Properties

Label 503.2.a.f.1.10
Level $503$
Weight $2$
Character 503.1
Self dual yes
Analytic conductor $4.016$
Analytic rank $0$
Dimension $26$
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] = [503,2,Mod(1,503)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(503, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("503.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 503 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 503.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: \(4.01647522167\)
Analytic rank: \(0\)
Dimension: \(26\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 503.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.462244 q^{2} +3.26409 q^{3} -1.78633 q^{4} +1.15565 q^{5} -1.50881 q^{6} -1.19216 q^{7} +1.75021 q^{8} +7.65430 q^{9} +O(q^{10})\) \(q-0.462244 q^{2} +3.26409 q^{3} -1.78633 q^{4} +1.15565 q^{5} -1.50881 q^{6} -1.19216 q^{7} +1.75021 q^{8} +7.65430 q^{9} -0.534193 q^{10} +4.40104 q^{11} -5.83075 q^{12} -5.45043 q^{13} +0.551071 q^{14} +3.77216 q^{15} +2.76364 q^{16} +1.75483 q^{17} -3.53816 q^{18} -0.615110 q^{19} -2.06438 q^{20} -3.89134 q^{21} -2.03436 q^{22} +3.56383 q^{23} +5.71284 q^{24} -3.66447 q^{25} +2.51943 q^{26} +15.1921 q^{27} +2.12960 q^{28} +5.04421 q^{29} -1.74366 q^{30} +3.23953 q^{31} -4.77789 q^{32} +14.3654 q^{33} -0.811158 q^{34} -1.37773 q^{35} -13.6731 q^{36} -8.64230 q^{37} +0.284331 q^{38} -17.7907 q^{39} +2.02263 q^{40} -6.82821 q^{41} +1.79875 q^{42} +4.42298 q^{43} -7.86172 q^{44} +8.84571 q^{45} -1.64736 q^{46} -4.24654 q^{47} +9.02077 q^{48} -5.57874 q^{49} +1.69388 q^{50} +5.72792 q^{51} +9.73627 q^{52} +9.55743 q^{53} -7.02245 q^{54} +5.08608 q^{55} -2.08654 q^{56} -2.00778 q^{57} -2.33166 q^{58} -7.62933 q^{59} -6.73832 q^{60} -11.7842 q^{61} -1.49745 q^{62} -9.12519 q^{63} -3.31873 q^{64} -6.29880 q^{65} -6.64033 q^{66} +1.28059 q^{67} -3.13470 q^{68} +11.6327 q^{69} +0.636846 q^{70} +2.48267 q^{71} +13.3966 q^{72} +14.5670 q^{73} +3.99485 q^{74} -11.9612 q^{75} +1.09879 q^{76} -5.24677 q^{77} +8.22365 q^{78} -7.25582 q^{79} +3.19380 q^{80} +26.6255 q^{81} +3.15630 q^{82} -16.6438 q^{83} +6.95121 q^{84} +2.02797 q^{85} -2.04450 q^{86} +16.4648 q^{87} +7.70274 q^{88} +1.65082 q^{89} -4.08888 q^{90} +6.49781 q^{91} -6.36618 q^{92} +10.5741 q^{93} +1.96294 q^{94} -0.710854 q^{95} -15.5955 q^{96} -5.02063 q^{97} +2.57874 q^{98} +33.6869 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.462244 −0.326856 −0.163428 0.986555i \(-0.552255\pi\)
−0.163428 + 0.986555i \(0.552255\pi\)
\(3\) 3.26409 1.88453 0.942263 0.334875i \(-0.108694\pi\)
0.942263 + 0.334875i \(0.108694\pi\)
\(4\) −1.78633 −0.893165
\(5\) 1.15565 0.516823 0.258412 0.966035i \(-0.416801\pi\)
0.258412 + 0.966035i \(0.416801\pi\)
\(6\) −1.50881 −0.615968
\(7\) −1.19216 −0.450596 −0.225298 0.974290i \(-0.572336\pi\)
−0.225298 + 0.974290i \(0.572336\pi\)
\(8\) 1.75021 0.618792
\(9\) 7.65430 2.55143
\(10\) −0.534193 −0.168927
\(11\) 4.40104 1.32696 0.663482 0.748192i \(-0.269078\pi\)
0.663482 + 0.748192i \(0.269078\pi\)
\(12\) −5.83075 −1.68319
\(13\) −5.45043 −1.51168 −0.755839 0.654758i \(-0.772771\pi\)
−0.755839 + 0.654758i \(0.772771\pi\)
\(14\) 0.551071 0.147280
\(15\) 3.77216 0.973966
\(16\) 2.76364 0.690910
\(17\) 1.75483 0.425608 0.212804 0.977095i \(-0.431740\pi\)
0.212804 + 0.977095i \(0.431740\pi\)
\(18\) −3.53816 −0.833951
\(19\) −0.615110 −0.141116 −0.0705580 0.997508i \(-0.522478\pi\)
−0.0705580 + 0.997508i \(0.522478\pi\)
\(20\) −2.06438 −0.461609
\(21\) −3.89134 −0.849159
\(22\) −2.03436 −0.433726
\(23\) 3.56383 0.743111 0.371555 0.928411i \(-0.378825\pi\)
0.371555 + 0.928411i \(0.378825\pi\)
\(24\) 5.71284 1.16613
\(25\) −3.66447 −0.732894
\(26\) 2.51943 0.494101
\(27\) 15.1921 2.92372
\(28\) 2.12960 0.402457
\(29\) 5.04421 0.936687 0.468344 0.883546i \(-0.344851\pi\)
0.468344 + 0.883546i \(0.344851\pi\)
\(30\) −1.74366 −0.318347
\(31\) 3.23953 0.581837 0.290919 0.956748i \(-0.406039\pi\)
0.290919 + 0.956748i \(0.406039\pi\)
\(32\) −4.77789 −0.844620
\(33\) 14.3654 2.50070
\(34\) −0.811158 −0.139112
\(35\) −1.37773 −0.232878
\(36\) −13.6731 −2.27885
\(37\) −8.64230 −1.42078 −0.710392 0.703806i \(-0.751482\pi\)
−0.710392 + 0.703806i \(0.751482\pi\)
\(38\) 0.284331 0.0461246
\(39\) −17.7907 −2.84879
\(40\) 2.02263 0.319806
\(41\) −6.82821 −1.06639 −0.533193 0.845993i \(-0.679008\pi\)
−0.533193 + 0.845993i \(0.679008\pi\)
\(42\) 1.79875 0.277553
\(43\) 4.42298 0.674498 0.337249 0.941415i \(-0.390504\pi\)
0.337249 + 0.941415i \(0.390504\pi\)
\(44\) −7.86172 −1.18520
\(45\) 8.84571 1.31864
\(46\) −1.64736 −0.242890
\(47\) −4.24654 −0.619422 −0.309711 0.950831i \(-0.600232\pi\)
−0.309711 + 0.950831i \(0.600232\pi\)
\(48\) 9.02077 1.30204
\(49\) −5.57874 −0.796963
\(50\) 1.69388 0.239551
\(51\) 5.72792 0.802069
\(52\) 9.73627 1.35018
\(53\) 9.55743 1.31281 0.656407 0.754407i \(-0.272075\pi\)
0.656407 + 0.754407i \(0.272075\pi\)
\(54\) −7.02245 −0.955634
\(55\) 5.08608 0.685806
\(56\) −2.08654 −0.278825
\(57\) −2.00778 −0.265937
\(58\) −2.33166 −0.306162
\(59\) −7.62933 −0.993254 −0.496627 0.867964i \(-0.665428\pi\)
−0.496627 + 0.867964i \(0.665428\pi\)
\(60\) −6.73832 −0.869913
\(61\) −11.7842 −1.50881 −0.754406 0.656408i \(-0.772075\pi\)
−0.754406 + 0.656408i \(0.772075\pi\)
\(62\) −1.49745 −0.190177
\(63\) −9.12519 −1.14967
\(64\) −3.31873 −0.414841
\(65\) −6.29880 −0.781270
\(66\) −6.64033 −0.817368
\(67\) 1.28059 0.156449 0.0782246 0.996936i \(-0.475075\pi\)
0.0782246 + 0.996936i \(0.475075\pi\)
\(68\) −3.13470 −0.380138
\(69\) 11.6327 1.40041
\(70\) 0.636846 0.0761177
\(71\) 2.48267 0.294639 0.147319 0.989089i \(-0.452936\pi\)
0.147319 + 0.989089i \(0.452936\pi\)
\(72\) 13.3966 1.57881
\(73\) 14.5670 1.70494 0.852471 0.522775i \(-0.175103\pi\)
0.852471 + 0.522775i \(0.175103\pi\)
\(74\) 3.99485 0.464392
\(75\) −11.9612 −1.38116
\(76\) 1.09879 0.126040
\(77\) −5.24677 −0.597925
\(78\) 8.22365 0.931145
\(79\) −7.25582 −0.816343 −0.408172 0.912905i \(-0.633833\pi\)
−0.408172 + 0.912905i \(0.633833\pi\)
\(80\) 3.19380 0.357078
\(81\) 26.6255 2.95838
\(82\) 3.15630 0.348555
\(83\) −16.6438 −1.82690 −0.913448 0.406955i \(-0.866591\pi\)
−0.913448 + 0.406955i \(0.866591\pi\)
\(84\) 6.95121 0.758440
\(85\) 2.02797 0.219964
\(86\) −2.04450 −0.220464
\(87\) 16.4648 1.76521
\(88\) 7.70274 0.821115
\(89\) 1.65082 0.174987 0.0874934 0.996165i \(-0.472114\pi\)
0.0874934 + 0.996165i \(0.472114\pi\)
\(90\) −4.08888 −0.431005
\(91\) 6.49781 0.681156
\(92\) −6.36618 −0.663721
\(93\) 10.5741 1.09649
\(94\) 1.96294 0.202462
\(95\) −0.710854 −0.0729320
\(96\) −15.5955 −1.59171
\(97\) −5.02063 −0.509768 −0.254884 0.966972i \(-0.582037\pi\)
−0.254884 + 0.966972i \(0.582037\pi\)
\(98\) 2.57874 0.260492
\(99\) 33.6869 3.38566
\(100\) 6.54595 0.654595
\(101\) −8.44195 −0.840005 −0.420003 0.907523i \(-0.637971\pi\)
−0.420003 + 0.907523i \(0.637971\pi\)
\(102\) −2.64769 −0.262161
\(103\) −1.87584 −0.184832 −0.0924160 0.995720i \(-0.529459\pi\)
−0.0924160 + 0.995720i \(0.529459\pi\)
\(104\) −9.53939 −0.935414
\(105\) −4.49703 −0.438865
\(106\) −4.41786 −0.429101
\(107\) 13.8463 1.33857 0.669287 0.743004i \(-0.266599\pi\)
0.669287 + 0.743004i \(0.266599\pi\)
\(108\) −27.1381 −2.61136
\(109\) −7.29763 −0.698986 −0.349493 0.936939i \(-0.613646\pi\)
−0.349493 + 0.936939i \(0.613646\pi\)
\(110\) −2.35101 −0.224160
\(111\) −28.2093 −2.67750
\(112\) −3.29471 −0.311321
\(113\) 13.2195 1.24358 0.621791 0.783183i \(-0.286405\pi\)
0.621791 + 0.783183i \(0.286405\pi\)
\(114\) 0.928083 0.0869229
\(115\) 4.11855 0.384057
\(116\) −9.01063 −0.836616
\(117\) −41.7193 −3.85695
\(118\) 3.52661 0.324651
\(119\) −2.09204 −0.191777
\(120\) 6.60206 0.602683
\(121\) 8.36920 0.760836
\(122\) 5.44718 0.493164
\(123\) −22.2879 −2.00963
\(124\) −5.78688 −0.519677
\(125\) −10.0131 −0.895600
\(126\) 4.21806 0.375775
\(127\) −17.3283 −1.53764 −0.768821 0.639464i \(-0.779156\pi\)
−0.768821 + 0.639464i \(0.779156\pi\)
\(128\) 11.0898 0.980213
\(129\) 14.4370 1.27111
\(130\) 2.91158 0.255363
\(131\) −17.4706 −1.52641 −0.763207 0.646154i \(-0.776376\pi\)
−0.763207 + 0.646154i \(0.776376\pi\)
\(132\) −25.6614 −2.23354
\(133\) 0.733313 0.0635863
\(134\) −0.591946 −0.0511363
\(135\) 17.5568 1.51105
\(136\) 3.07131 0.263363
\(137\) −4.00113 −0.341839 −0.170920 0.985285i \(-0.554674\pi\)
−0.170920 + 0.985285i \(0.554674\pi\)
\(138\) −5.37714 −0.457732
\(139\) 12.7881 1.08467 0.542336 0.840162i \(-0.317540\pi\)
0.542336 + 0.840162i \(0.317540\pi\)
\(140\) 2.46108 0.207999
\(141\) −13.8611 −1.16732
\(142\) −1.14760 −0.0963043
\(143\) −23.9876 −2.00594
\(144\) 21.1537 1.76281
\(145\) 5.82936 0.484102
\(146\) −6.73352 −0.557270
\(147\) −18.2095 −1.50190
\(148\) 15.4380 1.26900
\(149\) −16.2641 −1.33241 −0.666205 0.745768i \(-0.732083\pi\)
−0.666205 + 0.745768i \(0.732083\pi\)
\(150\) 5.52898 0.451439
\(151\) 2.50898 0.204178 0.102089 0.994775i \(-0.467447\pi\)
0.102089 + 0.994775i \(0.467447\pi\)
\(152\) −1.07657 −0.0873215
\(153\) 13.4320 1.08591
\(154\) 2.42529 0.195435
\(155\) 3.74377 0.300707
\(156\) 31.7801 2.54444
\(157\) −10.4154 −0.831241 −0.415620 0.909538i \(-0.636435\pi\)
−0.415620 + 0.909538i \(0.636435\pi\)
\(158\) 3.35396 0.266826
\(159\) 31.1964 2.47403
\(160\) −5.52158 −0.436519
\(161\) −4.24868 −0.334843
\(162\) −12.3075 −0.966965
\(163\) 19.0086 1.48887 0.744433 0.667698i \(-0.232720\pi\)
0.744433 + 0.667698i \(0.232720\pi\)
\(164\) 12.1974 0.952459
\(165\) 16.6014 1.29242
\(166\) 7.69350 0.597132
\(167\) −14.7463 −1.14110 −0.570552 0.821261i \(-0.693271\pi\)
−0.570552 + 0.821261i \(0.693271\pi\)
\(168\) −6.81065 −0.525453
\(169\) 16.7072 1.28517
\(170\) −0.937416 −0.0718965
\(171\) −4.70824 −0.360048
\(172\) −7.90091 −0.602438
\(173\) −7.94156 −0.603785 −0.301893 0.953342i \(-0.597618\pi\)
−0.301893 + 0.953342i \(0.597618\pi\)
\(174\) −7.61075 −0.576969
\(175\) 4.36865 0.330239
\(176\) 12.1629 0.916813
\(177\) −24.9028 −1.87181
\(178\) −0.763082 −0.0571954
\(179\) 10.0275 0.749489 0.374745 0.927128i \(-0.377730\pi\)
0.374745 + 0.927128i \(0.377730\pi\)
\(180\) −15.8014 −1.17776
\(181\) −14.7816 −1.09871 −0.549355 0.835589i \(-0.685126\pi\)
−0.549355 + 0.835589i \(0.685126\pi\)
\(182\) −3.00357 −0.222640
\(183\) −38.4647 −2.84340
\(184\) 6.23745 0.459831
\(185\) −9.98749 −0.734295
\(186\) −4.88783 −0.358393
\(187\) 7.72307 0.564767
\(188\) 7.58572 0.553246
\(189\) −18.1115 −1.31742
\(190\) 0.328588 0.0238383
\(191\) 16.9559 1.22689 0.613445 0.789738i \(-0.289783\pi\)
0.613445 + 0.789738i \(0.289783\pi\)
\(192\) −10.8326 −0.781778
\(193\) 13.2472 0.953552 0.476776 0.879025i \(-0.341805\pi\)
0.476776 + 0.879025i \(0.341805\pi\)
\(194\) 2.32076 0.166621
\(195\) −20.5599 −1.47232
\(196\) 9.96548 0.711820
\(197\) 20.2227 1.44081 0.720405 0.693554i \(-0.243956\pi\)
0.720405 + 0.693554i \(0.243956\pi\)
\(198\) −15.5716 −1.10662
\(199\) 12.8865 0.913496 0.456748 0.889596i \(-0.349014\pi\)
0.456748 + 0.889596i \(0.349014\pi\)
\(200\) −6.41358 −0.453509
\(201\) 4.17997 0.294832
\(202\) 3.90224 0.274561
\(203\) −6.01353 −0.422067
\(204\) −10.2320 −0.716380
\(205\) −7.89103 −0.551133
\(206\) 0.867095 0.0604134
\(207\) 27.2787 1.89600
\(208\) −15.0630 −1.04443
\(209\) −2.70713 −0.187256
\(210\) 2.07872 0.143446
\(211\) −21.1548 −1.45636 −0.728178 0.685388i \(-0.759633\pi\)
−0.728178 + 0.685388i \(0.759633\pi\)
\(212\) −17.0727 −1.17256
\(213\) 8.10366 0.555254
\(214\) −6.40038 −0.437521
\(215\) 5.11143 0.348596
\(216\) 26.5893 1.80917
\(217\) −3.86206 −0.262174
\(218\) 3.37329 0.228468
\(219\) 47.5481 3.21301
\(220\) −9.08541 −0.612538
\(221\) −9.56456 −0.643382
\(222\) 13.0396 0.875158
\(223\) 13.4569 0.901139 0.450570 0.892741i \(-0.351221\pi\)
0.450570 + 0.892741i \(0.351221\pi\)
\(224\) 5.69603 0.380582
\(225\) −28.0490 −1.86993
\(226\) −6.11062 −0.406472
\(227\) 7.40471 0.491468 0.245734 0.969337i \(-0.420971\pi\)
0.245734 + 0.969337i \(0.420971\pi\)
\(228\) 3.58655 0.237525
\(229\) 12.1885 0.805439 0.402719 0.915323i \(-0.368065\pi\)
0.402719 + 0.915323i \(0.368065\pi\)
\(230\) −1.90377 −0.125531
\(231\) −17.1259 −1.12680
\(232\) 8.82842 0.579614
\(233\) −1.43524 −0.0940258 −0.0470129 0.998894i \(-0.514970\pi\)
−0.0470129 + 0.998894i \(0.514970\pi\)
\(234\) 19.2845 1.26067
\(235\) −4.90752 −0.320131
\(236\) 13.6285 0.887140
\(237\) −23.6837 −1.53842
\(238\) 0.967034 0.0626835
\(239\) 2.26001 0.146188 0.0730938 0.997325i \(-0.476713\pi\)
0.0730938 + 0.997325i \(0.476713\pi\)
\(240\) 10.4249 0.672923
\(241\) 8.56718 0.551861 0.275930 0.961178i \(-0.411014\pi\)
0.275930 + 0.961178i \(0.411014\pi\)
\(242\) −3.86861 −0.248684
\(243\) 41.3317 2.65143
\(244\) 21.0505 1.34762
\(245\) −6.44709 −0.411889
\(246\) 10.3024 0.656860
\(247\) 3.35262 0.213322
\(248\) 5.66986 0.360036
\(249\) −54.3270 −3.44283
\(250\) 4.62850 0.292732
\(251\) 17.3286 1.09377 0.546886 0.837207i \(-0.315813\pi\)
0.546886 + 0.837207i \(0.315813\pi\)
\(252\) 16.3006 1.02684
\(253\) 15.6846 0.986082
\(254\) 8.00992 0.502587
\(255\) 6.61948 0.414528
\(256\) 1.51124 0.0944524
\(257\) −10.2141 −0.637141 −0.318571 0.947899i \(-0.603203\pi\)
−0.318571 + 0.947899i \(0.603203\pi\)
\(258\) −6.67343 −0.415469
\(259\) 10.3030 0.640200
\(260\) 11.2517 0.697803
\(261\) 38.6099 2.38990
\(262\) 8.07568 0.498917
\(263\) 13.5678 0.836624 0.418312 0.908303i \(-0.362622\pi\)
0.418312 + 0.908303i \(0.362622\pi\)
\(264\) 25.1425 1.54741
\(265\) 11.0451 0.678493
\(266\) −0.338969 −0.0207835
\(267\) 5.38844 0.329767
\(268\) −2.28756 −0.139735
\(269\) 15.6280 0.952854 0.476427 0.879214i \(-0.341932\pi\)
0.476427 + 0.879214i \(0.341932\pi\)
\(270\) −8.11551 −0.493894
\(271\) −16.9869 −1.03188 −0.515941 0.856624i \(-0.672558\pi\)
−0.515941 + 0.856624i \(0.672558\pi\)
\(272\) 4.84971 0.294057
\(273\) 21.2095 1.28366
\(274\) 1.84950 0.111732
\(275\) −16.1275 −0.972524
\(276\) −20.7798 −1.25080
\(277\) 30.4548 1.82985 0.914926 0.403622i \(-0.132249\pi\)
0.914926 + 0.403622i \(0.132249\pi\)
\(278\) −5.91122 −0.354531
\(279\) 24.7964 1.48452
\(280\) −2.41131 −0.144103
\(281\) 17.6683 1.05400 0.527001 0.849864i \(-0.323316\pi\)
0.527001 + 0.849864i \(0.323316\pi\)
\(282\) 6.40721 0.381544
\(283\) −18.5963 −1.10543 −0.552717 0.833369i \(-0.686409\pi\)
−0.552717 + 0.833369i \(0.686409\pi\)
\(284\) −4.43487 −0.263161
\(285\) −2.32029 −0.137442
\(286\) 11.0881 0.655654
\(287\) 8.14034 0.480509
\(288\) −36.5714 −2.15499
\(289\) −13.9206 −0.818858
\(290\) −2.69458 −0.158231
\(291\) −16.3878 −0.960670
\(292\) −26.0215 −1.52279
\(293\) −0.267742 −0.0156416 −0.00782082 0.999969i \(-0.502489\pi\)
−0.00782082 + 0.999969i \(0.502489\pi\)
\(294\) 8.41725 0.490904
\(295\) −8.81685 −0.513337
\(296\) −15.1258 −0.879170
\(297\) 66.8610 3.87967
\(298\) 7.51800 0.435506
\(299\) −19.4244 −1.12334
\(300\) 21.3666 1.23360
\(301\) −5.27292 −0.303926
\(302\) −1.15976 −0.0667366
\(303\) −27.5553 −1.58301
\(304\) −1.69994 −0.0974984
\(305\) −13.6184 −0.779790
\(306\) −6.20885 −0.354936
\(307\) 2.39292 0.136571 0.0682856 0.997666i \(-0.478247\pi\)
0.0682856 + 0.997666i \(0.478247\pi\)
\(308\) 9.37247 0.534046
\(309\) −6.12292 −0.348320
\(310\) −1.73054 −0.0982879
\(311\) −1.74135 −0.0987430 −0.0493715 0.998780i \(-0.515722\pi\)
−0.0493715 + 0.998780i \(0.515722\pi\)
\(312\) −31.1375 −1.76281
\(313\) 30.2027 1.70716 0.853578 0.520965i \(-0.174428\pi\)
0.853578 + 0.520965i \(0.174428\pi\)
\(314\) 4.81446 0.271696
\(315\) −10.5455 −0.594174
\(316\) 12.9613 0.729129
\(317\) 28.0579 1.57589 0.787943 0.615748i \(-0.211146\pi\)
0.787943 + 0.615748i \(0.211146\pi\)
\(318\) −14.4203 −0.808652
\(319\) 22.1998 1.24295
\(320\) −3.83529 −0.214399
\(321\) 45.1957 2.52258
\(322\) 1.96392 0.109445
\(323\) −1.07941 −0.0600601
\(324\) −47.5619 −2.64233
\(325\) 19.9729 1.10790
\(326\) −8.78659 −0.486644
\(327\) −23.8201 −1.31726
\(328\) −11.9508 −0.659871
\(329\) 5.06257 0.279109
\(330\) −7.67391 −0.422435
\(331\) 18.1592 0.998122 0.499061 0.866567i \(-0.333678\pi\)
0.499061 + 0.866567i \(0.333678\pi\)
\(332\) 29.7314 1.63172
\(333\) −66.1508 −3.62504
\(334\) 6.81640 0.372977
\(335\) 1.47992 0.0808566
\(336\) −10.7542 −0.586692
\(337\) 19.4108 1.05737 0.528686 0.848818i \(-0.322685\pi\)
0.528686 + 0.848818i \(0.322685\pi\)
\(338\) −7.72280 −0.420065
\(339\) 43.1496 2.34356
\(340\) −3.62262 −0.196464
\(341\) 14.2573 0.772078
\(342\) 2.17636 0.117684
\(343\) 14.9959 0.809704
\(344\) 7.74114 0.417374
\(345\) 13.4433 0.723765
\(346\) 3.67094 0.197351
\(347\) −21.9756 −1.17971 −0.589856 0.807508i \(-0.700816\pi\)
−0.589856 + 0.807508i \(0.700816\pi\)
\(348\) −29.4115 −1.57662
\(349\) −10.5591 −0.565216 −0.282608 0.959235i \(-0.591200\pi\)
−0.282608 + 0.959235i \(0.591200\pi\)
\(350\) −2.01938 −0.107940
\(351\) −82.8034 −4.41972
\(352\) −21.0277 −1.12078
\(353\) −30.9628 −1.64799 −0.823993 0.566600i \(-0.808258\pi\)
−0.823993 + 0.566600i \(0.808258\pi\)
\(354\) 11.5112 0.611813
\(355\) 2.86910 0.152276
\(356\) −2.94891 −0.156292
\(357\) −6.82862 −0.361409
\(358\) −4.63514 −0.244975
\(359\) −23.8149 −1.25690 −0.628450 0.777850i \(-0.716310\pi\)
−0.628450 + 0.777850i \(0.716310\pi\)
\(360\) 15.4818 0.815964
\(361\) −18.6216 −0.980086
\(362\) 6.83272 0.359120
\(363\) 27.3178 1.43381
\(364\) −11.6072 −0.608385
\(365\) 16.8344 0.881154
\(366\) 17.7801 0.929380
\(367\) −7.44635 −0.388696 −0.194348 0.980933i \(-0.562259\pi\)
−0.194348 + 0.980933i \(0.562259\pi\)
\(368\) 9.84915 0.513422
\(369\) −52.2652 −2.72082
\(370\) 4.61665 0.240008
\(371\) −11.3940 −0.591549
\(372\) −18.8889 −0.979344
\(373\) 33.4650 1.73275 0.866375 0.499394i \(-0.166444\pi\)
0.866375 + 0.499394i \(0.166444\pi\)
\(374\) −3.56994 −0.184597
\(375\) −32.6837 −1.68778
\(376\) −7.43233 −0.383293
\(377\) −27.4931 −1.41597
\(378\) 8.37191 0.430605
\(379\) −19.1182 −0.982036 −0.491018 0.871149i \(-0.663375\pi\)
−0.491018 + 0.871149i \(0.663375\pi\)
\(380\) 1.26982 0.0651404
\(381\) −56.5613 −2.89773
\(382\) −7.83778 −0.401016
\(383\) 13.8538 0.707897 0.353949 0.935265i \(-0.384839\pi\)
0.353949 + 0.935265i \(0.384839\pi\)
\(384\) 36.1983 1.84724
\(385\) −6.06344 −0.309021
\(386\) −6.12342 −0.311674
\(387\) 33.8548 1.72094
\(388\) 8.96851 0.455307
\(389\) 27.5211 1.39538 0.697688 0.716402i \(-0.254212\pi\)
0.697688 + 0.716402i \(0.254212\pi\)
\(390\) 9.50368 0.481237
\(391\) 6.25391 0.316274
\(392\) −9.76396 −0.493155
\(393\) −57.0257 −2.87657
\(394\) −9.34783 −0.470937
\(395\) −8.38520 −0.421905
\(396\) −60.1760 −3.02396
\(397\) 20.6312 1.03545 0.517725 0.855547i \(-0.326779\pi\)
0.517725 + 0.855547i \(0.326779\pi\)
\(398\) −5.95668 −0.298582
\(399\) 2.39360 0.119830
\(400\) −10.1273 −0.506363
\(401\) −29.9855 −1.49741 −0.748703 0.662906i \(-0.769323\pi\)
−0.748703 + 0.662906i \(0.769323\pi\)
\(402\) −1.93217 −0.0963677
\(403\) −17.6569 −0.879551
\(404\) 15.0801 0.750264
\(405\) 30.7698 1.52896
\(406\) 2.77972 0.137955
\(407\) −38.0351 −1.88533
\(408\) 10.0250 0.496314
\(409\) 6.08729 0.300997 0.150498 0.988610i \(-0.451912\pi\)
0.150498 + 0.988610i \(0.451912\pi\)
\(410\) 3.64758 0.180141
\(411\) −13.0600 −0.644205
\(412\) 3.35087 0.165086
\(413\) 9.09542 0.447556
\(414\) −12.6094 −0.619718
\(415\) −19.2345 −0.944183
\(416\) 26.0416 1.27679
\(417\) 41.7415 2.04409
\(418\) 1.25135 0.0612057
\(419\) 30.5039 1.49021 0.745107 0.666945i \(-0.232398\pi\)
0.745107 + 0.666945i \(0.232398\pi\)
\(420\) 8.03318 0.391979
\(421\) 5.63147 0.274461 0.137231 0.990539i \(-0.456180\pi\)
0.137231 + 0.990539i \(0.456180\pi\)
\(422\) 9.77868 0.476019
\(423\) −32.5043 −1.58041
\(424\) 16.7275 0.812359
\(425\) −6.43051 −0.311925
\(426\) −3.74587 −0.181488
\(427\) 14.0487 0.679865
\(428\) −24.7341 −1.19557
\(429\) −78.2977 −3.78025
\(430\) −2.36273 −0.113941
\(431\) 22.6727 1.09211 0.546053 0.837751i \(-0.316130\pi\)
0.546053 + 0.837751i \(0.316130\pi\)
\(432\) 41.9854 2.02002
\(433\) 28.4524 1.36733 0.683667 0.729794i \(-0.260384\pi\)
0.683667 + 0.729794i \(0.260384\pi\)
\(434\) 1.78521 0.0856929
\(435\) 19.0276 0.912302
\(436\) 13.0360 0.624310
\(437\) −2.19215 −0.104865
\(438\) −21.9788 −1.05019
\(439\) −26.2203 −1.25143 −0.625713 0.780053i \(-0.715192\pi\)
−0.625713 + 0.780053i \(0.715192\pi\)
\(440\) 8.90169 0.424371
\(441\) −42.7014 −2.03340
\(442\) 4.42116 0.210293
\(443\) 19.3673 0.920167 0.460083 0.887876i \(-0.347820\pi\)
0.460083 + 0.887876i \(0.347820\pi\)
\(444\) 50.3911 2.39145
\(445\) 1.90778 0.0904372
\(446\) −6.22036 −0.294543
\(447\) −53.0877 −2.51096
\(448\) 3.95647 0.186925
\(449\) −20.2189 −0.954191 −0.477095 0.878852i \(-0.658310\pi\)
−0.477095 + 0.878852i \(0.658310\pi\)
\(450\) 12.9655 0.611198
\(451\) −30.0512 −1.41506
\(452\) −23.6143 −1.11072
\(453\) 8.18953 0.384778
\(454\) −3.42278 −0.160639
\(455\) 7.50921 0.352037
\(456\) −3.51403 −0.164559
\(457\) 17.8331 0.834199 0.417100 0.908861i \(-0.363047\pi\)
0.417100 + 0.908861i \(0.363047\pi\)
\(458\) −5.63406 −0.263262
\(459\) 26.6595 1.24436
\(460\) −7.35709 −0.343026
\(461\) −1.01528 −0.0472865 −0.0236432 0.999720i \(-0.507527\pi\)
−0.0236432 + 0.999720i \(0.507527\pi\)
\(462\) 7.91636 0.368303
\(463\) −28.4914 −1.32411 −0.662054 0.749456i \(-0.730315\pi\)
−0.662054 + 0.749456i \(0.730315\pi\)
\(464\) 13.9404 0.647166
\(465\) 12.2200 0.566690
\(466\) 0.663432 0.0307329
\(467\) 24.1389 1.11701 0.558507 0.829500i \(-0.311374\pi\)
0.558507 + 0.829500i \(0.311374\pi\)
\(468\) 74.5244 3.44489
\(469\) −1.52668 −0.0704953
\(470\) 2.26847 0.104637
\(471\) −33.9969 −1.56649
\(472\) −13.3529 −0.614618
\(473\) 19.4657 0.895036
\(474\) 10.9476 0.502841
\(475\) 2.25405 0.103423
\(476\) 3.73708 0.171289
\(477\) 73.1555 3.34956
\(478\) −1.04467 −0.0477823
\(479\) 5.78476 0.264313 0.132156 0.991229i \(-0.457810\pi\)
0.132156 + 0.991229i \(0.457810\pi\)
\(480\) −18.0229 −0.822631
\(481\) 47.1042 2.14777
\(482\) −3.96013 −0.180379
\(483\) −13.8681 −0.631019
\(484\) −14.9501 −0.679552
\(485\) −5.80210 −0.263460
\(486\) −19.1053 −0.866636
\(487\) −11.7021 −0.530272 −0.265136 0.964211i \(-0.585417\pi\)
−0.265136 + 0.964211i \(0.585417\pi\)
\(488\) −20.6248 −0.933641
\(489\) 62.0457 2.80580
\(490\) 2.98013 0.134628
\(491\) −8.18439 −0.369356 −0.184678 0.982799i \(-0.559124\pi\)
−0.184678 + 0.982799i \(0.559124\pi\)
\(492\) 39.8136 1.79493
\(493\) 8.85172 0.398661
\(494\) −1.54973 −0.0697255
\(495\) 38.9304 1.74979
\(496\) 8.95290 0.401997
\(497\) −2.95975 −0.132763
\(498\) 25.1123 1.12531
\(499\) −33.1230 −1.48279 −0.741396 0.671068i \(-0.765836\pi\)
−0.741396 + 0.671068i \(0.765836\pi\)
\(500\) 17.8867 0.799919
\(501\) −48.1334 −2.15044
\(502\) −8.01004 −0.357506
\(503\) 1.00000 0.0445878
\(504\) −15.9710 −0.711404
\(505\) −9.75595 −0.434134
\(506\) −7.25011 −0.322306
\(507\) 54.5339 2.42193
\(508\) 30.9542 1.37337
\(509\) 23.0768 1.02286 0.511432 0.859324i \(-0.329115\pi\)
0.511432 + 0.859324i \(0.329115\pi\)
\(510\) −3.05981 −0.135491
\(511\) −17.3663 −0.768240
\(512\) −22.8782 −1.01109
\(513\) −9.34481 −0.412583
\(514\) 4.72143 0.208253
\(515\) −2.16782 −0.0955255
\(516\) −25.7893 −1.13531
\(517\) −18.6892 −0.821951
\(518\) −4.76252 −0.209253
\(519\) −25.9220 −1.13785
\(520\) −11.0242 −0.483444
\(521\) 20.0541 0.878587 0.439294 0.898344i \(-0.355229\pi\)
0.439294 + 0.898344i \(0.355229\pi\)
\(522\) −17.8472 −0.781151
\(523\) −16.3241 −0.713803 −0.356902 0.934142i \(-0.616167\pi\)
−0.356902 + 0.934142i \(0.616167\pi\)
\(524\) 31.2083 1.36334
\(525\) 14.2597 0.622343
\(526\) −6.27162 −0.273455
\(527\) 5.68482 0.247635
\(528\) 39.7008 1.72776
\(529\) −10.2991 −0.447787
\(530\) −5.10551 −0.221769
\(531\) −58.3972 −2.53422
\(532\) −1.30994 −0.0567931
\(533\) 37.2167 1.61203
\(534\) −2.49077 −0.107786
\(535\) 16.0015 0.691807
\(536\) 2.24130 0.0968095
\(537\) 32.7306 1.41243
\(538\) −7.22393 −0.311446
\(539\) −24.5523 −1.05754
\(540\) −31.3622 −1.34961
\(541\) 23.6199 1.01550 0.507748 0.861505i \(-0.330478\pi\)
0.507748 + 0.861505i \(0.330478\pi\)
\(542\) 7.85210 0.337277
\(543\) −48.2486 −2.07055
\(544\) −8.38437 −0.359477
\(545\) −8.43352 −0.361252
\(546\) −9.80394 −0.419570
\(547\) 16.8526 0.720565 0.360283 0.932843i \(-0.382680\pi\)
0.360283 + 0.932843i \(0.382680\pi\)
\(548\) 7.14733 0.305319
\(549\) −90.1999 −3.84964
\(550\) 7.45483 0.317875
\(551\) −3.10275 −0.132182
\(552\) 20.3596 0.866563
\(553\) 8.65013 0.367841
\(554\) −14.0775 −0.598097
\(555\) −32.6001 −1.38380
\(556\) −22.8438 −0.968791
\(557\) −5.57574 −0.236252 −0.118126 0.992999i \(-0.537689\pi\)
−0.118126 + 0.992999i \(0.537689\pi\)
\(558\) −11.4620 −0.485224
\(559\) −24.1072 −1.01962
\(560\) −3.80754 −0.160898
\(561\) 25.2088 1.06432
\(562\) −8.16707 −0.344507
\(563\) 10.4567 0.440697 0.220348 0.975421i \(-0.429281\pi\)
0.220348 + 0.975421i \(0.429281\pi\)
\(564\) 24.7605 1.04261
\(565\) 15.2771 0.642712
\(566\) 8.59602 0.361318
\(567\) −31.7419 −1.33304
\(568\) 4.34519 0.182320
\(569\) 13.4131 0.562308 0.281154 0.959663i \(-0.409283\pi\)
0.281154 + 0.959663i \(0.409283\pi\)
\(570\) 1.07254 0.0449238
\(571\) −24.1279 −1.00972 −0.504861 0.863201i \(-0.668456\pi\)
−0.504861 + 0.863201i \(0.668456\pi\)
\(572\) 42.8498 1.79164
\(573\) 55.3458 2.31210
\(574\) −3.76282 −0.157057
\(575\) −13.0596 −0.544621
\(576\) −25.4025 −1.05844
\(577\) −45.6091 −1.89873 −0.949367 0.314170i \(-0.898274\pi\)
−0.949367 + 0.314170i \(0.898274\pi\)
\(578\) 6.43470 0.267648
\(579\) 43.2400 1.79699
\(580\) −10.4132 −0.432383
\(581\) 19.8422 0.823192
\(582\) 7.57517 0.314001
\(583\) 42.0627 1.74206
\(584\) 25.4953 1.05500
\(585\) −48.2129 −1.99336
\(586\) 0.123762 0.00511256
\(587\) −24.7383 −1.02106 −0.510530 0.859860i \(-0.670551\pi\)
−0.510530 + 0.859860i \(0.670551\pi\)
\(588\) 32.5283 1.34144
\(589\) −1.99267 −0.0821066
\(590\) 4.07554 0.167787
\(591\) 66.0089 2.71524
\(592\) −23.8842 −0.981634
\(593\) 11.6796 0.479625 0.239813 0.970819i \(-0.422914\pi\)
0.239813 + 0.970819i \(0.422914\pi\)
\(594\) −30.9061 −1.26809
\(595\) −2.41767 −0.0991149
\(596\) 29.0531 1.19006
\(597\) 42.0626 1.72151
\(598\) 8.97882 0.367171
\(599\) −27.7786 −1.13500 −0.567502 0.823372i \(-0.692090\pi\)
−0.567502 + 0.823372i \(0.692090\pi\)
\(600\) −20.9345 −0.854649
\(601\) 7.88461 0.321620 0.160810 0.986985i \(-0.448589\pi\)
0.160810 + 0.986985i \(0.448589\pi\)
\(602\) 2.43738 0.0993400
\(603\) 9.80204 0.399170
\(604\) −4.48186 −0.182364
\(605\) 9.67188 0.393218
\(606\) 12.7373 0.517416
\(607\) 14.3700 0.583260 0.291630 0.956531i \(-0.405802\pi\)
0.291630 + 0.956531i \(0.405802\pi\)
\(608\) 2.93893 0.119189
\(609\) −19.6287 −0.795396
\(610\) 6.29504 0.254879
\(611\) 23.1455 0.936366
\(612\) −23.9940 −0.969898
\(613\) −41.7791 −1.68744 −0.843722 0.536781i \(-0.819640\pi\)
−0.843722 + 0.536781i \(0.819640\pi\)
\(614\) −1.10611 −0.0446391
\(615\) −25.7571 −1.03862
\(616\) −9.18294 −0.369991
\(617\) 28.8196 1.16023 0.580117 0.814533i \(-0.303007\pi\)
0.580117 + 0.814533i \(0.303007\pi\)
\(618\) 2.83028 0.113851
\(619\) −39.3446 −1.58139 −0.790697 0.612208i \(-0.790282\pi\)
−0.790697 + 0.612208i \(0.790282\pi\)
\(620\) −6.68762 −0.268581
\(621\) 54.1420 2.17265
\(622\) 0.804929 0.0322747
\(623\) −1.96805 −0.0788483
\(624\) −49.1671 −1.96826
\(625\) 6.75067 0.270027
\(626\) −13.9610 −0.557994
\(627\) −8.83632 −0.352889
\(628\) 18.6054 0.742435
\(629\) −15.1657 −0.604697
\(630\) 4.87461 0.194209
\(631\) 7.57350 0.301496 0.150748 0.988572i \(-0.451832\pi\)
0.150748 + 0.988572i \(0.451832\pi\)
\(632\) −12.6992 −0.505147
\(633\) −69.0513 −2.74454
\(634\) −12.9696 −0.515088
\(635\) −20.0255 −0.794689
\(636\) −55.7270 −2.20972
\(637\) 30.4066 1.20475
\(638\) −10.2617 −0.406266
\(639\) 19.0031 0.751751
\(640\) 12.8160 0.506597
\(641\) 22.7719 0.899435 0.449717 0.893171i \(-0.351525\pi\)
0.449717 + 0.893171i \(0.351525\pi\)
\(642\) −20.8914 −0.824519
\(643\) −34.1940 −1.34848 −0.674240 0.738512i \(-0.735529\pi\)
−0.674240 + 0.738512i \(0.735529\pi\)
\(644\) 7.58954 0.299070
\(645\) 16.6842 0.656939
\(646\) 0.498952 0.0196310
\(647\) 15.5363 0.610797 0.305398 0.952225i \(-0.401210\pi\)
0.305398 + 0.952225i \(0.401210\pi\)
\(648\) 46.6001 1.83062
\(649\) −33.5770 −1.31801
\(650\) −9.23237 −0.362123
\(651\) −12.6061 −0.494073
\(652\) −33.9556 −1.32980
\(653\) 23.1091 0.904328 0.452164 0.891935i \(-0.350652\pi\)
0.452164 + 0.891935i \(0.350652\pi\)
\(654\) 11.0107 0.430553
\(655\) −20.1899 −0.788886
\(656\) −18.8707 −0.736777
\(657\) 111.500 4.35005
\(658\) −2.34014 −0.0912283
\(659\) −20.3856 −0.794111 −0.397056 0.917795i \(-0.629968\pi\)
−0.397056 + 0.917795i \(0.629968\pi\)
\(660\) −29.6556 −1.15434
\(661\) −40.4678 −1.57401 −0.787007 0.616944i \(-0.788370\pi\)
−0.787007 + 0.616944i \(0.788370\pi\)
\(662\) −8.39400 −0.326242
\(663\) −31.2196 −1.21247
\(664\) −29.1302 −1.13047
\(665\) 0.847454 0.0328629
\(666\) 30.5778 1.18487
\(667\) 17.9767 0.696062
\(668\) 26.3418 1.01920
\(669\) 43.9245 1.69822
\(670\) −0.684083 −0.0264284
\(671\) −51.8628 −2.00214
\(672\) 18.5924 0.717217
\(673\) 28.4442 1.09644 0.548221 0.836333i \(-0.315305\pi\)
0.548221 + 0.836333i \(0.315305\pi\)
\(674\) −8.97250 −0.345608
\(675\) −55.6709 −2.14277
\(676\) −29.8446 −1.14787
\(677\) −19.4502 −0.747532 −0.373766 0.927523i \(-0.621934\pi\)
−0.373766 + 0.927523i \(0.621934\pi\)
\(678\) −19.9456 −0.766007
\(679\) 5.98542 0.229699
\(680\) 3.54937 0.136112
\(681\) 24.1697 0.926184
\(682\) −6.59037 −0.252358
\(683\) −5.80487 −0.222117 −0.111059 0.993814i \(-0.535424\pi\)
−0.111059 + 0.993814i \(0.535424\pi\)
\(684\) 8.41048 0.321583
\(685\) −4.62391 −0.176670
\(686\) −6.93178 −0.264657
\(687\) 39.7844 1.51787
\(688\) 12.2235 0.466017
\(689\) −52.0921 −1.98455
\(690\) −6.21410 −0.236567
\(691\) 25.7605 0.979974 0.489987 0.871730i \(-0.337001\pi\)
0.489987 + 0.871730i \(0.337001\pi\)
\(692\) 14.1862 0.539280
\(693\) −40.1604 −1.52557
\(694\) 10.1581 0.385596
\(695\) 14.7786 0.560584
\(696\) 28.8168 1.09230
\(697\) −11.9823 −0.453863
\(698\) 4.88088 0.184744
\(699\) −4.68476 −0.177194
\(700\) −7.80385 −0.294958
\(701\) 0.176178 0.00665414 0.00332707 0.999994i \(-0.498941\pi\)
0.00332707 + 0.999994i \(0.498941\pi\)
\(702\) 38.2754 1.44461
\(703\) 5.31597 0.200495
\(704\) −14.6059 −0.550479
\(705\) −16.0186 −0.603296
\(706\) 14.3124 0.538654
\(707\) 10.0642 0.378503
\(708\) 44.4847 1.67184
\(709\) 10.4585 0.392778 0.196389 0.980526i \(-0.437078\pi\)
0.196389 + 0.980526i \(0.437078\pi\)
\(710\) −1.32622 −0.0497723
\(711\) −55.5382 −2.08285
\(712\) 2.88928 0.108280
\(713\) 11.5452 0.432370
\(714\) 3.15649 0.118129
\(715\) −27.7213 −1.03672
\(716\) −17.9124 −0.669418
\(717\) 7.37687 0.275494
\(718\) 11.0083 0.410825
\(719\) −37.8811 −1.41273 −0.706364 0.707849i \(-0.749666\pi\)
−0.706364 + 0.707849i \(0.749666\pi\)
\(720\) 24.4463 0.911062
\(721\) 2.23631 0.0832845
\(722\) 8.60774 0.320347
\(723\) 27.9641 1.04000
\(724\) 26.4049 0.981329
\(725\) −18.4844 −0.686492
\(726\) −12.6275 −0.468651
\(727\) −0.827571 −0.0306929 −0.0153465 0.999882i \(-0.504885\pi\)
−0.0153465 + 0.999882i \(0.504885\pi\)
\(728\) 11.3725 0.421494
\(729\) 55.0343 2.03831
\(730\) −7.78161 −0.288010
\(731\) 7.76156 0.287072
\(732\) 68.7107 2.53962
\(733\) −1.87867 −0.0693902 −0.0346951 0.999398i \(-0.511046\pi\)
−0.0346951 + 0.999398i \(0.511046\pi\)
\(734\) 3.44203 0.127048
\(735\) −21.0439 −0.776216
\(736\) −17.0276 −0.627646
\(737\) 5.63594 0.207603
\(738\) 24.1593 0.889314
\(739\) −7.51194 −0.276331 −0.138166 0.990409i \(-0.544121\pi\)
−0.138166 + 0.990409i \(0.544121\pi\)
\(740\) 17.8410 0.655846
\(741\) 10.9433 0.402011
\(742\) 5.26682 0.193351
\(743\) −27.5006 −1.00890 −0.504450 0.863441i \(-0.668305\pi\)
−0.504450 + 0.863441i \(0.668305\pi\)
\(744\) 18.5069 0.678498
\(745\) −18.7957 −0.688621
\(746\) −15.4690 −0.566359
\(747\) −127.397 −4.66121
\(748\) −13.7960 −0.504430
\(749\) −16.5071 −0.603156
\(750\) 15.1079 0.551661
\(751\) 47.8281 1.74527 0.872636 0.488371i \(-0.162409\pi\)
0.872636 + 0.488371i \(0.162409\pi\)
\(752\) −11.7359 −0.427964
\(753\) 56.5622 2.06124
\(754\) 12.7085 0.462818
\(755\) 2.89950 0.105524
\(756\) 32.3531 1.17667
\(757\) −20.2702 −0.736732 −0.368366 0.929681i \(-0.620083\pi\)
−0.368366 + 0.929681i \(0.620083\pi\)
\(758\) 8.83727 0.320984
\(759\) 51.1960 1.85830
\(760\) −1.24414 −0.0451298
\(761\) 3.13530 0.113655 0.0568273 0.998384i \(-0.481902\pi\)
0.0568273 + 0.998384i \(0.481902\pi\)
\(762\) 26.1451 0.947138
\(763\) 8.69998 0.314960
\(764\) −30.2889 −1.09581
\(765\) 15.5227 0.561224
\(766\) −6.40384 −0.231380
\(767\) 41.5831 1.50148
\(768\) 4.93282 0.177998
\(769\) 4.09365 0.147621 0.0738104 0.997272i \(-0.476484\pi\)
0.0738104 + 0.997272i \(0.476484\pi\)
\(770\) 2.80279 0.101005
\(771\) −33.3399 −1.20071
\(772\) −23.6638 −0.851679
\(773\) −41.3716 −1.48803 −0.744017 0.668161i \(-0.767082\pi\)
−0.744017 + 0.668161i \(0.767082\pi\)
\(774\) −15.6492 −0.562499
\(775\) −11.8712 −0.426425
\(776\) −8.78715 −0.315440
\(777\) 33.6301 1.20647
\(778\) −12.7215 −0.456087
\(779\) 4.20010 0.150484
\(780\) 36.7267 1.31503
\(781\) 10.9263 0.390975
\(782\) −2.89083 −0.103376
\(783\) 76.6321 2.73861
\(784\) −15.4176 −0.550630
\(785\) −12.0366 −0.429605
\(786\) 26.3598 0.940222
\(787\) −7.19226 −0.256376 −0.128188 0.991750i \(-0.540916\pi\)
−0.128188 + 0.991750i \(0.540916\pi\)
\(788\) −36.1245 −1.28688
\(789\) 44.2864 1.57664
\(790\) 3.87601 0.137902
\(791\) −15.7598 −0.560353
\(792\) 58.9592 2.09502
\(793\) 64.2290 2.28084
\(794\) −9.53664 −0.338443
\(795\) 36.0521 1.27864
\(796\) −23.0195 −0.815903
\(797\) 25.2489 0.894362 0.447181 0.894443i \(-0.352428\pi\)
0.447181 + 0.894443i \(0.352428\pi\)
\(798\) −1.10643 −0.0391671
\(799\) −7.45194 −0.263631
\(800\) 17.5084 0.619017
\(801\) 12.6359 0.446467
\(802\) 13.8606 0.489436
\(803\) 64.1102 2.26240
\(804\) −7.46681 −0.263334
\(805\) −4.90999 −0.173054
\(806\) 8.16177 0.287486
\(807\) 51.0111 1.79568
\(808\) −14.7752 −0.519789
\(809\) −8.37431 −0.294425 −0.147212 0.989105i \(-0.547030\pi\)
−0.147212 + 0.989105i \(0.547030\pi\)
\(810\) −14.2231 −0.499750
\(811\) 8.34874 0.293164 0.146582 0.989199i \(-0.453173\pi\)
0.146582 + 0.989199i \(0.453173\pi\)
\(812\) 10.7422 0.376976
\(813\) −55.4469 −1.94461
\(814\) 17.5815 0.616231
\(815\) 21.9673 0.769480
\(816\) 15.8299 0.554157
\(817\) −2.72062 −0.0951825
\(818\) −2.81381 −0.0983826
\(819\) 49.7362 1.73792
\(820\) 14.0960 0.492253
\(821\) 22.5847 0.788210 0.394105 0.919065i \(-0.371055\pi\)
0.394105 + 0.919065i \(0.371055\pi\)
\(822\) 6.03693 0.210562
\(823\) −17.6855 −0.616479 −0.308239 0.951309i \(-0.599740\pi\)
−0.308239 + 0.951309i \(0.599740\pi\)
\(824\) −3.28311 −0.114373
\(825\) −52.6416 −1.83275
\(826\) −4.20430 −0.146286
\(827\) 1.43859 0.0500246 0.0250123 0.999687i \(-0.492038\pi\)
0.0250123 + 0.999687i \(0.492038\pi\)
\(828\) −48.7287 −1.69344
\(829\) −8.86981 −0.308061 −0.154031 0.988066i \(-0.549225\pi\)
−0.154031 + 0.988066i \(0.549225\pi\)
\(830\) 8.89101 0.308612
\(831\) 99.4073 3.44840
\(832\) 18.0885 0.627105
\(833\) −9.78973 −0.339194
\(834\) −19.2948 −0.668123
\(835\) −17.0416 −0.589749
\(836\) 4.83583 0.167251
\(837\) 49.2153 1.70113
\(838\) −14.1003 −0.487085
\(839\) −27.3712 −0.944957 −0.472479 0.881342i \(-0.656641\pi\)
−0.472479 + 0.881342i \(0.656641\pi\)
\(840\) −7.87074 −0.271566
\(841\) −3.55591 −0.122617
\(842\) −2.60311 −0.0897092
\(843\) 57.6710 1.98629
\(844\) 37.7895 1.30077
\(845\) 19.3077 0.664206
\(846\) 15.0249 0.516567
\(847\) −9.97746 −0.342830
\(848\) 26.4133 0.907036
\(849\) −60.7000 −2.08322
\(850\) 2.97246 0.101955
\(851\) −30.7997 −1.05580
\(852\) −14.4758 −0.495934
\(853\) 7.83097 0.268127 0.134064 0.990973i \(-0.457197\pi\)
0.134064 + 0.990973i \(0.457197\pi\)
\(854\) −6.49393 −0.222218
\(855\) −5.44109 −0.186081
\(856\) 24.2340 0.828300
\(857\) 18.5978 0.635288 0.317644 0.948210i \(-0.397108\pi\)
0.317644 + 0.948210i \(0.397108\pi\)
\(858\) 36.1927 1.23560
\(859\) 53.3853 1.82148 0.910742 0.412975i \(-0.135510\pi\)
0.910742 + 0.412975i \(0.135510\pi\)
\(860\) −9.13070 −0.311354
\(861\) 26.5708 0.905532
\(862\) −10.4803 −0.356961
\(863\) −7.76573 −0.264349 −0.132174 0.991226i \(-0.542196\pi\)
−0.132174 + 0.991226i \(0.542196\pi\)
\(864\) −72.5861 −2.46943
\(865\) −9.17768 −0.312050
\(866\) −13.1519 −0.446921
\(867\) −45.4381 −1.54316
\(868\) 6.89891 0.234164
\(869\) −31.9332 −1.08326
\(870\) −8.79537 −0.298191
\(871\) −6.97978 −0.236501
\(872\) −12.7724 −0.432527
\(873\) −38.4294 −1.30064
\(874\) 1.01331 0.0342757
\(875\) 11.9373 0.403554
\(876\) −84.9367 −2.86975
\(877\) −10.5052 −0.354735 −0.177367 0.984145i \(-0.556758\pi\)
−0.177367 + 0.984145i \(0.556758\pi\)
\(878\) 12.1202 0.409036
\(879\) −0.873934 −0.0294771
\(880\) 14.0561 0.473830
\(881\) −30.9478 −1.04266 −0.521329 0.853356i \(-0.674563\pi\)
−0.521329 + 0.853356i \(0.674563\pi\)
\(882\) 19.7385 0.664629
\(883\) −38.1189 −1.28280 −0.641402 0.767205i \(-0.721647\pi\)
−0.641402 + 0.767205i \(0.721647\pi\)
\(884\) 17.0855 0.574647
\(885\) −28.7790 −0.967396
\(886\) −8.95240 −0.300762
\(887\) 0.00758081 0.000254539 0 0.000127269 1.00000i \(-0.499959\pi\)
0.000127269 1.00000i \(0.499959\pi\)
\(888\) −49.3721 −1.65682
\(889\) 20.6582 0.692855
\(890\) −0.881857 −0.0295599
\(891\) 117.180 3.92567
\(892\) −24.0384 −0.804866
\(893\) 2.61209 0.0874103
\(894\) 24.5395 0.820722
\(895\) 11.5883 0.387354
\(896\) −13.2209 −0.441680
\(897\) −63.4031 −2.11697
\(898\) 9.34608 0.311883
\(899\) 16.3409 0.545000
\(900\) 50.1047 1.67016
\(901\) 16.7716 0.558744
\(902\) 13.8910 0.462520
\(903\) −17.2113 −0.572756
\(904\) 23.1368 0.769519
\(905\) −17.0824 −0.567839
\(906\) −3.78556 −0.125767
\(907\) −50.7472 −1.68503 −0.842516 0.538671i \(-0.818926\pi\)
−0.842516 + 0.538671i \(0.818926\pi\)
\(908\) −13.2273 −0.438962
\(909\) −64.6172 −2.14322
\(910\) −3.47109 −0.115065
\(911\) 22.5478 0.747042 0.373521 0.927622i \(-0.378150\pi\)
0.373521 + 0.927622i \(0.378150\pi\)
\(912\) −5.54877 −0.183738
\(913\) −73.2502 −2.42423
\(914\) −8.24326 −0.272663
\(915\) −44.4519 −1.46953
\(916\) −21.7727 −0.719390
\(917\) 20.8278 0.687796
\(918\) −12.3232 −0.406725
\(919\) −45.2864 −1.49386 −0.746930 0.664902i \(-0.768473\pi\)
−0.746930 + 0.664902i \(0.768473\pi\)
\(920\) 7.20832 0.237651
\(921\) 7.81072 0.257372
\(922\) 0.469309 0.0154559
\(923\) −13.5316 −0.445399
\(924\) 30.5926 1.00642
\(925\) 31.6694 1.04128
\(926\) 13.1700 0.432792
\(927\) −14.3582 −0.471587
\(928\) −24.1007 −0.791144
\(929\) −21.8628 −0.717297 −0.358648 0.933473i \(-0.616762\pi\)
−0.358648 + 0.933473i \(0.616762\pi\)
\(930\) −5.64863 −0.185226
\(931\) 3.43154 0.112464
\(932\) 2.56382 0.0839806
\(933\) −5.68394 −0.186084
\(934\) −11.1581 −0.365103
\(935\) 8.92518 0.291885
\(936\) −73.0174 −2.38665
\(937\) −50.1531 −1.63843 −0.819216 0.573485i \(-0.805591\pi\)
−0.819216 + 0.573485i \(0.805591\pi\)
\(938\) 0.705697 0.0230418
\(939\) 98.5843 3.21718
\(940\) 8.76646 0.285930
\(941\) 20.1369 0.656445 0.328222 0.944600i \(-0.393550\pi\)
0.328222 + 0.944600i \(0.393550\pi\)
\(942\) 15.7149 0.512018
\(943\) −24.3346 −0.792443
\(944\) −21.0847 −0.686249
\(945\) −20.9305 −0.680871
\(946\) −8.99792 −0.292548
\(947\) −33.7774 −1.09762 −0.548809 0.835948i \(-0.684919\pi\)
−0.548809 + 0.835948i \(0.684919\pi\)
\(948\) 42.3069 1.37406
\(949\) −79.3966 −2.57732
\(950\) −1.04192 −0.0338044
\(951\) 91.5835 2.96980
\(952\) −3.66151 −0.118670
\(953\) −15.4539 −0.500600 −0.250300 0.968168i \(-0.580529\pi\)
−0.250300 + 0.968168i \(0.580529\pi\)
\(954\) −33.8157 −1.09482
\(955\) 19.5952 0.634085
\(956\) −4.03712 −0.130570
\(957\) 72.4623 2.34237
\(958\) −2.67397 −0.0863921
\(959\) 4.77000 0.154031
\(960\) −12.5187 −0.404041
\(961\) −20.5054 −0.661465
\(962\) −21.7736 −0.702011
\(963\) 105.984 3.41529
\(964\) −15.3038 −0.492903
\(965\) 15.3091 0.492818
\(966\) 6.41043 0.206252
\(967\) −4.78054 −0.153732 −0.0768659 0.997041i \(-0.524491\pi\)
−0.0768659 + 0.997041i \(0.524491\pi\)
\(968\) 14.6478 0.470799
\(969\) −3.52330 −0.113185
\(970\) 2.68199 0.0861134
\(971\) 36.6685 1.17675 0.588374 0.808589i \(-0.299768\pi\)
0.588374 + 0.808589i \(0.299768\pi\)
\(972\) −73.8322 −2.36817
\(973\) −15.2455 −0.488749
\(974\) 5.40921 0.173322
\(975\) 65.1935 2.08786
\(976\) −32.5673 −1.04245
\(977\) −39.0452 −1.24917 −0.624583 0.780958i \(-0.714731\pi\)
−0.624583 + 0.780958i \(0.714731\pi\)
\(978\) −28.6802 −0.917093
\(979\) 7.26534 0.232201
\(980\) 11.5166 0.367885
\(981\) −55.8583 −1.78342
\(982\) 3.78318 0.120726
\(983\) −51.2714 −1.63530 −0.817652 0.575712i \(-0.804725\pi\)
−0.817652 + 0.575712i \(0.804725\pi\)
\(984\) −39.0085 −1.24354
\(985\) 23.3704 0.744644
\(986\) −4.09165 −0.130305
\(987\) 16.5247 0.525987
\(988\) −5.98888 −0.190532
\(989\) 15.7628 0.501227
\(990\) −17.9953 −0.571929
\(991\) 41.3736 1.31428 0.657138 0.753770i \(-0.271767\pi\)
0.657138 + 0.753770i \(0.271767\pi\)
\(992\) −15.4781 −0.491431
\(993\) 59.2734 1.88099
\(994\) 1.36813 0.0433943
\(995\) 14.8923 0.472116
\(996\) 97.0460 3.07502
\(997\) 20.3663 0.645008 0.322504 0.946568i \(-0.395475\pi\)
0.322504 + 0.946568i \(0.395475\pi\)
\(998\) 15.3109 0.484659
\(999\) −131.294 −4.15397
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 503.2.a.f.1.10 26
3.2 odd 2 4527.2.a.o.1.17 26
4.3 odd 2 8048.2.a.u.1.2 26
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
503.2.a.f.1.10 26 1.1 even 1 trivial
4527.2.a.o.1.17 26 3.2 odd 2
8048.2.a.u.1.2 26 4.3 odd 2