Properties

Label 8027.2.a.e.1.20
Level $8027$
Weight $2$
Character 8027.1
Self dual yes
Analytic conductor $64.096$
Analytic rank $0$
Dimension $169$
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] = [8027,2,Mod(1,8027)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8027, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([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("8027.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8027 = 23 \cdot 349 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8027.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: \(64.0959177025\)
Analytic rank: \(0\)
Dimension: \(169\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.20
Character \(\chi\) \(=\) 8027.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.31715 q^{2} +2.98534 q^{3} +3.36921 q^{4} +4.10060 q^{5} -6.91750 q^{6} +4.34971 q^{7} -3.17266 q^{8} +5.91228 q^{9} +O(q^{10})\) \(q-2.31715 q^{2} +2.98534 q^{3} +3.36921 q^{4} +4.10060 q^{5} -6.91750 q^{6} +4.34971 q^{7} -3.17266 q^{8} +5.91228 q^{9} -9.50172 q^{10} -0.545613 q^{11} +10.0582 q^{12} -0.963474 q^{13} -10.0789 q^{14} +12.2417 q^{15} +0.613135 q^{16} +2.94781 q^{17} -13.6997 q^{18} -6.11025 q^{19} +13.8158 q^{20} +12.9854 q^{21} +1.26427 q^{22} -1.00000 q^{23} -9.47148 q^{24} +11.8149 q^{25} +2.23252 q^{26} +8.69415 q^{27} +14.6551 q^{28} -0.866337 q^{29} -28.3659 q^{30} +3.20396 q^{31} +4.92459 q^{32} -1.62884 q^{33} -6.83054 q^{34} +17.8364 q^{35} +19.9197 q^{36} +6.46531 q^{37} +14.1584 q^{38} -2.87630 q^{39} -13.0098 q^{40} -8.92239 q^{41} -30.0891 q^{42} -0.710927 q^{43} -1.83828 q^{44} +24.2439 q^{45} +2.31715 q^{46} +10.6355 q^{47} +1.83042 q^{48} +11.9200 q^{49} -27.3770 q^{50} +8.80024 q^{51} -3.24614 q^{52} -9.69067 q^{53} -20.1457 q^{54} -2.23734 q^{55} -13.8001 q^{56} -18.2412 q^{57} +2.00744 q^{58} -3.15331 q^{59} +41.2448 q^{60} -4.91744 q^{61} -7.42406 q^{62} +25.7167 q^{63} -12.6373 q^{64} -3.95082 q^{65} +3.77428 q^{66} +10.8742 q^{67} +9.93179 q^{68} -2.98534 q^{69} -41.3297 q^{70} +0.572705 q^{71} -18.7577 q^{72} -10.5783 q^{73} -14.9811 q^{74} +35.2716 q^{75} -20.5867 q^{76} -2.37326 q^{77} +6.66483 q^{78} +3.84280 q^{79} +2.51422 q^{80} +8.21820 q^{81} +20.6746 q^{82} -13.4059 q^{83} +43.7504 q^{84} +12.0878 q^{85} +1.64733 q^{86} -2.58631 q^{87} +1.73104 q^{88} +8.15308 q^{89} -56.1768 q^{90} -4.19083 q^{91} -3.36921 q^{92} +9.56491 q^{93} -24.6442 q^{94} -25.0557 q^{95} +14.7016 q^{96} -5.38504 q^{97} -27.6204 q^{98} -3.22581 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 169 q + 6 q^{2} + 2 q^{3} + 186 q^{4} + 28 q^{5} + 5 q^{6} + 38 q^{7} + 18 q^{8} + 185 q^{9} + 28 q^{10} + 17 q^{11} + 10 q^{12} + 91 q^{13} + 20 q^{14} + 29 q^{15} + 200 q^{16} + 16 q^{17} + 31 q^{18} + 30 q^{19} + 45 q^{20} + 49 q^{21} + 76 q^{22} - 169 q^{23} + 3 q^{24} + 241 q^{25} - 15 q^{26} + 14 q^{27} + 118 q^{28} + 23 q^{29} + 52 q^{30} + 45 q^{31} + 42 q^{32} + 62 q^{33} + 65 q^{34} - 16 q^{35} + 199 q^{36} + 226 q^{37} + 49 q^{38} + 17 q^{39} + 95 q^{40} + 19 q^{41} + 32 q^{42} + 71 q^{43} + 46 q^{44} + 127 q^{45} - 6 q^{46} + 27 q^{47} + 5 q^{48} + 239 q^{49} + 24 q^{50} + 39 q^{51} + 154 q^{52} + 111 q^{53} + 22 q^{54} + 47 q^{55} + 39 q^{56} + 122 q^{57} + 146 q^{58} - 73 q^{59} + 109 q^{60} + 125 q^{61} + 14 q^{62} + 109 q^{63} + 260 q^{64} + 73 q^{65} + 26 q^{66} + 152 q^{67} + 40 q^{68} - 2 q^{69} + 76 q^{70} - 79 q^{71} + 126 q^{72} + 106 q^{73} + 23 q^{74} + 12 q^{75} + 122 q^{76} + 63 q^{77} + 101 q^{78} + 82 q^{79} + 134 q^{80} + 225 q^{81} + 125 q^{82} + 28 q^{83} + 73 q^{84} + 197 q^{85} + 97 q^{86} + 18 q^{87} + 183 q^{88} + 54 q^{89} + 52 q^{90} + 106 q^{91} - 186 q^{92} + 194 q^{93} + q^{94} + 18 q^{95} - 39 q^{96} + 239 q^{97} + 5 q^{98} + 85 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.31715 −1.63848 −0.819238 0.573454i \(-0.805603\pi\)
−0.819238 + 0.573454i \(0.805603\pi\)
\(3\) 2.98534 1.72359 0.861795 0.507257i \(-0.169341\pi\)
0.861795 + 0.507257i \(0.169341\pi\)
\(4\) 3.36921 1.68460
\(5\) 4.10060 1.83384 0.916922 0.399067i \(-0.130666\pi\)
0.916922 + 0.399067i \(0.130666\pi\)
\(6\) −6.91750 −2.82406
\(7\) 4.34971 1.64404 0.822018 0.569462i \(-0.192848\pi\)
0.822018 + 0.569462i \(0.192848\pi\)
\(8\) −3.17266 −1.12170
\(9\) 5.91228 1.97076
\(10\) −9.50172 −3.00471
\(11\) −0.545613 −0.164508 −0.0822542 0.996611i \(-0.526212\pi\)
−0.0822542 + 0.996611i \(0.526212\pi\)
\(12\) 10.0582 2.90356
\(13\) −0.963474 −0.267220 −0.133610 0.991034i \(-0.542657\pi\)
−0.133610 + 0.991034i \(0.542657\pi\)
\(14\) −10.0789 −2.69371
\(15\) 12.2417 3.16079
\(16\) 0.613135 0.153284
\(17\) 2.94781 0.714950 0.357475 0.933923i \(-0.383638\pi\)
0.357475 + 0.933923i \(0.383638\pi\)
\(18\) −13.6997 −3.22904
\(19\) −6.11025 −1.40179 −0.700894 0.713265i \(-0.747215\pi\)
−0.700894 + 0.713265i \(0.747215\pi\)
\(20\) 13.8158 3.08930
\(21\) 12.9854 2.83364
\(22\) 1.26427 0.269543
\(23\) −1.00000 −0.208514
\(24\) −9.47148 −1.93336
\(25\) 11.8149 2.36298
\(26\) 2.23252 0.437833
\(27\) 8.69415 1.67319
\(28\) 14.6551 2.76955
\(29\) −0.866337 −0.160875 −0.0804374 0.996760i \(-0.525632\pi\)
−0.0804374 + 0.996760i \(0.525632\pi\)
\(30\) −28.3659 −5.17888
\(31\) 3.20396 0.575447 0.287724 0.957713i \(-0.407102\pi\)
0.287724 + 0.957713i \(0.407102\pi\)
\(32\) 4.92459 0.870553
\(33\) −1.62884 −0.283545
\(34\) −6.83054 −1.17143
\(35\) 17.8364 3.01490
\(36\) 19.9197 3.31995
\(37\) 6.46531 1.06289 0.531445 0.847093i \(-0.321649\pi\)
0.531445 + 0.847093i \(0.321649\pi\)
\(38\) 14.1584 2.29680
\(39\) −2.87630 −0.460577
\(40\) −13.0098 −2.05703
\(41\) −8.92239 −1.39344 −0.696722 0.717342i \(-0.745359\pi\)
−0.696722 + 0.717342i \(0.745359\pi\)
\(42\) −30.0891 −4.64285
\(43\) −0.710927 −0.108415 −0.0542077 0.998530i \(-0.517263\pi\)
−0.0542077 + 0.998530i \(0.517263\pi\)
\(44\) −1.83828 −0.277131
\(45\) 24.2439 3.61407
\(46\) 2.31715 0.341646
\(47\) 10.6355 1.55135 0.775675 0.631132i \(-0.217409\pi\)
0.775675 + 0.631132i \(0.217409\pi\)
\(48\) 1.83042 0.264198
\(49\) 11.9200 1.70285
\(50\) −27.3770 −3.87169
\(51\) 8.80024 1.23228
\(52\) −3.24614 −0.450159
\(53\) −9.69067 −1.33112 −0.665558 0.746346i \(-0.731806\pi\)
−0.665558 + 0.746346i \(0.731806\pi\)
\(54\) −20.1457 −2.74148
\(55\) −2.23734 −0.301683
\(56\) −13.8001 −1.84412
\(57\) −18.2412 −2.41611
\(58\) 2.00744 0.263589
\(59\) −3.15331 −0.410527 −0.205263 0.978707i \(-0.565805\pi\)
−0.205263 + 0.978707i \(0.565805\pi\)
\(60\) 41.2448 5.32468
\(61\) −4.91744 −0.629614 −0.314807 0.949156i \(-0.601940\pi\)
−0.314807 + 0.949156i \(0.601940\pi\)
\(62\) −7.42406 −0.942857
\(63\) 25.7167 3.24000
\(64\) −12.6373 −1.57966
\(65\) −3.95082 −0.490039
\(66\) 3.77428 0.464581
\(67\) 10.8742 1.32849 0.664247 0.747513i \(-0.268752\pi\)
0.664247 + 0.747513i \(0.268752\pi\)
\(68\) 9.93179 1.20441
\(69\) −2.98534 −0.359393
\(70\) −41.3297 −4.93985
\(71\) 0.572705 0.0679676 0.0339838 0.999422i \(-0.489181\pi\)
0.0339838 + 0.999422i \(0.489181\pi\)
\(72\) −18.7577 −2.21061
\(73\) −10.5783 −1.23809 −0.619047 0.785354i \(-0.712481\pi\)
−0.619047 + 0.785354i \(0.712481\pi\)
\(74\) −14.9811 −1.74152
\(75\) 35.2716 4.07281
\(76\) −20.5867 −2.36146
\(77\) −2.37326 −0.270458
\(78\) 6.66483 0.754644
\(79\) 3.84280 0.432348 0.216174 0.976355i \(-0.430642\pi\)
0.216174 + 0.976355i \(0.430642\pi\)
\(80\) 2.51422 0.281098
\(81\) 8.21820 0.913133
\(82\) 20.6746 2.28312
\(83\) −13.4059 −1.47149 −0.735743 0.677261i \(-0.763167\pi\)
−0.735743 + 0.677261i \(0.763167\pi\)
\(84\) 43.7504 4.77356
\(85\) 12.0878 1.31111
\(86\) 1.64733 0.177636
\(87\) −2.58631 −0.277282
\(88\) 1.73104 0.184530
\(89\) 8.15308 0.864225 0.432112 0.901820i \(-0.357768\pi\)
0.432112 + 0.901820i \(0.357768\pi\)
\(90\) −56.1768 −5.92156
\(91\) −4.19083 −0.439318
\(92\) −3.36921 −0.351264
\(93\) 9.56491 0.991835
\(94\) −24.6442 −2.54185
\(95\) −25.0557 −2.57066
\(96\) 14.7016 1.50048
\(97\) −5.38504 −0.546768 −0.273384 0.961905i \(-0.588143\pi\)
−0.273384 + 0.961905i \(0.588143\pi\)
\(98\) −27.6204 −2.79008
\(99\) −3.22581 −0.324207
\(100\) 39.8069 3.98069
\(101\) 1.33080 0.132419 0.0662097 0.997806i \(-0.478909\pi\)
0.0662097 + 0.997806i \(0.478909\pi\)
\(102\) −20.3915 −2.01906
\(103\) −4.77051 −0.470052 −0.235026 0.971989i \(-0.575518\pi\)
−0.235026 + 0.971989i \(0.575518\pi\)
\(104\) 3.05678 0.299741
\(105\) 53.2478 5.19646
\(106\) 22.4548 2.18100
\(107\) 8.61297 0.832647 0.416324 0.909217i \(-0.363318\pi\)
0.416324 + 0.909217i \(0.363318\pi\)
\(108\) 29.2924 2.81866
\(109\) −10.6174 −1.01696 −0.508482 0.861073i \(-0.669793\pi\)
−0.508482 + 0.861073i \(0.669793\pi\)
\(110\) 5.18426 0.494300
\(111\) 19.3012 1.83199
\(112\) 2.66696 0.252004
\(113\) −6.70297 −0.630562 −0.315281 0.948998i \(-0.602099\pi\)
−0.315281 + 0.948998i \(0.602099\pi\)
\(114\) 42.2677 3.95873
\(115\) −4.10060 −0.382383
\(116\) −2.91887 −0.271010
\(117\) −5.69632 −0.526625
\(118\) 7.30672 0.672638
\(119\) 12.8221 1.17540
\(120\) −38.8388 −3.54548
\(121\) −10.7023 −0.972937
\(122\) 11.3945 1.03161
\(123\) −26.6364 −2.40172
\(124\) 10.7948 0.969400
\(125\) 27.9452 2.49950
\(126\) −59.5895 −5.30866
\(127\) −5.31105 −0.471279 −0.235640 0.971841i \(-0.575718\pi\)
−0.235640 + 0.971841i \(0.575718\pi\)
\(128\) 19.4334 1.71769
\(129\) −2.12236 −0.186864
\(130\) 9.15466 0.802917
\(131\) 4.17631 0.364886 0.182443 0.983216i \(-0.441600\pi\)
0.182443 + 0.983216i \(0.441600\pi\)
\(132\) −5.48790 −0.477661
\(133\) −26.5778 −2.30459
\(134\) −25.1972 −2.17671
\(135\) 35.6512 3.06837
\(136\) −9.35241 −0.801963
\(137\) 5.28181 0.451256 0.225628 0.974214i \(-0.427557\pi\)
0.225628 + 0.974214i \(0.427557\pi\)
\(138\) 6.91750 0.588857
\(139\) 7.86611 0.667195 0.333597 0.942716i \(-0.391737\pi\)
0.333597 + 0.942716i \(0.391737\pi\)
\(140\) 60.0945 5.07892
\(141\) 31.7507 2.67389
\(142\) −1.32705 −0.111363
\(143\) 0.525683 0.0439599
\(144\) 3.62502 0.302085
\(145\) −3.55250 −0.295019
\(146\) 24.5115 2.02859
\(147\) 35.5852 2.93502
\(148\) 21.7830 1.79055
\(149\) −9.19901 −0.753613 −0.376806 0.926292i \(-0.622978\pi\)
−0.376806 + 0.926292i \(0.622978\pi\)
\(150\) −81.7297 −6.67320
\(151\) 12.6149 1.02658 0.513292 0.858214i \(-0.328426\pi\)
0.513292 + 0.858214i \(0.328426\pi\)
\(152\) 19.3858 1.57239
\(153\) 17.4283 1.40899
\(154\) 5.49920 0.443138
\(155\) 13.1381 1.05528
\(156\) −9.69085 −0.775889
\(157\) −10.3294 −0.824374 −0.412187 0.911099i \(-0.635235\pi\)
−0.412187 + 0.911099i \(0.635235\pi\)
\(158\) −8.90436 −0.708392
\(159\) −28.9300 −2.29430
\(160\) 20.1938 1.59646
\(161\) −4.34971 −0.342805
\(162\) −19.0428 −1.49615
\(163\) −8.88713 −0.696094 −0.348047 0.937477i \(-0.613155\pi\)
−0.348047 + 0.937477i \(0.613155\pi\)
\(164\) −30.0614 −2.34740
\(165\) −6.67923 −0.519977
\(166\) 31.0635 2.41099
\(167\) −9.66583 −0.747964 −0.373982 0.927436i \(-0.622008\pi\)
−0.373982 + 0.927436i \(0.622008\pi\)
\(168\) −41.1982 −3.17851
\(169\) −12.0717 −0.928594
\(170\) −28.0093 −2.14822
\(171\) −36.1255 −2.76259
\(172\) −2.39526 −0.182637
\(173\) 15.9808 1.21500 0.607500 0.794320i \(-0.292172\pi\)
0.607500 + 0.794320i \(0.292172\pi\)
\(174\) 5.99289 0.454320
\(175\) 51.3914 3.88483
\(176\) −0.334534 −0.0252165
\(177\) −9.41373 −0.707579
\(178\) −18.8920 −1.41601
\(179\) 9.42663 0.704579 0.352290 0.935891i \(-0.385403\pi\)
0.352290 + 0.935891i \(0.385403\pi\)
\(180\) 81.6826 6.08826
\(181\) 2.94049 0.218565 0.109282 0.994011i \(-0.465145\pi\)
0.109282 + 0.994011i \(0.465145\pi\)
\(182\) 9.71080 0.719812
\(183\) −14.6803 −1.08520
\(184\) 3.17266 0.233892
\(185\) 26.5116 1.94917
\(186\) −22.1634 −1.62510
\(187\) −1.60836 −0.117615
\(188\) 35.8333 2.61341
\(189\) 37.8170 2.75078
\(190\) 58.0579 4.21197
\(191\) 13.0312 0.942906 0.471453 0.881891i \(-0.343730\pi\)
0.471453 + 0.881891i \(0.343730\pi\)
\(192\) −37.7267 −2.72269
\(193\) 3.51969 0.253353 0.126676 0.991944i \(-0.459569\pi\)
0.126676 + 0.991944i \(0.459569\pi\)
\(194\) 12.4780 0.895866
\(195\) −11.7946 −0.844626
\(196\) 40.1608 2.86863
\(197\) −24.0936 −1.71660 −0.858298 0.513152i \(-0.828478\pi\)
−0.858298 + 0.513152i \(0.828478\pi\)
\(198\) 7.47471 0.531205
\(199\) 3.34319 0.236993 0.118496 0.992954i \(-0.462193\pi\)
0.118496 + 0.992954i \(0.462193\pi\)
\(200\) −37.4847 −2.65057
\(201\) 32.4632 2.28978
\(202\) −3.08366 −0.216966
\(203\) −3.76831 −0.264484
\(204\) 29.6498 2.07590
\(205\) −36.5872 −2.55536
\(206\) 11.0540 0.770169
\(207\) −5.91228 −0.410932
\(208\) −0.590739 −0.0409604
\(209\) 3.33383 0.230606
\(210\) −123.383 −8.51427
\(211\) 25.8886 1.78224 0.891122 0.453764i \(-0.149919\pi\)
0.891122 + 0.453764i \(0.149919\pi\)
\(212\) −32.6498 −2.24240
\(213\) 1.70972 0.117148
\(214\) −19.9576 −1.36427
\(215\) −2.91523 −0.198817
\(216\) −27.5836 −1.87683
\(217\) 13.9363 0.946056
\(218\) 24.6022 1.66627
\(219\) −31.5798 −2.13396
\(220\) −7.53805 −0.508216
\(221\) −2.84014 −0.191049
\(222\) −44.7238 −3.00166
\(223\) −15.2530 −1.02142 −0.510710 0.859753i \(-0.670617\pi\)
−0.510710 + 0.859753i \(0.670617\pi\)
\(224\) 21.4205 1.43122
\(225\) 69.8531 4.65687
\(226\) 15.5318 1.03316
\(227\) 7.86731 0.522172 0.261086 0.965316i \(-0.415919\pi\)
0.261086 + 0.965316i \(0.415919\pi\)
\(228\) −61.4584 −4.07018
\(229\) 6.65203 0.439578 0.219789 0.975547i \(-0.429463\pi\)
0.219789 + 0.975547i \(0.429463\pi\)
\(230\) 9.50172 0.626525
\(231\) −7.08499 −0.466158
\(232\) 2.74859 0.180454
\(233\) −22.3251 −1.46256 −0.731282 0.682075i \(-0.761078\pi\)
−0.731282 + 0.682075i \(0.761078\pi\)
\(234\) 13.1993 0.862863
\(235\) 43.6120 2.84493
\(236\) −10.6242 −0.691574
\(237\) 11.4721 0.745191
\(238\) −29.7109 −1.92587
\(239\) −30.2276 −1.95526 −0.977632 0.210323i \(-0.932548\pi\)
−0.977632 + 0.210323i \(0.932548\pi\)
\(240\) 7.50581 0.484498
\(241\) 6.66082 0.429061 0.214531 0.976717i \(-0.431178\pi\)
0.214531 + 0.976717i \(0.431178\pi\)
\(242\) 24.7989 1.59413
\(243\) −1.54830 −0.0993237
\(244\) −16.5679 −1.06065
\(245\) 48.8790 3.12276
\(246\) 61.7207 3.93517
\(247\) 5.88707 0.374585
\(248\) −10.1651 −0.645482
\(249\) −40.0211 −2.53624
\(250\) −64.7534 −4.09537
\(251\) 12.5191 0.790198 0.395099 0.918639i \(-0.370710\pi\)
0.395099 + 0.918639i \(0.370710\pi\)
\(252\) 86.6448 5.45811
\(253\) 0.545613 0.0343024
\(254\) 12.3065 0.772179
\(255\) 36.0863 2.25981
\(256\) −19.7556 −1.23473
\(257\) −7.34261 −0.458020 −0.229010 0.973424i \(-0.573549\pi\)
−0.229010 + 0.973424i \(0.573549\pi\)
\(258\) 4.91784 0.306171
\(259\) 28.1222 1.74743
\(260\) −13.3111 −0.825521
\(261\) −5.12203 −0.317045
\(262\) −9.67715 −0.597856
\(263\) −14.2145 −0.876504 −0.438252 0.898852i \(-0.644402\pi\)
−0.438252 + 0.898852i \(0.644402\pi\)
\(264\) 5.16776 0.318054
\(265\) −39.7375 −2.44106
\(266\) 61.5849 3.77601
\(267\) 24.3398 1.48957
\(268\) 36.6374 2.23799
\(269\) 0.204183 0.0124493 0.00622464 0.999981i \(-0.498019\pi\)
0.00622464 + 0.999981i \(0.498019\pi\)
\(270\) −82.6094 −5.02745
\(271\) 27.2338 1.65434 0.827169 0.561953i \(-0.189950\pi\)
0.827169 + 0.561953i \(0.189950\pi\)
\(272\) 1.80741 0.109590
\(273\) −12.5111 −0.757204
\(274\) −12.2388 −0.739371
\(275\) −6.44637 −0.388731
\(276\) −10.0582 −0.605435
\(277\) 14.5703 0.875442 0.437721 0.899111i \(-0.355786\pi\)
0.437721 + 0.899111i \(0.355786\pi\)
\(278\) −18.2270 −1.09318
\(279\) 18.9427 1.13407
\(280\) −56.5889 −3.38183
\(281\) −0.382369 −0.0228102 −0.0114051 0.999935i \(-0.503630\pi\)
−0.0114051 + 0.999935i \(0.503630\pi\)
\(282\) −73.5713 −4.38111
\(283\) 20.5295 1.22035 0.610175 0.792267i \(-0.291099\pi\)
0.610175 + 0.792267i \(0.291099\pi\)
\(284\) 1.92956 0.114498
\(285\) −74.7999 −4.43076
\(286\) −1.21809 −0.0720272
\(287\) −38.8098 −2.29087
\(288\) 29.1156 1.71565
\(289\) −8.31039 −0.488847
\(290\) 8.23169 0.483382
\(291\) −16.0762 −0.942404
\(292\) −35.6404 −2.08570
\(293\) −3.41734 −0.199643 −0.0998217 0.995005i \(-0.531827\pi\)
−0.0998217 + 0.995005i \(0.531827\pi\)
\(294\) −82.4564 −4.80895
\(295\) −12.9305 −0.752842
\(296\) −20.5122 −1.19225
\(297\) −4.74364 −0.275254
\(298\) 21.3155 1.23478
\(299\) 0.963474 0.0557191
\(300\) 118.837 6.86107
\(301\) −3.09233 −0.178239
\(302\) −29.2306 −1.68203
\(303\) 3.97289 0.228236
\(304\) −3.74641 −0.214871
\(305\) −20.1645 −1.15461
\(306\) −40.3841 −2.30860
\(307\) −2.68413 −0.153191 −0.0765956 0.997062i \(-0.524405\pi\)
−0.0765956 + 0.997062i \(0.524405\pi\)
\(308\) −7.99599 −0.455614
\(309\) −14.2416 −0.810177
\(310\) −30.4431 −1.72905
\(311\) −20.9938 −1.19045 −0.595225 0.803559i \(-0.702937\pi\)
−0.595225 + 0.803559i \(0.702937\pi\)
\(312\) 9.12553 0.516631
\(313\) 19.4512 1.09945 0.549724 0.835346i \(-0.314733\pi\)
0.549724 + 0.835346i \(0.314733\pi\)
\(314\) 23.9348 1.35072
\(315\) 105.454 5.94165
\(316\) 12.9472 0.728335
\(317\) 32.8284 1.84382 0.921912 0.387399i \(-0.126627\pi\)
0.921912 + 0.387399i \(0.126627\pi\)
\(318\) 67.0352 3.75915
\(319\) 0.472684 0.0264652
\(320\) −51.8206 −2.89686
\(321\) 25.7127 1.43514
\(322\) 10.0789 0.561678
\(323\) −18.0119 −1.00221
\(324\) 27.6888 1.53827
\(325\) −11.3834 −0.631435
\(326\) 20.5928 1.14053
\(327\) −31.6966 −1.75283
\(328\) 28.3077 1.56303
\(329\) 46.2614 2.55048
\(330\) 15.4768 0.851970
\(331\) −15.1321 −0.831733 −0.415866 0.909426i \(-0.636522\pi\)
−0.415866 + 0.909426i \(0.636522\pi\)
\(332\) −45.1671 −2.47887
\(333\) 38.2247 2.09470
\(334\) 22.3972 1.22552
\(335\) 44.5907 2.43625
\(336\) 7.96178 0.434351
\(337\) 27.0690 1.47454 0.737272 0.675596i \(-0.236114\pi\)
0.737272 + 0.675596i \(0.236114\pi\)
\(338\) 27.9720 1.52148
\(339\) −20.0107 −1.08683
\(340\) 40.7263 2.20869
\(341\) −1.74812 −0.0946659
\(342\) 83.7084 4.52643
\(343\) 21.4004 1.15551
\(344\) 2.25553 0.121610
\(345\) −12.2417 −0.659071
\(346\) −37.0301 −1.99075
\(347\) −8.19856 −0.440122 −0.220061 0.975486i \(-0.570626\pi\)
−0.220061 + 0.975486i \(0.570626\pi\)
\(348\) −8.71382 −0.467110
\(349\) 1.00000 0.0535288
\(350\) −119.082 −6.36520
\(351\) −8.37659 −0.447109
\(352\) −2.68692 −0.143213
\(353\) 29.2908 1.55899 0.779496 0.626407i \(-0.215475\pi\)
0.779496 + 0.626407i \(0.215475\pi\)
\(354\) 21.8131 1.15935
\(355\) 2.34844 0.124642
\(356\) 27.4694 1.45588
\(357\) 38.2785 2.02591
\(358\) −21.8429 −1.15444
\(359\) 30.3730 1.60302 0.801512 0.597978i \(-0.204029\pi\)
0.801512 + 0.597978i \(0.204029\pi\)
\(360\) −76.9176 −4.05391
\(361\) 18.3352 0.965011
\(362\) −6.81357 −0.358113
\(363\) −31.9501 −1.67694
\(364\) −14.1198 −0.740077
\(365\) −43.3773 −2.27047
\(366\) 34.0164 1.77807
\(367\) −33.1909 −1.73255 −0.866275 0.499568i \(-0.833492\pi\)
−0.866275 + 0.499568i \(0.833492\pi\)
\(368\) −0.613135 −0.0319619
\(369\) −52.7517 −2.74614
\(370\) −61.4316 −3.19368
\(371\) −42.1516 −2.18840
\(372\) 32.2261 1.67085
\(373\) −2.09594 −0.108524 −0.0542618 0.998527i \(-0.517281\pi\)
−0.0542618 + 0.998527i \(0.517281\pi\)
\(374\) 3.72683 0.192710
\(375\) 83.4261 4.30811
\(376\) −33.7429 −1.74016
\(377\) 0.834693 0.0429889
\(378\) −87.6279 −4.50709
\(379\) −32.4212 −1.66537 −0.832683 0.553750i \(-0.813196\pi\)
−0.832683 + 0.553750i \(0.813196\pi\)
\(380\) −84.4178 −4.33054
\(381\) −15.8553 −0.812291
\(382\) −30.1954 −1.54493
\(383\) −10.0177 −0.511879 −0.255939 0.966693i \(-0.582385\pi\)
−0.255939 + 0.966693i \(0.582385\pi\)
\(384\) 58.0155 2.96059
\(385\) −9.73177 −0.495977
\(386\) −8.15566 −0.415112
\(387\) −4.20320 −0.213661
\(388\) −18.1433 −0.921087
\(389\) −26.3769 −1.33736 −0.668682 0.743548i \(-0.733141\pi\)
−0.668682 + 0.743548i \(0.733141\pi\)
\(390\) 27.3298 1.38390
\(391\) −2.94781 −0.149077
\(392\) −37.8180 −1.91010
\(393\) 12.4677 0.628913
\(394\) 55.8285 2.81260
\(395\) 15.7578 0.792860
\(396\) −10.8684 −0.546159
\(397\) 28.2842 1.41954 0.709772 0.704431i \(-0.248798\pi\)
0.709772 + 0.704431i \(0.248798\pi\)
\(398\) −7.74670 −0.388307
\(399\) −79.3439 −3.97217
\(400\) 7.24413 0.362207
\(401\) 7.52393 0.375727 0.187864 0.982195i \(-0.439844\pi\)
0.187864 + 0.982195i \(0.439844\pi\)
\(402\) −75.2223 −3.75175
\(403\) −3.08693 −0.153771
\(404\) 4.48373 0.223074
\(405\) 33.6995 1.67454
\(406\) 8.73176 0.433350
\(407\) −3.52755 −0.174854
\(408\) −27.9202 −1.38225
\(409\) −13.3689 −0.661049 −0.330525 0.943797i \(-0.607226\pi\)
−0.330525 + 0.943797i \(0.607226\pi\)
\(410\) 84.7781 4.18689
\(411\) 15.7680 0.777779
\(412\) −16.0728 −0.791851
\(413\) −13.7160 −0.674920
\(414\) 13.6997 0.673302
\(415\) −54.9721 −2.69847
\(416\) −4.74472 −0.232629
\(417\) 23.4830 1.14997
\(418\) −7.72500 −0.377842
\(419\) −34.6726 −1.69387 −0.846934 0.531698i \(-0.821554\pi\)
−0.846934 + 0.531698i \(0.821554\pi\)
\(420\) 179.403 8.75396
\(421\) 30.3224 1.47783 0.738913 0.673801i \(-0.235340\pi\)
0.738913 + 0.673801i \(0.235340\pi\)
\(422\) −59.9879 −2.92016
\(423\) 62.8802 3.05734
\(424\) 30.7452 1.49312
\(425\) 34.8282 1.68941
\(426\) −3.96169 −0.191945
\(427\) −21.3894 −1.03511
\(428\) 29.0189 1.40268
\(429\) 1.56935 0.0757687
\(430\) 6.75503 0.325757
\(431\) 9.64067 0.464375 0.232187 0.972671i \(-0.425412\pi\)
0.232187 + 0.972671i \(0.425412\pi\)
\(432\) 5.33069 0.256473
\(433\) 5.60750 0.269479 0.134740 0.990881i \(-0.456980\pi\)
0.134740 + 0.990881i \(0.456980\pi\)
\(434\) −32.2925 −1.55009
\(435\) −10.6054 −0.508492
\(436\) −35.7722 −1.71318
\(437\) 6.11025 0.292293
\(438\) 73.1753 3.49645
\(439\) 28.2288 1.34729 0.673644 0.739056i \(-0.264728\pi\)
0.673644 + 0.739056i \(0.264728\pi\)
\(440\) 7.09832 0.338399
\(441\) 70.4741 3.35591
\(442\) 6.58105 0.313028
\(443\) −40.8126 −1.93906 −0.969532 0.244965i \(-0.921224\pi\)
−0.969532 + 0.244965i \(0.921224\pi\)
\(444\) 65.0296 3.08617
\(445\) 33.4325 1.58485
\(446\) 35.3437 1.67357
\(447\) −27.4622 −1.29892
\(448\) −54.9686 −2.59702
\(449\) −6.57105 −0.310107 −0.155054 0.987906i \(-0.549555\pi\)
−0.155054 + 0.987906i \(0.549555\pi\)
\(450\) −161.860 −7.63017
\(451\) 4.86817 0.229233
\(452\) −22.5837 −1.06225
\(453\) 37.6597 1.76941
\(454\) −18.2298 −0.855566
\(455\) −17.1849 −0.805641
\(456\) 57.8732 2.71016
\(457\) −12.1378 −0.567783 −0.283891 0.958856i \(-0.591626\pi\)
−0.283891 + 0.958856i \(0.591626\pi\)
\(458\) −15.4138 −0.720239
\(459\) 25.6287 1.19625
\(460\) −13.8158 −0.644163
\(461\) 2.57942 0.120135 0.0600677 0.998194i \(-0.480868\pi\)
0.0600677 + 0.998194i \(0.480868\pi\)
\(462\) 16.4170 0.763788
\(463\) −4.77406 −0.221870 −0.110935 0.993828i \(-0.535384\pi\)
−0.110935 + 0.993828i \(0.535384\pi\)
\(464\) −0.531181 −0.0246595
\(465\) 39.2219 1.81887
\(466\) 51.7307 2.39638
\(467\) −28.0521 −1.29810 −0.649048 0.760748i \(-0.724832\pi\)
−0.649048 + 0.760748i \(0.724832\pi\)
\(468\) −19.1921 −0.887155
\(469\) 47.2996 2.18409
\(470\) −101.056 −4.66136
\(471\) −30.8367 −1.42088
\(472\) 10.0044 0.460490
\(473\) 0.387891 0.0178352
\(474\) −26.5826 −1.22098
\(475\) −72.1921 −3.31240
\(476\) 43.2004 1.98009
\(477\) −57.2939 −2.62331
\(478\) 70.0421 3.20365
\(479\) −28.4886 −1.30168 −0.650840 0.759215i \(-0.725583\pi\)
−0.650840 + 0.759215i \(0.725583\pi\)
\(480\) 60.2854 2.75164
\(481\) −6.22916 −0.284025
\(482\) −15.4341 −0.703006
\(483\) −12.9854 −0.590855
\(484\) −36.0583 −1.63901
\(485\) −22.0819 −1.00269
\(486\) 3.58766 0.162739
\(487\) −11.4957 −0.520922 −0.260461 0.965484i \(-0.583874\pi\)
−0.260461 + 0.965484i \(0.583874\pi\)
\(488\) 15.6014 0.706241
\(489\) −26.5311 −1.19978
\(490\) −113.260 −5.11657
\(491\) −12.1437 −0.548039 −0.274020 0.961724i \(-0.588353\pi\)
−0.274020 + 0.961724i \(0.588353\pi\)
\(492\) −89.7435 −4.04595
\(493\) −2.55380 −0.115017
\(494\) −13.6412 −0.613749
\(495\) −13.2278 −0.594544
\(496\) 1.96446 0.0882067
\(497\) 2.49110 0.111741
\(498\) 92.7351 4.15556
\(499\) 19.5588 0.875573 0.437786 0.899079i \(-0.355763\pi\)
0.437786 + 0.899079i \(0.355763\pi\)
\(500\) 94.1532 4.21066
\(501\) −28.8558 −1.28918
\(502\) −29.0087 −1.29472
\(503\) −25.8214 −1.15132 −0.575660 0.817689i \(-0.695255\pi\)
−0.575660 + 0.817689i \(0.695255\pi\)
\(504\) −81.5903 −3.63432
\(505\) 5.45707 0.242836
\(506\) −1.26427 −0.0562036
\(507\) −36.0382 −1.60051
\(508\) −17.8940 −0.793918
\(509\) −31.0418 −1.37590 −0.687952 0.725757i \(-0.741490\pi\)
−0.687952 + 0.725757i \(0.741490\pi\)
\(510\) −83.6174 −3.70264
\(511\) −46.0124 −2.03547
\(512\) 6.90998 0.305381
\(513\) −53.1235 −2.34546
\(514\) 17.0140 0.750454
\(515\) −19.5619 −0.862002
\(516\) −7.15067 −0.314791
\(517\) −5.80288 −0.255210
\(518\) −65.1635 −2.86312
\(519\) 47.7083 2.09416
\(520\) 12.5346 0.549679
\(521\) 25.6623 1.12428 0.562142 0.827041i \(-0.309977\pi\)
0.562142 + 0.827041i \(0.309977\pi\)
\(522\) 11.8685 0.519471
\(523\) 39.9316 1.74608 0.873042 0.487644i \(-0.162144\pi\)
0.873042 + 0.487644i \(0.162144\pi\)
\(524\) 14.0708 0.614687
\(525\) 153.421 6.69585
\(526\) 32.9372 1.43613
\(527\) 9.44467 0.411416
\(528\) −0.998699 −0.0434628
\(529\) 1.00000 0.0434783
\(530\) 92.0780 3.99961
\(531\) −18.6433 −0.809049
\(532\) −89.5461 −3.88232
\(533\) 8.59649 0.372355
\(534\) −56.3990 −2.44062
\(535\) 35.3183 1.52694
\(536\) −34.5001 −1.49018
\(537\) 28.1417 1.21440
\(538\) −0.473125 −0.0203979
\(539\) −6.50368 −0.280133
\(540\) 120.116 5.16898
\(541\) −27.1680 −1.16804 −0.584022 0.811738i \(-0.698522\pi\)
−0.584022 + 0.811738i \(0.698522\pi\)
\(542\) −63.1050 −2.71059
\(543\) 8.77837 0.376716
\(544\) 14.5168 0.622402
\(545\) −43.5377 −1.86495
\(546\) 28.9901 1.24066
\(547\) 38.6187 1.65122 0.825608 0.564244i \(-0.190832\pi\)
0.825608 + 0.564244i \(0.190832\pi\)
\(548\) 17.7955 0.760187
\(549\) −29.0733 −1.24082
\(550\) 14.9372 0.636926
\(551\) 5.29354 0.225512
\(552\) 9.47148 0.403133
\(553\) 16.7150 0.710796
\(554\) −33.7615 −1.43439
\(555\) 79.1464 3.35958
\(556\) 26.5025 1.12396
\(557\) −19.2525 −0.815755 −0.407877 0.913037i \(-0.633731\pi\)
−0.407877 + 0.913037i \(0.633731\pi\)
\(558\) −43.8931 −1.85814
\(559\) 0.684959 0.0289707
\(560\) 10.9361 0.462136
\(561\) −4.80152 −0.202720
\(562\) 0.886008 0.0373740
\(563\) −2.27043 −0.0956873 −0.0478437 0.998855i \(-0.515235\pi\)
−0.0478437 + 0.998855i \(0.515235\pi\)
\(564\) 106.975 4.50444
\(565\) −27.4862 −1.15635
\(566\) −47.5699 −1.99951
\(567\) 35.7468 1.50122
\(568\) −1.81700 −0.0762396
\(569\) −37.2414 −1.56124 −0.780621 0.625005i \(-0.785097\pi\)
−0.780621 + 0.625005i \(0.785097\pi\)
\(570\) 173.323 7.25970
\(571\) −29.3935 −1.23008 −0.615040 0.788496i \(-0.710860\pi\)
−0.615040 + 0.788496i \(0.710860\pi\)
\(572\) 1.77114 0.0740549
\(573\) 38.9027 1.62518
\(574\) 89.9283 3.75354
\(575\) −11.8149 −0.492716
\(576\) −74.7153 −3.11314
\(577\) 44.6680 1.85955 0.929776 0.368126i \(-0.120000\pi\)
0.929776 + 0.368126i \(0.120000\pi\)
\(578\) 19.2565 0.800963
\(579\) 10.5075 0.436676
\(580\) −11.9691 −0.496990
\(581\) −58.3116 −2.41917
\(582\) 37.2510 1.54411
\(583\) 5.28735 0.218980
\(584\) 33.5613 1.38878
\(585\) −23.3583 −0.965749
\(586\) 7.91851 0.327111
\(587\) −36.6454 −1.51252 −0.756258 0.654274i \(-0.772974\pi\)
−0.756258 + 0.654274i \(0.772974\pi\)
\(588\) 119.894 4.94434
\(589\) −19.5770 −0.806655
\(590\) 29.9619 1.23351
\(591\) −71.9276 −2.95871
\(592\) 3.96411 0.162924
\(593\) 13.4696 0.553132 0.276566 0.960995i \(-0.410804\pi\)
0.276566 + 0.960995i \(0.410804\pi\)
\(594\) 10.9917 0.450997
\(595\) 52.5784 2.15551
\(596\) −30.9934 −1.26954
\(597\) 9.98058 0.408478
\(598\) −2.23252 −0.0912944
\(599\) −8.07908 −0.330102 −0.165051 0.986285i \(-0.552779\pi\)
−0.165051 + 0.986285i \(0.552779\pi\)
\(600\) −111.905 −4.56849
\(601\) 27.9642 1.14068 0.570342 0.821407i \(-0.306811\pi\)
0.570342 + 0.821407i \(0.306811\pi\)
\(602\) 7.16540 0.292040
\(603\) 64.2913 2.61814
\(604\) 42.5021 1.72939
\(605\) −43.8859 −1.78421
\(606\) −9.20580 −0.373960
\(607\) −13.6400 −0.553629 −0.276815 0.960923i \(-0.589279\pi\)
−0.276815 + 0.960923i \(0.589279\pi\)
\(608\) −30.0905 −1.22033
\(609\) −11.2497 −0.455861
\(610\) 46.7242 1.89181
\(611\) −10.2470 −0.414551
\(612\) 58.7195 2.37360
\(613\) −29.5266 −1.19257 −0.596285 0.802773i \(-0.703357\pi\)
−0.596285 + 0.802773i \(0.703357\pi\)
\(614\) 6.21954 0.251000
\(615\) −109.225 −4.40439
\(616\) 7.52954 0.303374
\(617\) −12.2401 −0.492767 −0.246384 0.969172i \(-0.579242\pi\)
−0.246384 + 0.969172i \(0.579242\pi\)
\(618\) 33.0000 1.32745
\(619\) 22.1410 0.889922 0.444961 0.895550i \(-0.353218\pi\)
0.444961 + 0.895550i \(0.353218\pi\)
\(620\) 44.2651 1.77773
\(621\) −8.69415 −0.348884
\(622\) 48.6460 1.95052
\(623\) 35.4635 1.42082
\(624\) −1.76356 −0.0705989
\(625\) 55.5176 2.22071
\(626\) −45.0715 −1.80142
\(627\) 9.95264 0.397470
\(628\) −34.8018 −1.38874
\(629\) 19.0585 0.759913
\(630\) −244.353 −9.73525
\(631\) 21.9194 0.872597 0.436299 0.899802i \(-0.356289\pi\)
0.436299 + 0.899802i \(0.356289\pi\)
\(632\) −12.1919 −0.484967
\(633\) 77.2864 3.07186
\(634\) −76.0684 −3.02106
\(635\) −21.7785 −0.864252
\(636\) −97.4710 −3.86498
\(637\) −11.4846 −0.455035
\(638\) −1.09528 −0.0433627
\(639\) 3.38599 0.133948
\(640\) 79.6887 3.14997
\(641\) −1.55726 −0.0615081 −0.0307541 0.999527i \(-0.509791\pi\)
−0.0307541 + 0.999527i \(0.509791\pi\)
\(642\) −59.5802 −2.35144
\(643\) 4.67478 0.184355 0.0921777 0.995743i \(-0.470617\pi\)
0.0921777 + 0.995743i \(0.470617\pi\)
\(644\) −14.6551 −0.577490
\(645\) −8.70295 −0.342678
\(646\) 41.7363 1.64209
\(647\) 1.38033 0.0542663 0.0271332 0.999632i \(-0.491362\pi\)
0.0271332 + 0.999632i \(0.491362\pi\)
\(648\) −26.0736 −1.02427
\(649\) 1.72049 0.0675351
\(650\) 26.3770 1.03459
\(651\) 41.6046 1.63061
\(652\) −29.9426 −1.17264
\(653\) −26.3890 −1.03268 −0.516340 0.856384i \(-0.672706\pi\)
−0.516340 + 0.856384i \(0.672706\pi\)
\(654\) 73.4460 2.87196
\(655\) 17.1254 0.669143
\(656\) −5.47063 −0.213592
\(657\) −62.5417 −2.43998
\(658\) −107.195 −4.17889
\(659\) 17.3896 0.677404 0.338702 0.940894i \(-0.390012\pi\)
0.338702 + 0.940894i \(0.390012\pi\)
\(660\) −22.5037 −0.875955
\(661\) 37.7006 1.46638 0.733192 0.680021i \(-0.238029\pi\)
0.733192 + 0.680021i \(0.238029\pi\)
\(662\) 35.0633 1.36277
\(663\) −8.47880 −0.329289
\(664\) 42.5323 1.65057
\(665\) −108.985 −4.22626
\(666\) −88.5726 −3.43212
\(667\) 0.866337 0.0335447
\(668\) −32.5662 −1.26002
\(669\) −45.5356 −1.76051
\(670\) −103.324 −3.99174
\(671\) 2.68302 0.103577
\(672\) 63.9477 2.46684
\(673\) −38.3121 −1.47682 −0.738411 0.674351i \(-0.764423\pi\)
−0.738411 + 0.674351i \(0.764423\pi\)
\(674\) −62.7231 −2.41600
\(675\) 102.721 3.95372
\(676\) −40.6721 −1.56431
\(677\) 48.7721 1.87446 0.937232 0.348706i \(-0.113379\pi\)
0.937232 + 0.348706i \(0.113379\pi\)
\(678\) 46.3678 1.78074
\(679\) −23.4234 −0.898906
\(680\) −38.3505 −1.47067
\(681\) 23.4866 0.900009
\(682\) 4.05066 0.155108
\(683\) 23.2976 0.891459 0.445730 0.895168i \(-0.352944\pi\)
0.445730 + 0.895168i \(0.352944\pi\)
\(684\) −121.714 −4.65386
\(685\) 21.6586 0.827532
\(686\) −49.5881 −1.89328
\(687\) 19.8586 0.757653
\(688\) −0.435894 −0.0166183
\(689\) 9.33670 0.355700
\(690\) 28.3659 1.07987
\(691\) 34.5762 1.31534 0.657670 0.753306i \(-0.271542\pi\)
0.657670 + 0.753306i \(0.271542\pi\)
\(692\) 53.8427 2.04679
\(693\) −14.0314 −0.533007
\(694\) 18.9973 0.721129
\(695\) 32.2558 1.22353
\(696\) 8.20550 0.311029
\(697\) −26.3016 −0.996242
\(698\) −2.31715 −0.0877056
\(699\) −66.6480 −2.52086
\(700\) 173.148 6.54439
\(701\) −4.83133 −0.182477 −0.0912384 0.995829i \(-0.529083\pi\)
−0.0912384 + 0.995829i \(0.529083\pi\)
\(702\) 19.4098 0.732578
\(703\) −39.5047 −1.48995
\(704\) 6.89508 0.259868
\(705\) 130.197 4.90350
\(706\) −67.8713 −2.55437
\(707\) 5.78858 0.217702
\(708\) −31.7168 −1.19199
\(709\) −0.742927 −0.0279012 −0.0139506 0.999903i \(-0.504441\pi\)
−0.0139506 + 0.999903i \(0.504441\pi\)
\(710\) −5.44169 −0.204223
\(711\) 22.7197 0.852055
\(712\) −25.8670 −0.969405
\(713\) −3.20396 −0.119989
\(714\) −88.6971 −3.31941
\(715\) 2.15562 0.0806155
\(716\) 31.7602 1.18694
\(717\) −90.2399 −3.37007
\(718\) −70.3789 −2.62652
\(719\) 35.8759 1.33794 0.668972 0.743288i \(-0.266735\pi\)
0.668972 + 0.743288i \(0.266735\pi\)
\(720\) 14.8648 0.553977
\(721\) −20.7503 −0.772782
\(722\) −42.4855 −1.58115
\(723\) 19.8848 0.739525
\(724\) 9.90711 0.368195
\(725\) −10.2357 −0.380144
\(726\) 74.0332 2.74763
\(727\) −46.6303 −1.72942 −0.864712 0.502268i \(-0.832499\pi\)
−0.864712 + 0.502268i \(0.832499\pi\)
\(728\) 13.2961 0.492786
\(729\) −29.2768 −1.08433
\(730\) 100.512 3.72011
\(731\) −2.09568 −0.0775115
\(732\) −49.4608 −1.82812
\(733\) −46.4369 −1.71519 −0.857593 0.514329i \(-0.828041\pi\)
−0.857593 + 0.514329i \(0.828041\pi\)
\(734\) 76.9084 2.83874
\(735\) 145.921 5.38236
\(736\) −4.92459 −0.181523
\(737\) −5.93310 −0.218549
\(738\) 122.234 4.49949
\(739\) −38.6135 −1.42042 −0.710211 0.703989i \(-0.751400\pi\)
−0.710211 + 0.703989i \(0.751400\pi\)
\(740\) 89.3232 3.28359
\(741\) 17.5749 0.645631
\(742\) 97.6717 3.58564
\(743\) −33.7719 −1.23897 −0.619486 0.785008i \(-0.712659\pi\)
−0.619486 + 0.785008i \(0.712659\pi\)
\(744\) −30.3462 −1.11255
\(745\) −37.7215 −1.38201
\(746\) 4.85661 0.177813
\(747\) −79.2592 −2.89994
\(748\) −5.41891 −0.198135
\(749\) 37.4639 1.36890
\(750\) −193.311 −7.05873
\(751\) −12.6038 −0.459920 −0.229960 0.973200i \(-0.573860\pi\)
−0.229960 + 0.973200i \(0.573860\pi\)
\(752\) 6.52101 0.237797
\(753\) 37.3738 1.36198
\(754\) −1.93411 −0.0704362
\(755\) 51.7286 1.88259
\(756\) 127.413 4.63398
\(757\) 32.1846 1.16977 0.584884 0.811117i \(-0.301140\pi\)
0.584884 + 0.811117i \(0.301140\pi\)
\(758\) 75.1250 2.72866
\(759\) 1.62884 0.0591232
\(760\) 79.4932 2.88352
\(761\) 1.28667 0.0466417 0.0233209 0.999728i \(-0.492576\pi\)
0.0233209 + 0.999728i \(0.492576\pi\)
\(762\) 36.7392 1.33092
\(763\) −46.1826 −1.67192
\(764\) 43.9049 1.58842
\(765\) 71.4665 2.58388
\(766\) 23.2125 0.838701
\(767\) 3.03814 0.109701
\(768\) −58.9773 −2.12816
\(769\) 35.5882 1.28334 0.641671 0.766980i \(-0.278241\pi\)
0.641671 + 0.766980i \(0.278241\pi\)
\(770\) 22.5500 0.812646
\(771\) −21.9202 −0.789438
\(772\) 11.8586 0.426799
\(773\) 25.6472 0.922464 0.461232 0.887280i \(-0.347408\pi\)
0.461232 + 0.887280i \(0.347408\pi\)
\(774\) 9.73946 0.350078
\(775\) 37.8545 1.35977
\(776\) 17.0849 0.613313
\(777\) 83.9545 3.01185
\(778\) 61.1195 2.19124
\(779\) 54.5181 1.95331
\(780\) −39.7383 −1.42286
\(781\) −0.312475 −0.0111812
\(782\) 6.83054 0.244260
\(783\) −7.53207 −0.269174
\(784\) 7.30854 0.261019
\(785\) −42.3566 −1.51177
\(786\) −28.8896 −1.03046
\(787\) −5.50017 −0.196060 −0.0980299 0.995183i \(-0.531254\pi\)
−0.0980299 + 0.995183i \(0.531254\pi\)
\(788\) −81.1762 −2.89178
\(789\) −42.4352 −1.51073
\(790\) −36.5132 −1.29908
\(791\) −29.1560 −1.03667
\(792\) 10.2344 0.363664
\(793\) 4.73783 0.168245
\(794\) −65.5389 −2.32589
\(795\) −118.630 −4.20738
\(796\) 11.2639 0.399239
\(797\) −9.98728 −0.353767 −0.176884 0.984232i \(-0.556602\pi\)
−0.176884 + 0.984232i \(0.556602\pi\)
\(798\) 183.852 6.50830
\(799\) 31.3515 1.10914
\(800\) 58.1837 2.05710
\(801\) 48.2033 1.70318
\(802\) −17.4341 −0.615620
\(803\) 5.77164 0.203677
\(804\) 109.375 3.85737
\(805\) −17.8364 −0.628651
\(806\) 7.15289 0.251950
\(807\) 0.609558 0.0214575
\(808\) −4.22217 −0.148535
\(809\) 20.4557 0.719184 0.359592 0.933110i \(-0.382916\pi\)
0.359592 + 0.933110i \(0.382916\pi\)
\(810\) −78.0871 −2.74370
\(811\) −29.6616 −1.04156 −0.520779 0.853691i \(-0.674359\pi\)
−0.520779 + 0.853691i \(0.674359\pi\)
\(812\) −12.6962 −0.445550
\(813\) 81.3024 2.85140
\(814\) 8.17389 0.286495
\(815\) −36.4425 −1.27653
\(816\) 5.39573 0.188888
\(817\) 4.34394 0.151975
\(818\) 30.9778 1.08311
\(819\) −24.7774 −0.865791
\(820\) −123.270 −4.30476
\(821\) −9.28615 −0.324089 −0.162044 0.986783i \(-0.551809\pi\)
−0.162044 + 0.986783i \(0.551809\pi\)
\(822\) −36.5370 −1.27437
\(823\) 3.11075 0.108434 0.0542169 0.998529i \(-0.482734\pi\)
0.0542169 + 0.998529i \(0.482734\pi\)
\(824\) 15.1352 0.527260
\(825\) −19.2446 −0.670012
\(826\) 31.7821 1.10584
\(827\) −43.0032 −1.49537 −0.747684 0.664055i \(-0.768834\pi\)
−0.747684 + 0.664055i \(0.768834\pi\)
\(828\) −19.9197 −0.692257
\(829\) 36.2793 1.26003 0.630016 0.776582i \(-0.283048\pi\)
0.630016 + 0.776582i \(0.283048\pi\)
\(830\) 127.379 4.42138
\(831\) 43.4972 1.50890
\(832\) 12.1757 0.422117
\(833\) 35.1378 1.21745
\(834\) −54.4138 −1.88420
\(835\) −39.6357 −1.37165
\(836\) 11.2324 0.388479
\(837\) 27.8557 0.962833
\(838\) 80.3418 2.77536
\(839\) −7.09339 −0.244891 −0.122445 0.992475i \(-0.539074\pi\)
−0.122445 + 0.992475i \(0.539074\pi\)
\(840\) −168.937 −5.82889
\(841\) −28.2495 −0.974119
\(842\) −70.2618 −2.42138
\(843\) −1.14150 −0.0393155
\(844\) 87.2240 3.00237
\(845\) −49.5013 −1.70290
\(846\) −145.703 −5.00938
\(847\) −46.5519 −1.59954
\(848\) −5.94168 −0.204038
\(849\) 61.2875 2.10338
\(850\) −80.7023 −2.76806
\(851\) −6.46531 −0.221628
\(852\) 5.76041 0.197348
\(853\) −29.5462 −1.01164 −0.505821 0.862638i \(-0.668810\pi\)
−0.505821 + 0.862638i \(0.668810\pi\)
\(854\) 49.5626 1.69600
\(855\) −148.136 −5.06615
\(856\) −27.3260 −0.933984
\(857\) −19.0737 −0.651544 −0.325772 0.945448i \(-0.605624\pi\)
−0.325772 + 0.945448i \(0.605624\pi\)
\(858\) −3.63642 −0.124145
\(859\) 21.9360 0.748447 0.374224 0.927339i \(-0.377909\pi\)
0.374224 + 0.927339i \(0.377909\pi\)
\(860\) −9.82200 −0.334927
\(861\) −115.861 −3.94852
\(862\) −22.3389 −0.760867
\(863\) −48.8604 −1.66323 −0.831613 0.555356i \(-0.812582\pi\)
−0.831613 + 0.555356i \(0.812582\pi\)
\(864\) 42.8152 1.45660
\(865\) 65.5310 2.22812
\(866\) −12.9934 −0.441535
\(867\) −24.8094 −0.842571
\(868\) 46.9542 1.59373
\(869\) −2.09668 −0.0711250
\(870\) 24.5744 0.833151
\(871\) −10.4770 −0.355000
\(872\) 33.6854 1.14073
\(873\) −31.8379 −1.07755
\(874\) −14.1584 −0.478915
\(875\) 121.554 4.10926
\(876\) −106.399 −3.59488
\(877\) 16.4276 0.554722 0.277361 0.960766i \(-0.410540\pi\)
0.277361 + 0.960766i \(0.410540\pi\)
\(878\) −65.4105 −2.20750
\(879\) −10.2019 −0.344103
\(880\) −1.37179 −0.0462430
\(881\) 1.92067 0.0647090 0.0323545 0.999476i \(-0.489699\pi\)
0.0323545 + 0.999476i \(0.489699\pi\)
\(882\) −163.299 −5.49858
\(883\) 11.5051 0.387179 0.193589 0.981083i \(-0.437987\pi\)
0.193589 + 0.981083i \(0.437987\pi\)
\(884\) −9.56902 −0.321841
\(885\) −38.6019 −1.29759
\(886\) 94.5691 3.17711
\(887\) 53.8440 1.80791 0.903953 0.427632i \(-0.140652\pi\)
0.903953 + 0.427632i \(0.140652\pi\)
\(888\) −61.2361 −2.05495
\(889\) −23.1015 −0.774799
\(890\) −77.4683 −2.59674
\(891\) −4.48395 −0.150218
\(892\) −51.3906 −1.72069
\(893\) −64.9858 −2.17467
\(894\) 63.6342 2.12825
\(895\) 38.6548 1.29209
\(896\) 84.5297 2.82394
\(897\) 2.87630 0.0960369
\(898\) 15.2261 0.508103
\(899\) −2.77571 −0.0925749
\(900\) 235.349 7.84498
\(901\) −28.5663 −0.951681
\(902\) −11.2803 −0.375593
\(903\) −9.23165 −0.307210
\(904\) 21.2662 0.707305
\(905\) 12.0578 0.400814
\(906\) −87.2635 −2.89913
\(907\) −44.7141 −1.48471 −0.742353 0.670008i \(-0.766290\pi\)
−0.742353 + 0.670008i \(0.766290\pi\)
\(908\) 26.5066 0.879652
\(909\) 7.86805 0.260967
\(910\) 39.8201 1.32002
\(911\) −56.4648 −1.87076 −0.935381 0.353641i \(-0.884943\pi\)
−0.935381 + 0.353641i \(0.884943\pi\)
\(912\) −11.1843 −0.370350
\(913\) 7.31441 0.242072
\(914\) 28.1252 0.930298
\(915\) −60.1979 −1.99008
\(916\) 22.4121 0.740515
\(917\) 18.1657 0.599885
\(918\) −59.3858 −1.96002
\(919\) 41.2827 1.36179 0.680894 0.732382i \(-0.261591\pi\)
0.680894 + 0.732382i \(0.261591\pi\)
\(920\) 13.0098 0.428921
\(921\) −8.01304 −0.264039
\(922\) −5.97691 −0.196839
\(923\) −0.551787 −0.0181623
\(924\) −23.8708 −0.785291
\(925\) 76.3871 2.51159
\(926\) 11.0622 0.363528
\(927\) −28.2046 −0.926360
\(928\) −4.26636 −0.140050
\(929\) 16.4305 0.539066 0.269533 0.962991i \(-0.413131\pi\)
0.269533 + 0.962991i \(0.413131\pi\)
\(930\) −90.8831 −2.98017
\(931\) −72.8340 −2.38704
\(932\) −75.2178 −2.46384
\(933\) −62.6738 −2.05185
\(934\) 65.0010 2.12690
\(935\) −6.59526 −0.215688
\(936\) 18.0725 0.590718
\(937\) −42.2225 −1.37935 −0.689675 0.724119i \(-0.742246\pi\)
−0.689675 + 0.724119i \(0.742246\pi\)
\(938\) −109.600 −3.57858
\(939\) 58.0686 1.89500
\(940\) 146.938 4.79259
\(941\) 15.7266 0.512672 0.256336 0.966588i \(-0.417485\pi\)
0.256336 + 0.966588i \(0.417485\pi\)
\(942\) 71.4535 2.32808
\(943\) 8.92239 0.290553
\(944\) −1.93341 −0.0629270
\(945\) 155.072 5.04451
\(946\) −0.898803 −0.0292226
\(947\) 8.32328 0.270470 0.135235 0.990814i \(-0.456821\pi\)
0.135235 + 0.990814i \(0.456821\pi\)
\(948\) 38.6518 1.25535
\(949\) 10.1919 0.330843
\(950\) 167.280 5.42729
\(951\) 98.0039 3.17800
\(952\) −40.6803 −1.31846
\(953\) 8.24534 0.267093 0.133546 0.991043i \(-0.457363\pi\)
0.133546 + 0.991043i \(0.457363\pi\)
\(954\) 132.759 4.29823
\(955\) 53.4358 1.72914
\(956\) −101.843 −3.29384
\(957\) 1.41113 0.0456152
\(958\) 66.0126 2.13277
\(959\) 22.9743 0.741880
\(960\) −154.702 −4.99299
\(961\) −20.7347 −0.668860
\(962\) 14.4339 0.465368
\(963\) 50.9223 1.64095
\(964\) 22.4417 0.722797
\(965\) 14.4328 0.464609
\(966\) 30.0891 0.968102
\(967\) 4.91301 0.157992 0.0789958 0.996875i \(-0.474829\pi\)
0.0789958 + 0.996875i \(0.474829\pi\)
\(968\) 33.9548 1.09135
\(969\) −53.7717 −1.72740
\(970\) 51.1672 1.64288
\(971\) 58.3791 1.87347 0.936737 0.350035i \(-0.113830\pi\)
0.936737 + 0.350035i \(0.113830\pi\)
\(972\) −5.21655 −0.167321
\(973\) 34.2153 1.09689
\(974\) 26.6374 0.853518
\(975\) −33.9832 −1.08833
\(976\) −3.01505 −0.0965096
\(977\) −29.7116 −0.950559 −0.475280 0.879835i \(-0.657653\pi\)
−0.475280 + 0.879835i \(0.657653\pi\)
\(978\) 61.4767 1.96581
\(979\) −4.44842 −0.142172
\(980\) 164.683 5.26062
\(981\) −62.7731 −2.00419
\(982\) 28.1389 0.897949
\(983\) 21.6379 0.690141 0.345071 0.938577i \(-0.387855\pi\)
0.345071 + 0.938577i \(0.387855\pi\)
\(984\) 84.5083 2.69403
\(985\) −98.7981 −3.14797
\(986\) 5.91755 0.188453
\(987\) 138.106 4.39597
\(988\) 19.8347 0.631027
\(989\) 0.710927 0.0226062
\(990\) 30.6508 0.974146
\(991\) 8.25744 0.262306 0.131153 0.991362i \(-0.458132\pi\)
0.131153 + 0.991362i \(0.458132\pi\)
\(992\) 15.7782 0.500958
\(993\) −45.1744 −1.43357
\(994\) −5.77227 −0.183085
\(995\) 13.7091 0.434608
\(996\) −134.839 −4.27255
\(997\) 29.6257 0.938254 0.469127 0.883131i \(-0.344569\pi\)
0.469127 + 0.883131i \(0.344569\pi\)
\(998\) −45.3208 −1.43460
\(999\) 56.2104 1.77842
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 8027.2.a.e.1.20 169
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8027.2.a.e.1.20 169 1.1 even 1 trivial