.7215 −1.05279 −0.526396 0.850239i \(-0.676457\pi\)
−0.526396 + 0.850239i \(0.676457\pi\)
\(224\) −9.02018 −0.602686
\(225\) −2.01913 −0.134609
\(226\) −25.5809 −1.70162
\(227\) −2.40794 −0.159821 −0.0799103 0.996802i \(-0.525463\pi\)
−0.0799103 + 0.996802i \(0.525463\pi\)
\(228\) −11.4766 −0.760055
\(229\) −1.00000 −0.0660819
\(230\) −7.27620 −0.479778
\(231\) 2.66759 0.175514
\(232\) 30.8238 2.02368
\(233\) 16.1465 1.05779 0.528895 0.848687i \(-0.322606\pi\)
0.528895 + 0.848687i \(0.322606\pi\)
\(234\) −6.70311 −0.438196
\(235\) −5.38153 −0.351053
\(236\) −3.47771 −0.226380
\(237\) −4.29174 −0.278779
\(238\) −9.08952 −0.589186
\(239\) 0.439911 0.0284555 0.0142277 0.999899i \(-0.495471\pi\)
0.0142277 + 0.999899i \(0.495471\pi\)
\(240\) 8.85840 0.571807
\(241\) 23.2685 1.49885 0.749427 0.662087i \(-0.230329\pi\)
0.749427 + 0.662087i \(0.230329\pi\)
\(242\) 9.71893 0.624757
\(243\) 16.0360 1.02871
\(244\) −4.12507 −0.264081
\(245\) 1.00000 0.0638877
\(246\) 25.7508 1.64181
\(247\) 3.13132 0.199241
\(248\) −35.0561 −2.22606
\(249\) −9.10264 −0.576856
\(250\) −2.59504 −0.164125
\(251\) −18.2483 −1.15182 −0.575911 0.817513i \(-0.695352\pi\)
−0.575911 + 0.817513i \(0.695352\pi\)
\(252\) −9.55899 −0.602160
\(253\) 7.55221 0.474803
\(254\) −5.88836 −0.369468
\(255\) 3.46899 0.217237
\(256\) −20.6874 −1.29296
\(257\) 28.9291 1.80455 0.902273 0.431166i \(-0.141898\pi\)
0.902273 + 0.431166i \(0.141898\pi\)
\(258\) −23.1412 −1.44071
\(259\) −7.74705 −0.481378
\(260\) −6.05643 −0.375604
\(261\) 8.77150 0.542942
\(262\) −7.65780 −0.473101
\(263\) −5.98973 −0.369342 −0.184671 0.982800i \(-0.559122\pi\)
−0.184671 + 0.982800i \(0.559122\pi\)
\(264\) −18.9276 −1.16491
\(265\) −2.10468 −0.129290
\(266\) 6.35188 0.389459
\(267\) 0.0527880 0.00323057
\(268\) −73.2084 −4.47191
\(269\) −20.6362 −1.25821 −0.629106 0.777319i \(-0.716579\pi\)
−0.629106 + 0.777319i \(0.716579\pi\)
\(270\) 12.8996 0.785047
\(271\) −22.5419 −1.36933 −0.684663 0.728860i \(-0.740051\pi\)
−0.684663 + 0.728860i \(0.740051\pi\)
\(272\) 31.3290 1.89960
\(273\) −1.26699 −0.0766820
\(274\) −4.09979 −0.247677
\(275\) 2.69347 0.162423
\(276\) 13.1466 0.791335
\(277\) 5.12409 0.307877 0.153938 0.988080i \(-0.450804\pi\)
0.153938 + 0.988080i \(0.450804\pi\)
\(278\) 37.8157 2.26803
\(279\) −9.97589 −0.597241
\(280\) −7.09539 −0.424031
\(281\) 16.5014 0.984390 0.492195 0.870485i \(-0.336195\pi\)
0.492195 + 0.870485i \(0.336195\pi\)
\(282\) 13.8311 0.823627
\(283\) −8.68452 −0.516241 −0.258121 0.966113i \(-0.583103\pi\)
−0.258121 + 0.966113i \(0.583103\pi\)
\(284\) −36.4553 −2.16323
\(285\) −2.42418 −0.143596
\(286\) 8.94180 0.528740
\(287\) −10.0194 −0.591425
\(288\) 18.2129 1.07321
\(289\) −4.73140 −0.278318
\(290\) 11.2734 0.661994
\(291\) 4.66968 0.273741
\(292\) −69.8539 −4.08789
\(293\) −0.0280092 −0.00163631 −0.000818157 1.00000i \(-0.500260\pi\)
−0.000818157 1.00000i \(0.500260\pi\)
\(294\) −2.57010 −0.149891
\(295\) −0.734590 −0.0427695
\(296\) 54.9683 3.19497
\(297\) −13.3890 −0.776906
\(298\) 56.1727 3.25399
\(299\) −3.58699 −0.207441
\(300\) 4.68871 0.270703
\(301\) 9.00403 0.518984
\(302\) 25.1996 1.45008
\(303\) 13.3355 0.766106
\(304\) −21.8932 −1.25566
\(305\) −0.871332 −0.0498923
\(306\) 18.3529 1.04917
\(307\) 11.4750 0.654910 0.327455 0.944867i \(-0.393809\pi\)
0.327455 + 0.944867i \(0.393809\pi\)
\(308\) 12.7515 0.726583
\(309\) 6.61640 0.376394
\(310\) −12.8213 −0.728199
\(311\) 32.2145 1.82672 0.913358 0.407158i \(-0.133480\pi\)
0.913358 + 0.407158i \(0.133480\pi\)
\(312\) 8.98982 0.508948
\(313\) −5.59802 −0.316419 −0.158209 0.987406i \(-0.550572\pi\)
−0.158209 + 0.987406i \(0.550572\pi\)
\(314\) −13.3182 −0.751591
\(315\) −2.01913 −0.113765
\(316\) −20.5152 −1.15407
\(317\) −25.2480 −1.41807 −0.709035 0.705173i \(-0.750869\pi\)
−0.709035 + 0.705173i \(0.750869\pi\)
\(318\) 5.40924 0.303335
\(319\) −11.7010 −0.655129
\(320\) 5.51896 0.308519
\(321\) 13.5320 0.755281
\(322\) −7.27620 −0.405487
\(323\) −8.57346 −0.477040
\(324\) 5.36990 0.298328
\(325\) −1.27929 −0.0709622
\(326\) −4.07422 −0.225650
\(327\) 2.69254 0.148898
\(328\) 71.0914 3.92537
\(329\) −5.38153 −0.296694
\(330\) −6.92249 −0.381070
\(331\) −27.7811 −1.52699 −0.763495 0.645814i \(-0.776518\pi\)
−0.763495 + 0.645814i \(0.776518\pi\)
\(332\) −43.5121 −2.38803
\(333\) 15.6423 0.857192
\(334\) 33.7489 1.84666
\(335\) −15.4637 −0.844871
\(336\) 8.85840 0.483265
\(337\) −17.1041 −0.931720 −0.465860 0.884858i \(-0.654255\pi\)
−0.465860 + 0.884858i \(0.654255\pi\)
\(338\) 29.4885 1.60396
\(339\) 9.76290 0.530248
\(340\) 16.5823 0.899303
\(341\) 13.3076 0.720647
\(342\) −12.8253 −0.693511
\(343\) 1.00000 0.0539949
\(344\) −63.8871 −3.44456
\(345\) 2.77694 0.149506
\(346\) −49.4801 −2.66006
\(347\) 21.6884 1.16429 0.582147 0.813084i \(-0.302213\pi\)
0.582147 + 0.813084i \(0.302213\pi\)
\(348\) −20.3687 −1.09188
\(349\) 18.7174 1.00192 0.500960 0.865471i \(-0.332980\pi\)
0.500960 + 0.865471i \(0.332980\pi\)
\(350\) −2.59504 −0.138711
\(351\) 6.35921 0.339429
\(352\) −24.2956 −1.29496
\(353\) −11.6226 −0.618610 −0.309305 0.950963i \(-0.600096\pi\)
−0.309305 + 0.950963i \(0.600096\pi\)
\(354\) 1.88797 0.100344
\(355\) −7.70039 −0.408695
\(356\) 0.252335 0.0133737
\(357\) 3.46899 0.183599
\(358\) 26.9265 1.42311
\(359\) 30.8335 1.62733 0.813665 0.581334i \(-0.197469\pi\)
0.813665 + 0.581334i \(0.197469\pi\)
\(360\) 14.3265 0.755073
\(361\) −13.0087 −0.684671
\(362\) 29.7032 1.56117
\(363\) −3.70921 −0.194683
\(364\) −6.05643 −0.317443
\(365\) −14.7551 −0.772319
\(366\) 2.23941 0.117056
\(367\) 10.4553 0.545760 0.272880 0.962048i \(-0.412024\pi\)
0.272880 + 0.962048i \(0.412024\pi\)
\(368\) 25.0790 1.30733
\(369\) 20.2304 1.05315
\(370\) 20.1039 1.04515
\(371\) −2.10468 −0.109270
\(372\) 23.1655 1.20107
\(373\) −15.3002 −0.792213 −0.396106 0.918205i \(-0.629639\pi\)
−0.396106 + 0.918205i \(0.629639\pi\)
\(374\) −24.4824 −1.26595
\(375\) 0.990389 0.0511435
\(376\) 38.1841 1.96919
\(377\) 5.55749 0.286225
\(378\) 12.8996 0.663486
\(379\) 30.9733 1.59099 0.795497 0.605958i \(-0.207210\pi\)
0.795497 + 0.605958i \(0.207210\pi\)
\(380\) −11.5880 −0.594450
\(381\) 2.24728 0.115131
\(382\) 2.81816 0.144190
\(383\) 27.3605 1.39806 0.699029 0.715093i \(-0.253616\pi\)
0.699029 + 0.715093i \(0.253616\pi\)
\(384\) 3.68271 0.187933
\(385\) 2.69347 0.137272
\(386\) −37.8366 −1.92583
\(387\) −18.1803 −0.924157
\(388\) 22.3218 1.13322
\(389\) 22.6420 1.14799 0.573997 0.818858i \(-0.305392\pi\)
0.573997 + 0.818858i \(0.305392\pi\)
\(390\) 3.28790 0.166489
\(391\) 9.82107 0.496673
\(392\) −7.09539 −0.358371
\(393\) 2.92258 0.147425
\(394\) −2.24843 −0.113274
\(395\) −4.33339 −0.218037
\(396\) −25.7469 −1.29383
\(397\) −16.8989 −0.848132 −0.424066 0.905631i \(-0.639398\pi\)
−0.424066 + 0.905631i \(0.639398\pi\)
\(398\) 37.7989 1.89469
\(399\) −2.42418 −0.121361
\(400\) 8.94437 0.447218
\(401\) −3.12680 −0.156145 −0.0780724 0.996948i \(-0.524877\pi\)
−0.0780724 + 0.996948i \(0.524877\pi\)
\(402\) 39.7431 1.98221
\(403\) −6.32057 −0.314850
\(404\) 63.7459 3.17148
\(405\) 1.13427 0.0563625
\(406\) 11.2734 0.559487
\(407\) −20.8665 −1.03431
\(408\) −24.6139 −1.21857
\(409\) −20.2809 −1.00283 −0.501413 0.865208i \(-0.667186\pi\)
−0.501413 + 0.865208i \(0.667186\pi\)
\(410\) 26.0007 1.28408
\(411\) 1.56467 0.0771796
\(412\) 31.6274 1.55817
\(413\) −0.734590 −0.0361468
\(414\) 14.6916 0.722052
\(415\) −9.19097 −0.451167
\(416\) 11.5394 0.565766
\(417\) −14.4323 −0.706750
\(418\) 17.1086 0.836810
\(419\) −26.0715 −1.27368 −0.636839 0.770997i \(-0.719758\pi\)
−0.636839 + 0.770997i \(0.719758\pi\)
\(420\) 4.68871 0.228786
\(421\) 17.9304 0.873874 0.436937 0.899492i \(-0.356063\pi\)
0.436937 + 0.899492i \(0.356063\pi\)
\(422\) 59.6728 2.90482
\(423\) 10.8660 0.528324
\(424\) 14.9336 0.725238
\(425\) 3.50266 0.169904
\(426\) 19.7908 0.958865
\(427\) −0.871332 −0.0421667
\(428\) 64.6850 3.12667
\(429\) −3.41261 −0.164763
\(430\) −23.3658 −1.12680
\(431\) −19.9206 −0.959542 −0.479771 0.877394i \(-0.659280\pi\)
−0.479771 + 0.877394i \(0.659280\pi\)
\(432\) −44.4615 −2.13915
\(433\) −30.9701 −1.48833 −0.744165 0.667996i \(-0.767152\pi\)
−0.744165 + 0.667996i \(0.767152\pi\)
\(434\) −12.8213 −0.615440
\(435\) −4.30245 −0.206287
\(436\) 12.8708 0.616398
\(437\) −6.86309 −0.328306
\(438\) 37.9221 1.81199
\(439\) 12.8854 0.614987 0.307494 0.951550i \(-0.400510\pi\)
0.307494 + 0.951550i \(0.400510\pi\)
\(440\) −19.1112 −0.911093
\(441\) −2.01913 −0.0961490
\(442\) 11.6281 0.553094
\(443\) 34.6147 1.64460 0.822298 0.569057i \(-0.192692\pi\)
0.822298 + 0.569057i \(0.192692\pi\)
\(444\) −36.3237 −1.72385
\(445\) 0.0533003 0.00252667
\(446\) 40.7980 1.93184
\(447\) −21.4382 −1.01399
\(448\) 5.51896 0.260746
\(449\) −36.1360 −1.70536 −0.852682 0.522431i \(-0.825025\pi\)
−0.852682 + 0.522431i \(0.825025\pi\)
\(450\) 5.23972 0.247003
\(451\) −26.9869 −1.27076
\(452\) 46.6682 2.19509
\(453\) −9.61737 −0.451864
\(454\) 6.24869 0.293266
\(455\) −1.27929 −0.0599740
\(456\) 17.2005 0.805487
\(457\) 3.02590 0.141546 0.0707729 0.997492i \(-0.477453\pi\)
0.0707729 + 0.997492i \(0.477453\pi\)
\(458\) 2.59504 0.121258
\(459\) −17.4113 −0.812691
\(460\) 13.2742 0.618914
\(461\) 17.4608 0.813232 0.406616 0.913599i \(-0.366709\pi\)
0.406616 + 0.913599i \(0.366709\pi\)
\(462\) −6.92249 −0.322063
\(463\) −18.8781 −0.877340 −0.438670 0.898648i \(-0.644550\pi\)
−0.438670 + 0.898648i \(0.644550\pi\)
\(464\) −38.8561 −1.80385
\(465\) 4.89320 0.226917
\(466\) −41.9007 −1.94101
\(467\) −19.9635 −0.923799 −0.461900 0.886932i \(-0.652832\pi\)
−0.461900 + 0.886932i \(0.652832\pi\)
\(468\) 12.2287 0.565273
\(469\) −15.4637 −0.714046
\(470\) 13.9653 0.644170
\(471\) 5.08286 0.234206
\(472\) 5.21220 0.239911
\(473\) 24.2521 1.11511
\(474\) 11.1372 0.511550
\(475\) −2.44770 −0.112308
\(476\) 16.5823 0.760050
\(477\) 4.24963 0.194577
\(478\) −1.14159 −0.0522149
\(479\) −14.1639 −0.647165 −0.323583 0.946200i \(-0.604887\pi\)
−0.323583 + 0.946200i \(0.604887\pi\)
\(480\) −8.93348 −0.407756
\(481\) 9.91071 0.451890
\(482\) −60.3825 −2.75035
\(483\) 2.77694 0.126355
\(484\) −17.7306 −0.805936
\(485\) 4.71499 0.214097
\(486\) −41.6141 −1.88765
\(487\) −16.7022 −0.756847 −0.378424 0.925633i \(-0.623534\pi\)
−0.378424 + 0.925633i \(0.623534\pi\)
\(488\) 6.18244 0.279866
\(489\) 1.55491 0.0703156
\(490\) −2.59504 −0.117232
\(491\) −0.998906 −0.0450800 −0.0225400 0.999746i \(-0.507175\pi\)
−0.0225400 + 0.999746i \(0.507175\pi\)
\(492\) −46.9780 −2.11793
\(493\) −15.2162 −0.685305
\(494\) −8.12589 −0.365601
\(495\) −5.43847 −0.244441
\(496\) 44.1913 1.98425
\(497\) −7.70039 −0.345410
\(498\) 23.6217 1.05851
\(499\) −24.6197 −1.10213 −0.551064 0.834463i \(-0.685778\pi\)
−0.551064 + 0.834463i \(0.685778\pi\)
\(500\) 4.73422 0.211721
\(501\) −12.8802 −0.575443
\(502\) 47.3550 2.11356
\(503\) 19.5548 0.871904 0.435952 0.899970i \(-0.356412\pi\)
0.435952 + 0.899970i \(0.356412\pi\)
\(504\) 14.3265 0.638154
\(505\) 13.4649 0.599182
\(506\) −19.5983 −0.871249
\(507\) −11.2542 −0.499817
\(508\) 10.7423 0.476614
\(509\) 30.1264 1.33533 0.667665 0.744462i \(-0.267294\pi\)
0.667665 + 0.744462i \(0.267294\pi\)
\(510\) −9.00216 −0.398622
\(511\) −14.7551 −0.652728
\(512\) 46.2478 2.04388
\(513\) 12.1673 0.537198
\(514\) −75.0720 −3.31128
\(515\) 6.68061 0.294383
\(516\) 42.2173 1.85852
\(517\) −14.4950 −0.637490
\(518\) 20.1039 0.883313
\(519\) 18.8839 0.828913
\(520\) 9.07706 0.398055
\(521\) 29.3534 1.28600 0.642998 0.765868i \(-0.277690\pi\)
0.642998 + 0.765868i \(0.277690\pi\)
\(522\) −22.7624 −0.996282
\(523\) 29.8661 1.30595 0.652976 0.757378i \(-0.273520\pi\)
0.652976 + 0.757378i \(0.273520\pi\)
\(524\) 13.9704 0.610300
\(525\) 0.990389 0.0432241
\(526\) 15.5436 0.677731
\(527\) 17.3055 0.753841
\(528\) 23.8599 1.03837
\(529\) −15.1382 −0.658182
\(530\) 5.46173 0.237243
\(531\) 1.48323 0.0643668
\(532\) −11.5880 −0.502402
\(533\) 12.8177 0.555195
\(534\) −0.136987 −0.00592800
\(535\) 13.6633 0.590716
\(536\) 109.721 4.73922
\(537\) −10.2764 −0.443460
\(538\) 53.5517 2.30878
\(539\) 2.69347 0.116016
\(540\) −23.5333 −1.01271
\(541\) −8.61854 −0.370540 −0.185270 0.982688i \(-0.559316\pi\)
−0.185270 + 0.982688i \(0.559316\pi\)
\(542\) 58.4972 2.51267
\(543\) −11.3362 −0.486481
\(544\) −31.5946 −1.35461
\(545\) 2.71867 0.116455
\(546\) 3.28790 0.140709
\(547\) −9.97991 −0.426710 −0.213355 0.976975i \(-0.568439\pi\)
−0.213355 + 0.976975i \(0.568439\pi\)
\(548\) 7.47938 0.319503
\(549\) 1.75933 0.0750864
\(550\) −6.98966 −0.298040
\(551\) 10.6333 0.452994
\(552\) −19.7035 −0.838636
\(553\) −4.33339 −0.184275
\(554\) −13.2972 −0.564944
\(555\) −7.67259 −0.325683
\(556\) −68.9884 −2.92576
\(557\) 25.6136 1.08528 0.542642 0.839964i \(-0.317424\pi\)
0.542642 + 0.839964i \(0.317424\pi\)
\(558\) 25.8878 1.09592
\(559\) −11.5188 −0.487192
\(560\) 8.94437 0.377968
\(561\) 9.34364 0.394489
\(562\) −42.8217 −1.80632
\(563\) −21.0959 −0.889087 −0.444544 0.895757i \(-0.646634\pi\)
−0.444544 + 0.895757i \(0.646634\pi\)
\(564\) −25.2325 −1.06248
\(565\) 9.85764 0.414714
\(566\) 22.5367 0.947286
\(567\) 1.13427 0.0476350
\(568\) 54.6373 2.29253
\(569\) −19.9563 −0.836610 −0.418305 0.908307i \(-0.637376\pi\)
−0.418305 + 0.908307i \(0.637376\pi\)
\(570\) 6.29083 0.263494
\(571\) 17.6773 0.739773 0.369886 0.929077i \(-0.379397\pi\)
0.369886 + 0.929077i \(0.379397\pi\)
\(572\) −16.3128 −0.682074
\(573\) −1.07554 −0.0449315
\(574\) 26.0007 1.08525
\(575\) 2.80389 0.116930
\(576\) −11.1435 −0.464312
\(577\) 30.0343 1.25034 0.625172 0.780487i \(-0.285029\pi\)
0.625172 + 0.780487i \(0.285029\pi\)
\(578\) 12.2782 0.510704
\(579\) 14.4402 0.600116
\(580\) −20.5664 −0.853972
\(581\) −9.19097 −0.381306
\(582\) −12.1180 −0.502307
\(583\) −5.66891 −0.234782
\(584\) 104.693 4.33224
\(585\) 2.58305 0.106796
\(586\) 0.0726849 0.00300258
\(587\) 24.6305 1.01661 0.508306 0.861177i \(-0.330272\pi\)
0.508306 + 0.861177i \(0.330272\pi\)
\(588\) 4.68871 0.193359
\(589\) −12.0933 −0.498297
\(590\) 1.90629 0.0784807
\(591\) 0.858107 0.0352978
\(592\) −69.2924 −2.84790
\(593\) −12.9044 −0.529921 −0.264960 0.964259i \(-0.585359\pi\)
−0.264960 + 0.964259i \(0.585359\pi\)
\(594\) 34.7448 1.42560
\(595\) 3.50266 0.143595
\(596\) −102.478 −4.19765
\(597\) −14.4259 −0.590411
\(598\) 9.30836 0.380647
\(599\) 13.1927 0.539041 0.269520 0.962995i \(-0.413135\pi\)
0.269520 + 0.962995i \(0.413135\pi\)
\(600\) −7.02720 −0.286884
\(601\) 33.1806 1.35346 0.676732 0.736229i \(-0.263396\pi\)
0.676732 + 0.736229i \(0.263396\pi\)
\(602\) −23.3658 −0.952319
\(603\) 31.2232 1.27151
\(604\) −45.9726 −1.87060
\(605\) −3.74520 −0.152264
\(606\) −34.6062 −1.40578
\(607\) −40.1475 −1.62954 −0.814768 0.579788i \(-0.803136\pi\)
−0.814768 + 0.579788i \(0.803136\pi\)
\(608\) 22.0787 0.895410
\(609\) −4.30245 −0.174344
\(610\) 2.26114 0.0915508
\(611\) 6.88454 0.278519
\(612\) −33.4819 −1.35342
\(613\) −30.4976 −1.23179 −0.615894 0.787829i \(-0.711205\pi\)
−0.615894 + 0.787829i \(0.711205\pi\)
\(614\) −29.7779 −1.20174
\(615\) −9.92308 −0.400137
\(616\) −19.1112 −0.770014
\(617\) 23.1289 0.931135 0.465567 0.885012i \(-0.345850\pi\)
0.465567 + 0.885012i \(0.345850\pi\)
\(618\) −17.1698 −0.690671
\(619\) 18.9162 0.760307 0.380154 0.924923i \(-0.375871\pi\)
0.380154 + 0.924923i \(0.375871\pi\)
\(620\) 23.3903 0.939376
\(621\) −13.9378 −0.559306
\(622\) −83.5978 −3.35196
\(623\) 0.0533003 0.00213543
\(624\) −11.3325 −0.453661
\(625\) 1.00000 0.0400000
\(626\) 14.5271 0.580619
\(627\) −6.52946 −0.260762
\(628\) 24.2969 0.969552
\(629\) −27.1352 −1.08195
\(630\) 5.23972 0.208755
\(631\) 6.28127 0.250053 0.125027 0.992153i \(-0.460098\pi\)
0.125027 + 0.992153i \(0.460098\pi\)
\(632\) 30.7471 1.22305
\(633\) −22.7740 −0.905184
\(634\) 65.5195 2.60211
\(635\) 2.26909 0.0900459
\(636\) −9.86827 −0.391302
\(637\) −1.27929 −0.0506873
\(638\) 30.3645 1.20214
\(639\) 15.5481 0.615073
\(640\) 3.71845 0.146985
\(641\) −13.2055 −0.521584 −0.260792 0.965395i \(-0.583984\pi\)
−0.260792 + 0.965395i \(0.583984\pi\)
\(642\) −35.1160 −1.38592
\(643\) 20.4234 0.805420 0.402710 0.915328i \(-0.368068\pi\)
0.402710 + 0.915328i \(0.368068\pi\)
\(644\) 13.2742 0.523078
\(645\) 8.91750 0.351126
\(646\) 22.2485 0.875354
\(647\) −36.3831 −1.43037 −0.715183 0.698937i \(-0.753657\pi\)
−0.715183 + 0.698937i \(0.753657\pi\)
\(648\) −8.04811 −0.316160
\(649\) −1.97860 −0.0776668
\(650\) 3.31980 0.130213
\(651\) 4.89320 0.191780
\(652\) 7.43273 0.291088
\(653\) 34.5184 1.35081 0.675405 0.737447i \(-0.263969\pi\)
0.675405 + 0.737447i \(0.263969\pi\)
\(654\) −6.98724 −0.273223
\(655\) 2.95094 0.115303
\(656\) −89.6170 −3.49895
\(657\) 29.7925 1.16232
\(658\) 13.9653 0.544423
\(659\) 37.1315 1.44644 0.723220 0.690618i \(-0.242661\pi\)
0.723220 + 0.690618i \(0.242661\pi\)
\(660\) 12.6289 0.491580
\(661\) 14.0781 0.547573 0.273787 0.961790i \(-0.411724\pi\)
0.273787 + 0.961790i \(0.411724\pi\)
\(662\) 72.0931 2.80198
\(663\) −4.43784 −0.172352
\(664\) 65.2135 2.53078
\(665\) −2.44770 −0.0949179
\(666\) −40.5923 −1.57292
\(667\) −12.1807 −0.471637
\(668\) −61.5692 −2.38218
\(669\) −15.5704 −0.601988
\(670\) 40.1288 1.55031
\(671\) −2.34691 −0.0906014
\(672\) −8.93348 −0.344617
\(673\) −20.7242 −0.798861 −0.399430 0.916764i \(-0.630792\pi\)
−0.399430 + 0.916764i \(0.630792\pi\)
\(674\) 44.3858 1.70968
\(675\) −4.97089 −0.191330
\(676\) −53.7969 −2.06911
\(677\) −27.3335 −1.05051 −0.525255 0.850945i \(-0.676030\pi\)
−0.525255 + 0.850945i \(0.676030\pi\)
\(678\) −25.3351 −0.972988
\(679\) 4.71499 0.180945
\(680\) −24.8527 −0.953058
\(681\) −2.38480 −0.0913856
\(682\) −34.5337 −1.32237
\(683\) 21.3011 0.815065 0.407532 0.913191i \(-0.366389\pi\)
0.407532 + 0.913191i \(0.366389\pi\)
\(684\) 23.3976 0.894629
\(685\) 1.57986 0.0603632
\(686\) −2.59504 −0.0990790
\(687\) −0.990389 −0.0377857
\(688\) 80.5354 3.07038
\(689\) 2.69250 0.102576
\(690\) −7.20627 −0.274338
\(691\) −36.4636 −1.38714 −0.693571 0.720388i \(-0.743964\pi\)
−0.693571 + 0.720388i \(0.743964\pi\)
\(692\) 90.2682 3.43148
\(693\) −5.43847 −0.206590
\(694\) −56.2821 −2.13644
\(695\) −14.5723 −0.552759
\(696\) 30.5275 1.15714
\(697\) −35.0944 −1.32930
\(698\) −48.5723 −1.83849
\(699\) 15.9913 0.604846
\(700\) 4.73422 0.178937
\(701\) −30.5707 −1.15464 −0.577319 0.816519i \(-0.695901\pi\)
−0.577319 + 0.816519i \(0.695901\pi\)
\(702\) −16.5024 −0.622842
\(703\) 18.9625 0.715183
\(704\) 14.8652 0.560252
\(705\) −5.32981 −0.200732
\(706\) 30.1612 1.13513
\(707\) 13.4649 0.506401
\(708\) −3.44428 −0.129444
\(709\) −26.2595 −0.986197 −0.493099 0.869973i \(-0.664136\pi\)
−0.493099 + 0.869973i \(0.664136\pi\)
\(710\) 19.9828 0.749941
\(711\) 8.74968 0.328139
\(712\) −0.378186 −0.0141731
\(713\) 13.8531 0.518804
\(714\) −9.00216 −0.336897
\(715\) −3.44573 −0.128863
\(716\) −49.1229 −1.83581
\(717\) 0.435683 0.0162709
\(718\) −80.0140 −2.98610
\(719\) −26.3878 −0.984098 −0.492049 0.870567i \(-0.663752\pi\)
−0.492049 + 0.870567i \(0.663752\pi\)
\(720\) −18.0598 −0.673050
\(721\) 6.68061 0.248799
\(722\) 33.7582 1.25635
\(723\) 23.0448 0.857047
\(724\) −54.1886 −2.01390
\(725\) −4.34420 −0.161340
\(726\) 9.62552 0.357237
\(727\) −0.973822 −0.0361171 −0.0180585 0.999837i \(-0.505749\pi\)
−0.0180585 + 0.999837i \(0.505749\pi\)
\(728\) 9.07706 0.336418
\(729\) 12.4791 0.462189
\(730\) 38.2901 1.41718
\(731\) 31.5380 1.16648
\(732\) −4.08543 −0.151002
\(733\) 1.68221 0.0621337 0.0310668 0.999517i \(-0.490110\pi\)
0.0310668 + 0.999517i \(0.490110\pi\)
\(734\) −27.1318 −1.00145
\(735\) 0.990389 0.0365310
\(736\) −25.2916 −0.932261
\(737\) −41.6510 −1.53423
\(738\) −52.4987 −1.93250
\(739\) 40.6856 1.49665 0.748323 0.663335i \(-0.230859\pi\)
0.748323 + 0.663335i \(0.230859\pi\)
\(740\) −36.6762 −1.34824
\(741\) 3.10123 0.113926
\(742\) 5.46173 0.200507
\(743\) 47.3864 1.73844 0.869219 0.494428i \(-0.164622\pi\)
0.869219 + 0.494428i \(0.164622\pi\)
\(744\) −34.7192 −1.27287
\(745\) −21.6462 −0.793055
\(746\) 39.7045 1.45369
\(747\) 18.5578 0.678993
\(748\) 44.6641 1.63308
\(749\) 13.6633 0.499246
\(750\) −2.57010 −0.0938466
\(751\) −27.7022 −1.01087 −0.505433 0.862866i \(-0.668667\pi\)
−0.505433 + 0.862866i \(0.668667\pi\)
\(752\) −48.1344 −1.75528
\(753\) −18.0729 −0.658613
\(754\) −14.4219 −0.525214
\(755\) −9.71070 −0.353409
\(756\) −23.5333 −0.855897
\(757\) 32.1679 1.16916 0.584582 0.811335i \(-0.301259\pi\)
0.584582 + 0.811335i \(0.301259\pi\)
\(758\) −80.3770 −2.91942
\(759\) 7.47962 0.271493
\(760\) 17.3674 0.629982
\(761\) −40.7100 −1.47574 −0.737869 0.674944i \(-0.764168\pi\)
−0.737869 + 0.674944i \(0.764168\pi\)
\(762\) −5.83177 −0.211263
\(763\) 2.71867 0.0984224
\(764\) −5.14127 −0.186004
\(765\) −7.07232 −0.255700
\(766\) −71.0016 −2.56539
\(767\) 0.939753 0.0339325
\(768\) −20.4886 −0.739319
\(769\) 0.978215 0.0352754 0.0176377 0.999844i \(-0.494385\pi\)
0.0176377 + 0.999844i \(0.494385\pi\)
\(770\) −6.98966 −0.251890
\(771\) 28.6510 1.03184
\(772\) 69.0266 2.48432
\(773\) −23.2725 −0.837055 −0.418527 0.908204i \(-0.637454\pi\)
−0.418527 + 0.908204i \(0.637454\pi\)
\(774\) 47.1786 1.69580
\(775\) 4.94069 0.177475
\(776\) −33.4547 −1.20095
\(777\) −7.67259 −0.275253
\(778\) −58.7568 −2.10653
\(779\) 24.5245 0.878680
\(780\) −5.99822 −0.214771
\(781\) −20.7408 −0.742165
\(782\) −25.4860 −0.911378
\(783\) 21.5945 0.771726
\(784\) 8.94437 0.319442
\(785\) 5.13219 0.183176
\(786\) −7.58420 −0.270520
\(787\) −32.8283 −1.17020 −0.585102 0.810960i \(-0.698945\pi\)
−0.585102 + 0.810960i \(0.698945\pi\)
\(788\) 4.10189 0.146124
\(789\) −5.93216 −0.211190
\(790\) 11.2453 0.400090
\(791\) 9.85764 0.350497
\(792\) 38.5881 1.37117
\(793\) 1.11469 0.0395836
\(794\) 43.8533 1.55630
\(795\) −2.08446 −0.0739281
\(796\) −68.9579 −2.44415
\(797\) −10.1817 −0.360656 −0.180328 0.983607i \(-0.557716\pi\)
−0.180328 + 0.983607i \(0.557716\pi\)
\(798\) 6.29083 0.222693
\(799\) −18.8497 −0.666853
\(800\) −9.02018 −0.318911
\(801\) −0.107620 −0.00380257
\(802\) 8.11416 0.286521
\(803\) −39.7425 −1.40248
\(804\) −72.5048 −2.55705
\(805\) 2.80389 0.0988242
\(806\) 16.4021 0.577739
\(807\) −20.4379 −0.719448
\(808\) −95.5390 −3.36105
\(809\) −30.5692 −1.07475 −0.537377 0.843342i \(-0.680585\pi\)
−0.537377 + 0.843342i \(0.680585\pi\)
\(810\) −2.94348 −0.103423
\(811\) −6.04757 −0.212359 −0.106180 0.994347i \(-0.533862\pi\)
−0.106180 + 0.994347i \(0.533862\pi\)
\(812\) −20.5664 −0.721738
\(813\) −22.3253 −0.782982
\(814\) 54.1492 1.89793
\(815\) 1.57000 0.0549948
\(816\) 31.0279 1.08619
\(817\) −22.0392 −0.771054
\(818\) 52.6296 1.84015
\(819\) 2.58305 0.0902591
\(820\) −47.4339 −1.65646
\(821\) 29.0789 1.01486 0.507431 0.861692i \(-0.330595\pi\)
0.507431 + 0.861692i \(0.330595\pi\)
\(822\) −4.06038 −0.141622
\(823\) −19.9138 −0.694151 −0.347075 0.937837i \(-0.612825\pi\)
−0.347075 + 0.937837i \(0.612825\pi\)
\(824\) −47.4015 −1.65131
\(825\) 2.66759 0.0928734
\(826\) 1.90629 0.0663283
\(827\) −12.1688 −0.423151 −0.211576 0.977362i \(-0.567859\pi\)
−0.211576 + 0.977362i \(0.567859\pi\)
\(828\) −26.8024 −0.931447
\(829\) −24.9627 −0.866992 −0.433496 0.901155i \(-0.642720\pi\)
−0.433496 + 0.901155i \(0.642720\pi\)
\(830\) 23.8509 0.827877
\(831\) 5.07484 0.176044
\(832\) −7.06035 −0.244773
\(833\) 3.50266 0.121360
\(834\) 37.4522 1.29686
\(835\) −13.0052 −0.450062
\(836\) −31.2119 −1.07948
\(837\) −24.5596 −0.848904
\(838\) 67.6566 2.33716
\(839\) −42.5503 −1.46900 −0.734499 0.678609i \(-0.762583\pi\)
−0.734499 + 0.678609i \(0.762583\pi\)
\(840\) −7.02720 −0.242461
\(841\) −10.1279 −0.349239
\(842\) −46.5300 −1.60353
\(843\) 16.3428 0.562876
\(844\) −108.863 −3.74722
\(845\) −11.3634 −0.390914
\(846\) −28.1977 −0.969457
\(847\) −3.74520 −0.128687
\(848\) −18.8251 −0.646456
\(849\) −8.60106 −0.295188
\(850\) −9.08952 −0.311768
\(851\) −21.7219 −0.744616
\(852\) −36.1050 −1.23694
\(853\) 37.1701 1.27268 0.636339 0.771409i \(-0.280448\pi\)
0.636339 + 0.771409i \(0.280448\pi\)
\(854\) 2.26114 0.0773745
\(855\) 4.94223 0.169021
\(856\) −96.9464 −3.31356
\(857\) −12.8464 −0.438825 −0.219412 0.975632i \(-0.570414\pi\)
−0.219412 + 0.975632i \(0.570414\pi\)
\(858\) 8.85586 0.302334
\(859\) −16.5681 −0.565296 −0.282648 0.959224i \(-0.591213\pi\)
−0.282648 + 0.959224i \(0.591213\pi\)
\(860\) 42.6270 1.45357
\(861\) −9.92308 −0.338178
\(862\) 51.6947 1.76073
\(863\) 1.76156 0.0599641 0.0299821 0.999550i \(-0.490455\pi\)
0.0299821 + 0.999550i \(0.490455\pi\)
\(864\) 44.8383 1.52543
\(865\) 19.0672 0.648304
\(866\) 80.3687 2.73104
\(867\) −4.68593 −0.159142
\(868\) 23.3903 0.793918
\(869\) −11.6719 −0.395941
\(870\) 11.1650 0.378529
\(871\) 19.7825 0.670305
\(872\) −19.2900 −0.653242
\(873\) −9.52019 −0.322209
\(874\) 17.8100 0.602432
\(875\) 1.00000 0.0338062
\(876\) −69.1826 −2.33746
\(877\) −35.8668 −1.21114 −0.605568 0.795793i \(-0.707054\pi\)
−0.605568 + 0.795793i \(0.707054\pi\)
\(878\) −33.4381 −1.12848
\(879\) −0.0277400 −0.000935646 0
\(880\) 24.0914 0.812121
\(881\) 0.656615 0.0221219 0.0110610 0.999939i \(-0.496479\pi\)
0.0110610 + 0.999939i \(0.496479\pi\)
\(882\) 5.23972 0.176430
\(883\) 20.1607 0.678461 0.339231 0.940703i \(-0.389833\pi\)
0.339231 + 0.940703i \(0.389833\pi\)
\(884\) −21.2136 −0.713490
\(885\) −0.727530 −0.0244557
\(886\) −89.8265 −3.01778
\(887\) −22.4538 −0.753926 −0.376963 0.926228i \(-0.623032\pi\)
−0.376963 + 0.926228i \(0.623032\pi\)
\(888\) 54.4400 1.82689
\(889\) 2.26909 0.0761027
\(890\) −0.138316 −0.00463637
\(891\) 3.05514 0.102351
\(892\) −74.4292 −2.49207
\(893\) 13.1724 0.440798
\(894\) 55.6328 1.86064
\(895\) −10.3762 −0.346836
\(896\) 3.71845 0.124225
\(897\) −3.55251 −0.118615
\(898\) 93.7743 3.12929
\(899\) −21.4633 −0.715842
\(900\) −9.55899 −0.318633
\(901\) −7.37199 −0.245597
\(902\) 70.0321 2.33181
\(903\) 8.91750 0.296756
\(904\) −69.9438 −2.32630
\(905\) −11.4462 −0.380483
\(906\) 24.9574 0.829155
\(907\) −40.7443 −1.35289 −0.676447 0.736492i \(-0.736481\pi\)
−0.676447 + 0.736492i \(0.736481\pi\)
\(908\) −11.3997 −0.378313
\(909\) −27.1875 −0.901751
\(910\) 3.31980 0.110050
\(911\) −30.4871 −1.01008 −0.505042 0.863095i \(-0.668523\pi\)
−0.505042 + 0.863095i \(0.668523\pi\)
\(912\) −21.6827 −0.717987
\(913\) −24.7556 −0.819292
\(914\) −7.85233 −0.259732
\(915\) −0.862957 −0.0285285
\(916\) −4.73422 −0.156423
\(917\) 2.95094 0.0974487
\(918\) 45.1830 1.49126
\(919\) −34.2060 −1.12835 −0.564175 0.825655i \(-0.690806\pi\)
−0.564175 + 0.825655i \(0.690806\pi\)
\(920\) −19.8947 −0.655909
\(921\) 11.3647 0.374479
\(922\) −45.3115 −1.49225
\(923\) 9.85103 0.324251
\(924\) 12.6289 0.415461
\(925\) −7.74705 −0.254721
\(926\) 48.9894 1.60989
\(927\) −13.4890 −0.443037
\(928\) 39.1854 1.28633
\(929\) −50.3737 −1.65271 −0.826353 0.563152i \(-0.809589\pi\)
−0.826353 + 0.563152i \(0.809589\pi\)
\(930\) −12.6980 −0.416385
\(931\) −2.44770 −0.0802202
\(932\) 76.4409 2.50390
\(933\) 31.9049 1.04452
\(934\) 51.8059 1.69514
\(935\) 9.43431 0.308535
\(936\) −18.3278 −0.599061
\(937\) −15.2255 −0.497395 −0.248698 0.968581i \(-0.580003\pi\)
−0.248698 + 0.968581i \(0.580003\pi\)
\(938\) 40.1288 1.31025
\(939\) −5.54422 −0.180929
\(940\) −25.4773 −0.830979
\(941\) −30.8436 −1.00547 −0.502736 0.864440i \(-0.667673\pi\)
−0.502736 + 0.864440i \(0.667673\pi\)
\(942\) −13.1902 −0.429761
\(943\) −28.0932 −0.914842
\(944\) −6.57044 −0.213850
\(945\) −4.97089 −0.161703
\(946\) −62.9352 −2.04620
\(947\) −16.7112 −0.543042 −0.271521 0.962433i \(-0.587527\pi\)
−0.271521 + 0.962433i \(0.587527\pi\)
\(948\) −20.3180 −0.659899
\(949\) 18.8761 0.612743
\(950\) 6.35188 0.206082
\(951\) −25.0054 −0.810854
\(952\) −24.8527 −0.805481
\(953\) 35.2087 1.14052 0.570260 0.821464i \(-0.306842\pi\)
0.570260 + 0.821464i \(0.306842\pi\)
\(954\) −11.0280 −0.357043
\(955\) −1.08598 −0.0351415
\(956\) 2.08263 0.0673572
\(957\) −11.5885 −0.374604
\(958\) 36.7558 1.18753
\(959\) 1.57986 0.0510162
\(960\) 5.46592 0.176412
\(961\) −6.58961 −0.212568
\(962\) −25.7187 −0.829203
\(963\) −27.5880 −0.889010
\(964\) 110.158 3.54795
\(965\) 14.5804 0.469359
\(966\) −7.20627 −0.231858
\(967\) −13.3997 −0.430906 −0.215453 0.976514i \(-0.569123\pi\)
−0.215453 + 0.976514i \(0.569123\pi\)
\(968\) 26.5737 0.854110
\(969\) −8.49106 −0.272772
\(970\) −12.2356 −0.392861
\(971\) −17.2830 −0.554636 −0.277318 0.960778i \(-0.589446\pi\)
−0.277318 + 0.960778i \(0.589446\pi\)
\(972\) 75.9181 2.43507
\(973\) −14.5723 −0.467167
\(974\) 43.3427 1.38879
\(975\) −1.26699 −0.0405763
\(976\) −7.79351 −0.249464
\(977\) −53.1612 −1.70078 −0.850389 0.526155i \(-0.823633\pi\)
−0.850389 + 0.526155i \(0.823633\pi\)
\(978\) −4.03506 −0.129027
\(979\) 0.143563 0.00458829
\(980\) 4.73422 0.151229
\(981\) −5.48935 −0.175261
\(982\) 2.59220 0.0827203
\(983\) 29.4385 0.938941 0.469470 0.882948i \(-0.344445\pi\)
0.469470 + 0.882948i \(0.344445\pi\)
\(984\) 70.4081 2.24453
\(985\) 0.866434 0.0276069
\(986\) 39.4867 1.25751
\(987\) −5.32981 −0.169650
\(988\) 14.8243 0.471625
\(989\) 25.2463 0.802787
\(990\) 14.1130 0.448542
\(991\) −41.0658 −1.30450 −0.652249 0.758005i \(-0.726174\pi\)
−0.652249 + 0.758005i \(0.726174\pi\)
\(992\) −44.5659 −1.41497
\(993\) −27.5141 −0.873134
\(994\) 19.9828 0.633816
\(995\) −14.5659 −0.461769
\(996\) −43.0939 −1.36548
\(997\) 3.32687 0.105363 0.0526816 0.998611i \(-0.483223\pi\)
0.0526816 + 0.998611i \(0.483223\pi\)
\(998\) 63.8890 2.02237
\(999\) 38.5097 1.21839
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.h.1.2 38
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8015.2.a.h.1.2 38 1.1 even 1 trivial