Properties

Label 8007.2.a.d.1.18
Level $8007$
Weight $2$
Character 8007.1
Self dual yes
Analytic conductor $63.936$
Analytic rank $1$
Dimension $40$
CM no
Inner twists $1$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [8007,2,Mod(1,8007)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(8007, 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("8007.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 8007 = 3 \cdot 17 \cdot 157 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 8007.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: \(63.9362168984\)
Analytic rank: \(1\)
Dimension: \(40\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Character \(\chi\) \(=\) 8007.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-0.524942 q^{2} +1.00000 q^{3} -1.72444 q^{4} -0.0309405 q^{5} -0.524942 q^{6} +4.53114 q^{7} +1.95511 q^{8} +1.00000 q^{9} +O(q^{10})\) \(q-0.524942 q^{2} +1.00000 q^{3} -1.72444 q^{4} -0.0309405 q^{5} -0.524942 q^{6} +4.53114 q^{7} +1.95511 q^{8} +1.00000 q^{9} +0.0162420 q^{10} -5.92549 q^{11} -1.72444 q^{12} +1.49218 q^{13} -2.37858 q^{14} -0.0309405 q^{15} +2.42255 q^{16} +1.00000 q^{17} -0.524942 q^{18} -0.562629 q^{19} +0.0533549 q^{20} +4.53114 q^{21} +3.11054 q^{22} +2.44586 q^{23} +1.95511 q^{24} -4.99904 q^{25} -0.783310 q^{26} +1.00000 q^{27} -7.81366 q^{28} -2.50610 q^{29} +0.0162420 q^{30} -4.61927 q^{31} -5.18192 q^{32} -5.92549 q^{33} -0.524942 q^{34} -0.140196 q^{35} -1.72444 q^{36} +6.57170 q^{37} +0.295347 q^{38} +1.49218 q^{39} -0.0604922 q^{40} -0.878038 q^{41} -2.37858 q^{42} -10.7343 q^{43} +10.2181 q^{44} -0.0309405 q^{45} -1.28393 q^{46} -7.87731 q^{47} +2.42255 q^{48} +13.5312 q^{49} +2.62421 q^{50} +1.00000 q^{51} -2.57318 q^{52} +0.351352 q^{53} -0.524942 q^{54} +0.183338 q^{55} +8.85889 q^{56} -0.562629 q^{57} +1.31556 q^{58} -9.83165 q^{59} +0.0533549 q^{60} -0.530009 q^{61} +2.42485 q^{62} +4.53114 q^{63} -2.12490 q^{64} -0.0461689 q^{65} +3.11054 q^{66} +1.53198 q^{67} -1.72444 q^{68} +2.44586 q^{69} +0.0735946 q^{70} +1.53716 q^{71} +1.95511 q^{72} -6.42822 q^{73} -3.44976 q^{74} -4.99904 q^{75} +0.970218 q^{76} -26.8492 q^{77} -0.783310 q^{78} -0.447691 q^{79} -0.0749550 q^{80} +1.00000 q^{81} +0.460919 q^{82} +4.15544 q^{83} -7.81366 q^{84} -0.0309405 q^{85} +5.63490 q^{86} -2.50610 q^{87} -11.5850 q^{88} -8.61151 q^{89} +0.0162420 q^{90} +6.76130 q^{91} -4.21773 q^{92} -4.61927 q^{93} +4.13513 q^{94} +0.0174080 q^{95} -5.18192 q^{96} -13.7697 q^{97} -7.10311 q^{98} -5.92549 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.524942 −0.371190 −0.185595 0.982626i \(-0.559421\pi\)
−0.185595 + 0.982626i \(0.559421\pi\)
\(3\) 1.00000 0.577350
\(4\) −1.72444 −0.862218
\(5\) −0.0309405 −0.0138370 −0.00691851 0.999976i \(-0.502202\pi\)
−0.00691851 + 0.999976i \(0.502202\pi\)
\(6\) −0.524942 −0.214307
\(7\) 4.53114 1.71261 0.856305 0.516470i \(-0.172754\pi\)
0.856305 + 0.516470i \(0.172754\pi\)
\(8\) 1.95511 0.691236
\(9\) 1.00000 0.333333
\(10\) 0.0162420 0.00513616
\(11\) −5.92549 −1.78660 −0.893301 0.449459i \(-0.851617\pi\)
−0.893301 + 0.449459i \(0.851617\pi\)
\(12\) −1.72444 −0.497802
\(13\) 1.49218 0.413857 0.206929 0.978356i \(-0.433653\pi\)
0.206929 + 0.978356i \(0.433653\pi\)
\(14\) −2.37858 −0.635703
\(15\) −0.0309405 −0.00798880
\(16\) 2.42255 0.605638
\(17\) 1.00000 0.242536
\(18\) −0.524942 −0.123730
\(19\) −0.562629 −0.129076 −0.0645380 0.997915i \(-0.520557\pi\)
−0.0645380 + 0.997915i \(0.520557\pi\)
\(20\) 0.0533549 0.0119305
\(21\) 4.53114 0.988776
\(22\) 3.11054 0.663169
\(23\) 2.44586 0.509997 0.254998 0.966941i \(-0.417925\pi\)
0.254998 + 0.966941i \(0.417925\pi\)
\(24\) 1.95511 0.399086
\(25\) −4.99904 −0.999809
\(26\) −0.783310 −0.153620
\(27\) 1.00000 0.192450
\(28\) −7.81366 −1.47664
\(29\) −2.50610 −0.465372 −0.232686 0.972552i \(-0.574751\pi\)
−0.232686 + 0.972552i \(0.574751\pi\)
\(30\) 0.0162420 0.00296536
\(31\) −4.61927 −0.829645 −0.414823 0.909902i \(-0.636156\pi\)
−0.414823 + 0.909902i \(0.636156\pi\)
\(32\) −5.18192 −0.916043
\(33\) −5.92549 −1.03150
\(34\) −0.524942 −0.0900268
\(35\) −0.140196 −0.0236974
\(36\) −1.72444 −0.287406
\(37\) 6.57170 1.08038 0.540190 0.841543i \(-0.318352\pi\)
0.540190 + 0.841543i \(0.318352\pi\)
\(38\) 0.295347 0.0479117
\(39\) 1.49218 0.238941
\(40\) −0.0604922 −0.00956465
\(41\) −0.878038 −0.137127 −0.0685633 0.997647i \(-0.521841\pi\)
−0.0685633 + 0.997647i \(0.521841\pi\)
\(42\) −2.37858 −0.367024
\(43\) −10.7343 −1.63697 −0.818485 0.574527i \(-0.805186\pi\)
−0.818485 + 0.574527i \(0.805186\pi\)
\(44\) 10.2181 1.54044
\(45\) −0.0309405 −0.00461234
\(46\) −1.28393 −0.189306
\(47\) −7.87731 −1.14902 −0.574512 0.818496i \(-0.694808\pi\)
−0.574512 + 0.818496i \(0.694808\pi\)
\(48\) 2.42255 0.349665
\(49\) 13.5312 1.93303
\(50\) 2.62421 0.371119
\(51\) 1.00000 0.140028
\(52\) −2.57318 −0.356835
\(53\) 0.351352 0.0482620 0.0241310 0.999709i \(-0.492318\pi\)
0.0241310 + 0.999709i \(0.492318\pi\)
\(54\) −0.524942 −0.0714355
\(55\) 0.183338 0.0247212
\(56\) 8.85889 1.18382
\(57\) −0.562629 −0.0745220
\(58\) 1.31556 0.172741
\(59\) −9.83165 −1.27997 −0.639986 0.768387i \(-0.721060\pi\)
−0.639986 + 0.768387i \(0.721060\pi\)
\(60\) 0.0533549 0.00688809
\(61\) −0.530009 −0.0678607 −0.0339303 0.999424i \(-0.510802\pi\)
−0.0339303 + 0.999424i \(0.510802\pi\)
\(62\) 2.42485 0.307956
\(63\) 4.53114 0.570870
\(64\) −2.12490 −0.265612
\(65\) −0.0461689 −0.00572655
\(66\) 3.11054 0.382881
\(67\) 1.53198 0.187161 0.0935805 0.995612i \(-0.470169\pi\)
0.0935805 + 0.995612i \(0.470169\pi\)
\(68\) −1.72444 −0.209119
\(69\) 2.44586 0.294447
\(70\) 0.0735946 0.00879624
\(71\) 1.53716 0.182427 0.0912136 0.995831i \(-0.470925\pi\)
0.0912136 + 0.995831i \(0.470925\pi\)
\(72\) 1.95511 0.230412
\(73\) −6.42822 −0.752367 −0.376183 0.926545i \(-0.622764\pi\)
−0.376183 + 0.926545i \(0.622764\pi\)
\(74\) −3.44976 −0.401026
\(75\) −4.99904 −0.577240
\(76\) 0.970218 0.111292
\(77\) −26.8492 −3.05975
\(78\) −0.783310 −0.0886924
\(79\) −0.447691 −0.0503692 −0.0251846 0.999683i \(-0.508017\pi\)
−0.0251846 + 0.999683i \(0.508017\pi\)
\(80\) −0.0749550 −0.00838022
\(81\) 1.00000 0.111111
\(82\) 0.460919 0.0509000
\(83\) 4.15544 0.456119 0.228060 0.973647i \(-0.426762\pi\)
0.228060 + 0.973647i \(0.426762\pi\)
\(84\) −7.81366 −0.852540
\(85\) −0.0309405 −0.00335597
\(86\) 5.63490 0.607627
\(87\) −2.50610 −0.268682
\(88\) −11.5850 −1.23496
\(89\) −8.61151 −0.912819 −0.456409 0.889770i \(-0.650865\pi\)
−0.456409 + 0.889770i \(0.650865\pi\)
\(90\) 0.0162420 0.00171205
\(91\) 6.76130 0.708776
\(92\) −4.21773 −0.439728
\(93\) −4.61927 −0.478996
\(94\) 4.13513 0.426506
\(95\) 0.0174080 0.00178603
\(96\) −5.18192 −0.528878
\(97\) −13.7697 −1.39810 −0.699050 0.715072i \(-0.746394\pi\)
−0.699050 + 0.715072i \(0.746394\pi\)
\(98\) −7.10311 −0.717522
\(99\) −5.92549 −0.595534
\(100\) 8.62053 0.862053
\(101\) −8.08193 −0.804182 −0.402091 0.915600i \(-0.631716\pi\)
−0.402091 + 0.915600i \(0.631716\pi\)
\(102\) −0.524942 −0.0519770
\(103\) 9.81552 0.967152 0.483576 0.875302i \(-0.339338\pi\)
0.483576 + 0.875302i \(0.339338\pi\)
\(104\) 2.91739 0.286073
\(105\) −0.140196 −0.0136817
\(106\) −0.184440 −0.0179143
\(107\) −6.78931 −0.656347 −0.328174 0.944617i \(-0.606433\pi\)
−0.328174 + 0.944617i \(0.606433\pi\)
\(108\) −1.72444 −0.165934
\(109\) 5.80214 0.555744 0.277872 0.960618i \(-0.410371\pi\)
0.277872 + 0.960618i \(0.410371\pi\)
\(110\) −0.0962416 −0.00917627
\(111\) 6.57170 0.623758
\(112\) 10.9769 1.03722
\(113\) −6.40828 −0.602841 −0.301420 0.953491i \(-0.597461\pi\)
−0.301420 + 0.953491i \(0.597461\pi\)
\(114\) 0.295347 0.0276618
\(115\) −0.0756761 −0.00705683
\(116\) 4.32161 0.401252
\(117\) 1.49218 0.137952
\(118\) 5.16104 0.475113
\(119\) 4.53114 0.415369
\(120\) −0.0604922 −0.00552215
\(121\) 24.1114 2.19195
\(122\) 0.278224 0.0251892
\(123\) −0.878038 −0.0791700
\(124\) 7.96563 0.715335
\(125\) 0.309375 0.0276714
\(126\) −2.37858 −0.211901
\(127\) 7.90321 0.701297 0.350648 0.936507i \(-0.385961\pi\)
0.350648 + 0.936507i \(0.385961\pi\)
\(128\) 11.4793 1.01464
\(129\) −10.7343 −0.945105
\(130\) 0.0242360 0.00212564
\(131\) −0.454147 −0.0396790 −0.0198395 0.999803i \(-0.506316\pi\)
−0.0198395 + 0.999803i \(0.506316\pi\)
\(132\) 10.2181 0.889374
\(133\) −2.54935 −0.221057
\(134\) −0.804199 −0.0694723
\(135\) −0.0309405 −0.00266293
\(136\) 1.95511 0.167649
\(137\) 9.90148 0.845940 0.422970 0.906144i \(-0.360988\pi\)
0.422970 + 0.906144i \(0.360988\pi\)
\(138\) −1.28393 −0.109296
\(139\) 11.3340 0.961334 0.480667 0.876903i \(-0.340395\pi\)
0.480667 + 0.876903i \(0.340395\pi\)
\(140\) 0.241759 0.0204323
\(141\) −7.87731 −0.663389
\(142\) −0.806919 −0.0677151
\(143\) −8.84192 −0.739399
\(144\) 2.42255 0.201879
\(145\) 0.0775401 0.00643935
\(146\) 3.37444 0.279271
\(147\) 13.5312 1.11604
\(148\) −11.3325 −0.931524
\(149\) −15.8946 −1.30214 −0.651068 0.759019i \(-0.725679\pi\)
−0.651068 + 0.759019i \(0.725679\pi\)
\(150\) 2.62421 0.214266
\(151\) 11.9027 0.968631 0.484315 0.874894i \(-0.339069\pi\)
0.484315 + 0.874894i \(0.339069\pi\)
\(152\) −1.10000 −0.0892220
\(153\) 1.00000 0.0808452
\(154\) 14.0943 1.13575
\(155\) 0.142923 0.0114798
\(156\) −2.57318 −0.206019
\(157\) −1.00000 −0.0798087
\(158\) 0.235012 0.0186965
\(159\) 0.351352 0.0278641
\(160\) 0.160331 0.0126753
\(161\) 11.0825 0.873425
\(162\) −0.524942 −0.0412433
\(163\) −0.825261 −0.0646394 −0.0323197 0.999478i \(-0.510289\pi\)
−0.0323197 + 0.999478i \(0.510289\pi\)
\(164\) 1.51412 0.118233
\(165\) 0.183338 0.0142728
\(166\) −2.18137 −0.169307
\(167\) −20.8423 −1.61282 −0.806412 0.591354i \(-0.798594\pi\)
−0.806412 + 0.591354i \(0.798594\pi\)
\(168\) 8.85889 0.683478
\(169\) −10.7734 −0.828722
\(170\) 0.0162420 0.00124570
\(171\) −0.562629 −0.0430253
\(172\) 18.5107 1.41143
\(173\) −7.60663 −0.578321 −0.289161 0.957281i \(-0.593376\pi\)
−0.289161 + 0.957281i \(0.593376\pi\)
\(174\) 1.31556 0.0997322
\(175\) −22.6514 −1.71228
\(176\) −14.3548 −1.08203
\(177\) −9.83165 −0.738992
\(178\) 4.52054 0.338829
\(179\) 8.25507 0.617013 0.308507 0.951222i \(-0.400171\pi\)
0.308507 + 0.951222i \(0.400171\pi\)
\(180\) 0.0533549 0.00397684
\(181\) −12.8556 −0.955546 −0.477773 0.878483i \(-0.658556\pi\)
−0.477773 + 0.878483i \(0.658556\pi\)
\(182\) −3.54929 −0.263091
\(183\) −0.530009 −0.0391794
\(184\) 4.78193 0.352528
\(185\) −0.203332 −0.0149492
\(186\) 2.42485 0.177798
\(187\) −5.92549 −0.433315
\(188\) 13.5839 0.990709
\(189\) 4.53114 0.329592
\(190\) −0.00913820 −0.000662955 0
\(191\) −18.4625 −1.33590 −0.667949 0.744207i \(-0.732828\pi\)
−0.667949 + 0.744207i \(0.732828\pi\)
\(192\) −2.12490 −0.153351
\(193\) −18.6825 −1.34480 −0.672399 0.740189i \(-0.734736\pi\)
−0.672399 + 0.740189i \(0.734736\pi\)
\(194\) 7.22829 0.518961
\(195\) −0.0461689 −0.00330623
\(196\) −23.3337 −1.66670
\(197\) 14.4077 1.02650 0.513252 0.858238i \(-0.328441\pi\)
0.513252 + 0.858238i \(0.328441\pi\)
\(198\) 3.11054 0.221056
\(199\) 4.63934 0.328874 0.164437 0.986388i \(-0.447419\pi\)
0.164437 + 0.986388i \(0.447419\pi\)
\(200\) −9.77369 −0.691104
\(201\) 1.53198 0.108057
\(202\) 4.24254 0.298504
\(203\) −11.3555 −0.797000
\(204\) −1.72444 −0.120735
\(205\) 0.0271669 0.00189742
\(206\) −5.15258 −0.358997
\(207\) 2.44586 0.169999
\(208\) 3.61489 0.250648
\(209\) 3.33385 0.230607
\(210\) 0.0735946 0.00507851
\(211\) −20.8553 −1.43574 −0.717869 0.696178i \(-0.754883\pi\)
−0.717869 + 0.696178i \(0.754883\pi\)
\(212\) −0.605885 −0.0416123
\(213\) 1.53716 0.105324
\(214\) 3.56399 0.243629
\(215\) 0.332126 0.0226508
\(216\) 1.95511 0.133029
\(217\) −20.9306 −1.42086
\(218\) −3.04578 −0.206287
\(219\) −6.42822 −0.434379
\(220\) −0.316154 −0.0213151
\(221\) 1.49218 0.100375
\(222\) −3.44976 −0.231533
\(223\) −5.38829 −0.360827 −0.180413 0.983591i \(-0.557744\pi\)
−0.180413 + 0.983591i \(0.557744\pi\)
\(224\) −23.4800 −1.56882
\(225\) −4.99904 −0.333270
\(226\) 3.36398 0.223768
\(227\) 15.8982 1.05520 0.527600 0.849493i \(-0.323092\pi\)
0.527600 + 0.849493i \(0.323092\pi\)
\(228\) 0.970218 0.0642542
\(229\) 15.6755 1.03587 0.517934 0.855421i \(-0.326701\pi\)
0.517934 + 0.855421i \(0.326701\pi\)
\(230\) 0.0397255 0.00261942
\(231\) −26.8492 −1.76655
\(232\) −4.89971 −0.321682
\(233\) −17.1629 −1.12438 −0.562190 0.827008i \(-0.690041\pi\)
−0.562190 + 0.827008i \(0.690041\pi\)
\(234\) −0.783310 −0.0512066
\(235\) 0.243728 0.0158991
\(236\) 16.9541 1.10362
\(237\) −0.447691 −0.0290807
\(238\) −2.37858 −0.154181
\(239\) −11.7555 −0.760398 −0.380199 0.924905i \(-0.624144\pi\)
−0.380199 + 0.924905i \(0.624144\pi\)
\(240\) −0.0749550 −0.00483832
\(241\) 27.8965 1.79697 0.898485 0.439005i \(-0.144669\pi\)
0.898485 + 0.439005i \(0.144669\pi\)
\(242\) −12.6571 −0.813628
\(243\) 1.00000 0.0641500
\(244\) 0.913967 0.0585107
\(245\) −0.418663 −0.0267474
\(246\) 0.460919 0.0293871
\(247\) −0.839546 −0.0534190
\(248\) −9.03119 −0.573481
\(249\) 4.15544 0.263341
\(250\) −0.162404 −0.0102713
\(251\) 4.10976 0.259406 0.129703 0.991553i \(-0.458598\pi\)
0.129703 + 0.991553i \(0.458598\pi\)
\(252\) −7.81366 −0.492214
\(253\) −14.4929 −0.911161
\(254\) −4.14873 −0.260314
\(255\) −0.0309405 −0.00193757
\(256\) −1.77616 −0.111010
\(257\) 6.27533 0.391445 0.195722 0.980659i \(-0.437295\pi\)
0.195722 + 0.980659i \(0.437295\pi\)
\(258\) 5.63490 0.350814
\(259\) 29.7773 1.85027
\(260\) 0.0796154 0.00493754
\(261\) −2.50610 −0.155124
\(262\) 0.238401 0.0147284
\(263\) 17.8354 1.09978 0.549889 0.835238i \(-0.314670\pi\)
0.549889 + 0.835238i \(0.314670\pi\)
\(264\) −11.5850 −0.713007
\(265\) −0.0108710 −0.000667801 0
\(266\) 1.33826 0.0820540
\(267\) −8.61151 −0.527016
\(268\) −2.64180 −0.161374
\(269\) 22.4357 1.36793 0.683965 0.729515i \(-0.260254\pi\)
0.683965 + 0.729515i \(0.260254\pi\)
\(270\) 0.0162420 0.000988454 0
\(271\) 14.1161 0.857495 0.428747 0.903424i \(-0.358955\pi\)
0.428747 + 0.903424i \(0.358955\pi\)
\(272\) 2.42255 0.146889
\(273\) 6.76130 0.409212
\(274\) −5.19770 −0.314004
\(275\) 29.6218 1.78626
\(276\) −4.21773 −0.253877
\(277\) 17.8122 1.07023 0.535117 0.844778i \(-0.320267\pi\)
0.535117 + 0.844778i \(0.320267\pi\)
\(278\) −5.94967 −0.356838
\(279\) −4.61927 −0.276548
\(280\) −0.274098 −0.0163805
\(281\) −16.7597 −0.999802 −0.499901 0.866083i \(-0.666630\pi\)
−0.499901 + 0.866083i \(0.666630\pi\)
\(282\) 4.13513 0.246243
\(283\) 12.2689 0.729311 0.364656 0.931142i \(-0.381187\pi\)
0.364656 + 0.931142i \(0.381187\pi\)
\(284\) −2.65073 −0.157292
\(285\) 0.0174080 0.00103116
\(286\) 4.64149 0.274457
\(287\) −3.97851 −0.234844
\(288\) −5.18192 −0.305348
\(289\) 1.00000 0.0588235
\(290\) −0.0407040 −0.00239022
\(291\) −13.7697 −0.807194
\(292\) 11.0851 0.648704
\(293\) −20.0852 −1.17339 −0.586696 0.809807i \(-0.699572\pi\)
−0.586696 + 0.809807i \(0.699572\pi\)
\(294\) −7.10311 −0.414262
\(295\) 0.304196 0.0177110
\(296\) 12.8484 0.746799
\(297\) −5.92549 −0.343832
\(298\) 8.34374 0.483340
\(299\) 3.64967 0.211066
\(300\) 8.62053 0.497707
\(301\) −48.6388 −2.80349
\(302\) −6.24824 −0.359546
\(303\) −8.08193 −0.464295
\(304\) −1.36300 −0.0781733
\(305\) 0.0163987 0.000938989 0
\(306\) −0.524942 −0.0300089
\(307\) 19.0510 1.08730 0.543648 0.839313i \(-0.317043\pi\)
0.543648 + 0.839313i \(0.317043\pi\)
\(308\) 46.2998 2.63817
\(309\) 9.81552 0.558386
\(310\) −0.0750260 −0.00426119
\(311\) −0.143909 −0.00816033 −0.00408017 0.999992i \(-0.501299\pi\)
−0.00408017 + 0.999992i \(0.501299\pi\)
\(312\) 2.91739 0.165165
\(313\) −28.3493 −1.60239 −0.801197 0.598400i \(-0.795803\pi\)
−0.801197 + 0.598400i \(0.795803\pi\)
\(314\) 0.524942 0.0296242
\(315\) −0.140196 −0.00789914
\(316\) 0.772015 0.0434292
\(317\) −9.16101 −0.514533 −0.257267 0.966340i \(-0.582822\pi\)
−0.257267 + 0.966340i \(0.582822\pi\)
\(318\) −0.184440 −0.0103429
\(319\) 14.8499 0.831434
\(320\) 0.0657454 0.00367528
\(321\) −6.78931 −0.378942
\(322\) −5.81768 −0.324207
\(323\) −0.562629 −0.0313055
\(324\) −1.72444 −0.0958020
\(325\) −7.45949 −0.413778
\(326\) 0.433214 0.0239935
\(327\) 5.80214 0.320859
\(328\) −1.71666 −0.0947868
\(329\) −35.6932 −1.96783
\(330\) −0.0962416 −0.00529792
\(331\) 21.5231 1.18301 0.591507 0.806300i \(-0.298533\pi\)
0.591507 + 0.806300i \(0.298533\pi\)
\(332\) −7.16580 −0.393274
\(333\) 6.57170 0.360127
\(334\) 10.9410 0.598664
\(335\) −0.0474002 −0.00258975
\(336\) 10.9769 0.598840
\(337\) −22.4052 −1.22049 −0.610245 0.792212i \(-0.708929\pi\)
−0.610245 + 0.792212i \(0.708929\pi\)
\(338\) 5.65540 0.307613
\(339\) −6.40828 −0.348050
\(340\) 0.0533549 0.00289358
\(341\) 27.3714 1.48225
\(342\) 0.295347 0.0159706
\(343\) 29.5939 1.59792
\(344\) −20.9868 −1.13153
\(345\) −0.0756761 −0.00407426
\(346\) 3.99304 0.214667
\(347\) 23.2977 1.25068 0.625342 0.780351i \(-0.284959\pi\)
0.625342 + 0.780351i \(0.284959\pi\)
\(348\) 4.32161 0.231663
\(349\) −15.4419 −0.826587 −0.413293 0.910598i \(-0.635622\pi\)
−0.413293 + 0.910598i \(0.635622\pi\)
\(350\) 11.8906 0.635582
\(351\) 1.49218 0.0796469
\(352\) 30.7054 1.63660
\(353\) 10.5563 0.561855 0.280927 0.959729i \(-0.409358\pi\)
0.280927 + 0.959729i \(0.409358\pi\)
\(354\) 5.16104 0.274306
\(355\) −0.0475605 −0.00252425
\(356\) 14.8500 0.787049
\(357\) 4.53114 0.239813
\(358\) −4.33343 −0.229029
\(359\) −34.4105 −1.81612 −0.908058 0.418844i \(-0.862435\pi\)
−0.908058 + 0.418844i \(0.862435\pi\)
\(360\) −0.0604922 −0.00318822
\(361\) −18.6834 −0.983339
\(362\) 6.74842 0.354689
\(363\) 24.1114 1.26552
\(364\) −11.6594 −0.611120
\(365\) 0.198893 0.0104105
\(366\) 0.278224 0.0145430
\(367\) −33.5629 −1.75197 −0.875983 0.482341i \(-0.839787\pi\)
−0.875983 + 0.482341i \(0.839787\pi\)
\(368\) 5.92522 0.308873
\(369\) −0.878038 −0.0457088
\(370\) 0.106737 0.00554901
\(371\) 1.59203 0.0826539
\(372\) 7.96563 0.412999
\(373\) −0.701734 −0.0363344 −0.0181672 0.999835i \(-0.505783\pi\)
−0.0181672 + 0.999835i \(0.505783\pi\)
\(374\) 3.11054 0.160842
\(375\) 0.309375 0.0159761
\(376\) −15.4010 −0.794247
\(377\) −3.73957 −0.192598
\(378\) −2.37858 −0.122341
\(379\) −14.4778 −0.743677 −0.371839 0.928297i \(-0.621272\pi\)
−0.371839 + 0.928297i \(0.621272\pi\)
\(380\) −0.0300190 −0.00153994
\(381\) 7.90321 0.404894
\(382\) 9.69172 0.495872
\(383\) 11.0025 0.562204 0.281102 0.959678i \(-0.409300\pi\)
0.281102 + 0.959678i \(0.409300\pi\)
\(384\) 11.4793 0.585800
\(385\) 0.830728 0.0423378
\(386\) 9.80724 0.499175
\(387\) −10.7343 −0.545657
\(388\) 23.7450 1.20547
\(389\) −20.1603 −1.02217 −0.511083 0.859532i \(-0.670755\pi\)
−0.511083 + 0.859532i \(0.670755\pi\)
\(390\) 0.0242360 0.00122724
\(391\) 2.44586 0.123692
\(392\) 26.4551 1.33618
\(393\) −0.454147 −0.0229087
\(394\) −7.56318 −0.381028
\(395\) 0.0138518 0.000696959 0
\(396\) 10.2181 0.513480
\(397\) 19.5587 0.981624 0.490812 0.871266i \(-0.336700\pi\)
0.490812 + 0.871266i \(0.336700\pi\)
\(398\) −2.43538 −0.122075
\(399\) −2.54935 −0.127627
\(400\) −12.1104 −0.605522
\(401\) 24.4094 1.21895 0.609474 0.792806i \(-0.291381\pi\)
0.609474 + 0.792806i \(0.291381\pi\)
\(402\) −0.804199 −0.0401098
\(403\) −6.89280 −0.343355
\(404\) 13.9368 0.693380
\(405\) −0.0309405 −0.00153745
\(406\) 5.96098 0.295838
\(407\) −38.9405 −1.93021
\(408\) 1.95511 0.0967925
\(409\) 0.789075 0.0390173 0.0195086 0.999810i \(-0.493790\pi\)
0.0195086 + 0.999810i \(0.493790\pi\)
\(410\) −0.0142611 −0.000704304 0
\(411\) 9.90148 0.488404
\(412\) −16.9262 −0.833896
\(413\) −44.5486 −2.19209
\(414\) −1.28393 −0.0631019
\(415\) −0.128572 −0.00631133
\(416\) −7.73238 −0.379111
\(417\) 11.3340 0.555027
\(418\) −1.75008 −0.0855991
\(419\) 38.5004 1.88087 0.940433 0.339979i \(-0.110420\pi\)
0.940433 + 0.339979i \(0.110420\pi\)
\(420\) 0.241759 0.0117966
\(421\) −7.81654 −0.380955 −0.190477 0.981692i \(-0.561004\pi\)
−0.190477 + 0.981692i \(0.561004\pi\)
\(422\) 10.9478 0.532932
\(423\) −7.87731 −0.383008
\(424\) 0.686933 0.0333604
\(425\) −4.99904 −0.242489
\(426\) −0.806919 −0.0390953
\(427\) −2.40154 −0.116219
\(428\) 11.7077 0.565915
\(429\) −8.84192 −0.426892
\(430\) −0.174347 −0.00840774
\(431\) −10.7740 −0.518965 −0.259482 0.965748i \(-0.583552\pi\)
−0.259482 + 0.965748i \(0.583552\pi\)
\(432\) 2.42255 0.116555
\(433\) −12.5623 −0.603706 −0.301853 0.953354i \(-0.597605\pi\)
−0.301853 + 0.953354i \(0.597605\pi\)
\(434\) 10.9873 0.527408
\(435\) 0.0775401 0.00371776
\(436\) −10.0054 −0.479173
\(437\) −1.37611 −0.0658283
\(438\) 3.37444 0.161237
\(439\) 0.678118 0.0323648 0.0161824 0.999869i \(-0.494849\pi\)
0.0161824 + 0.999869i \(0.494849\pi\)
\(440\) 0.358446 0.0170882
\(441\) 13.5312 0.644344
\(442\) −0.783310 −0.0372582
\(443\) 3.86683 0.183719 0.0918594 0.995772i \(-0.470719\pi\)
0.0918594 + 0.995772i \(0.470719\pi\)
\(444\) −11.3325 −0.537816
\(445\) 0.266445 0.0126307
\(446\) 2.82854 0.133935
\(447\) −15.8946 −0.751789
\(448\) −9.62821 −0.454890
\(449\) −40.2731 −1.90061 −0.950303 0.311326i \(-0.899227\pi\)
−0.950303 + 0.311326i \(0.899227\pi\)
\(450\) 2.62421 0.123706
\(451\) 5.20280 0.244991
\(452\) 11.0507 0.519780
\(453\) 11.9027 0.559239
\(454\) −8.34563 −0.391680
\(455\) −0.209198 −0.00980735
\(456\) −1.10000 −0.0515123
\(457\) 0.293289 0.0137195 0.00685973 0.999976i \(-0.497816\pi\)
0.00685973 + 0.999976i \(0.497816\pi\)
\(458\) −8.22874 −0.384504
\(459\) 1.00000 0.0466760
\(460\) 0.130499 0.00608453
\(461\) −3.86658 −0.180085 −0.0900423 0.995938i \(-0.528700\pi\)
−0.0900423 + 0.995938i \(0.528700\pi\)
\(462\) 14.0943 0.655725
\(463\) 3.44425 0.160068 0.0800339 0.996792i \(-0.474497\pi\)
0.0800339 + 0.996792i \(0.474497\pi\)
\(464\) −6.07117 −0.281847
\(465\) 0.142923 0.00662787
\(466\) 9.00953 0.417359
\(467\) −28.1616 −1.30316 −0.651582 0.758578i \(-0.725894\pi\)
−0.651582 + 0.758578i \(0.725894\pi\)
\(468\) −2.57318 −0.118945
\(469\) 6.94161 0.320534
\(470\) −0.127943 −0.00590157
\(471\) −1.00000 −0.0460776
\(472\) −19.2220 −0.884763
\(473\) 63.6062 2.92462
\(474\) 0.235012 0.0107944
\(475\) 2.81261 0.129051
\(476\) −7.81366 −0.358139
\(477\) 0.351352 0.0160873
\(478\) 6.17093 0.282252
\(479\) −21.2150 −0.969340 −0.484670 0.874697i \(-0.661060\pi\)
−0.484670 + 0.874697i \(0.661060\pi\)
\(480\) 0.160331 0.00731809
\(481\) 9.80619 0.447124
\(482\) −14.6440 −0.667017
\(483\) 11.0825 0.504272
\(484\) −41.5786 −1.88994
\(485\) 0.426041 0.0193455
\(486\) −0.524942 −0.0238118
\(487\) −4.25591 −0.192853 −0.0964267 0.995340i \(-0.530741\pi\)
−0.0964267 + 0.995340i \(0.530741\pi\)
\(488\) −1.03623 −0.0469078
\(489\) −0.825261 −0.0373196
\(490\) 0.219774 0.00992837
\(491\) −6.76995 −0.305524 −0.152762 0.988263i \(-0.548817\pi\)
−0.152762 + 0.988263i \(0.548817\pi\)
\(492\) 1.51412 0.0682618
\(493\) −2.50610 −0.112869
\(494\) 0.440713 0.0198286
\(495\) 0.183338 0.00824041
\(496\) −11.1904 −0.502465
\(497\) 6.96508 0.312427
\(498\) −2.18137 −0.0977493
\(499\) 0.405409 0.0181486 0.00907431 0.999959i \(-0.497112\pi\)
0.00907431 + 0.999959i \(0.497112\pi\)
\(500\) −0.533498 −0.0238588
\(501\) −20.8423 −0.931165
\(502\) −2.15738 −0.0962887
\(503\) −8.71444 −0.388558 −0.194279 0.980946i \(-0.562237\pi\)
−0.194279 + 0.980946i \(0.562237\pi\)
\(504\) 8.85889 0.394606
\(505\) 0.250059 0.0111275
\(506\) 7.60793 0.338214
\(507\) −10.7734 −0.478463
\(508\) −13.6286 −0.604671
\(509\) −17.2021 −0.762472 −0.381236 0.924478i \(-0.624501\pi\)
−0.381236 + 0.924478i \(0.624501\pi\)
\(510\) 0.0162420 0.000719206 0
\(511\) −29.1272 −1.28851
\(512\) −22.0262 −0.973430
\(513\) −0.562629 −0.0248407
\(514\) −3.29418 −0.145300
\(515\) −0.303697 −0.0133825
\(516\) 18.5107 0.814887
\(517\) 46.6769 2.05285
\(518\) −15.6313 −0.686802
\(519\) −7.60663 −0.333894
\(520\) −0.0902654 −0.00395840
\(521\) 12.7255 0.557514 0.278757 0.960362i \(-0.410078\pi\)
0.278757 + 0.960362i \(0.410078\pi\)
\(522\) 1.31556 0.0575804
\(523\) −27.3908 −1.19772 −0.598859 0.800855i \(-0.704379\pi\)
−0.598859 + 0.800855i \(0.704379\pi\)
\(524\) 0.783147 0.0342119
\(525\) −22.6514 −0.988587
\(526\) −9.36255 −0.408227
\(527\) −4.61927 −0.201219
\(528\) −14.3548 −0.624713
\(529\) −17.0178 −0.739903
\(530\) 0.00570665 0.000247881 0
\(531\) −9.83165 −0.426657
\(532\) 4.39619 0.190599
\(533\) −1.31019 −0.0567508
\(534\) 4.52054 0.195623
\(535\) 0.210065 0.00908189
\(536\) 2.99519 0.129372
\(537\) 8.25507 0.356233
\(538\) −11.7774 −0.507762
\(539\) −80.1792 −3.45356
\(540\) 0.0533549 0.00229603
\(541\) −16.7552 −0.720361 −0.360180 0.932883i \(-0.617285\pi\)
−0.360180 + 0.932883i \(0.617285\pi\)
\(542\) −7.41015 −0.318293
\(543\) −12.8556 −0.551685
\(544\) −5.18192 −0.222173
\(545\) −0.179521 −0.00768984
\(546\) −3.54929 −0.151895
\(547\) 26.2453 1.12217 0.561084 0.827759i \(-0.310385\pi\)
0.561084 + 0.827759i \(0.310385\pi\)
\(548\) −17.0745 −0.729385
\(549\) −0.530009 −0.0226202
\(550\) −15.5497 −0.663042
\(551\) 1.41001 0.0600683
\(552\) 4.78193 0.203532
\(553\) −2.02855 −0.0862628
\(554\) −9.35039 −0.397260
\(555\) −0.203332 −0.00863095
\(556\) −19.5447 −0.828880
\(557\) 15.9331 0.675107 0.337553 0.941306i \(-0.390401\pi\)
0.337553 + 0.941306i \(0.390401\pi\)
\(558\) 2.42485 0.102652
\(559\) −16.0176 −0.677472
\(560\) −0.339632 −0.0143521
\(561\) −5.92549 −0.250174
\(562\) 8.79788 0.371116
\(563\) 13.9202 0.586667 0.293333 0.956010i \(-0.405235\pi\)
0.293333 + 0.956010i \(0.405235\pi\)
\(564\) 13.5839 0.571986
\(565\) 0.198276 0.00834152
\(566\) −6.44047 −0.270713
\(567\) 4.53114 0.190290
\(568\) 3.00532 0.126100
\(569\) −10.4683 −0.438855 −0.219428 0.975629i \(-0.570419\pi\)
−0.219428 + 0.975629i \(0.570419\pi\)
\(570\) −0.00913820 −0.000382757 0
\(571\) −29.5260 −1.23563 −0.617813 0.786325i \(-0.711981\pi\)
−0.617813 + 0.786325i \(0.711981\pi\)
\(572\) 15.2473 0.637523
\(573\) −18.4625 −0.771281
\(574\) 2.08849 0.0871718
\(575\) −12.2269 −0.509899
\(576\) −2.12490 −0.0885374
\(577\) −24.6124 −1.02463 −0.512313 0.858799i \(-0.671211\pi\)
−0.512313 + 0.858799i \(0.671211\pi\)
\(578\) −0.524942 −0.0218347
\(579\) −18.6825 −0.776420
\(580\) −0.133713 −0.00555213
\(581\) 18.8289 0.781154
\(582\) 7.22829 0.299622
\(583\) −2.08193 −0.0862249
\(584\) −12.5679 −0.520063
\(585\) −0.0461689 −0.00190885
\(586\) 10.5436 0.435551
\(587\) 21.0256 0.867819 0.433909 0.900956i \(-0.357134\pi\)
0.433909 + 0.900956i \(0.357134\pi\)
\(588\) −23.3337 −0.962268
\(589\) 2.59893 0.107087
\(590\) −0.159685 −0.00657414
\(591\) 14.4077 0.592652
\(592\) 15.9203 0.654320
\(593\) −33.0646 −1.35780 −0.678899 0.734231i \(-0.737543\pi\)
−0.678899 + 0.734231i \(0.737543\pi\)
\(594\) 3.11054 0.127627
\(595\) −0.140196 −0.00574747
\(596\) 27.4092 1.12273
\(597\) 4.63934 0.189876
\(598\) −1.91586 −0.0783455
\(599\) −2.05784 −0.0840811 −0.0420406 0.999116i \(-0.513386\pi\)
−0.0420406 + 0.999116i \(0.513386\pi\)
\(600\) −9.77369 −0.399009
\(601\) 0.390478 0.0159279 0.00796397 0.999968i \(-0.497465\pi\)
0.00796397 + 0.999968i \(0.497465\pi\)
\(602\) 25.5325 1.04063
\(603\) 1.53198 0.0623870
\(604\) −20.5255 −0.835171
\(605\) −0.746019 −0.0303300
\(606\) 4.24254 0.172342
\(607\) −0.531510 −0.0215733 −0.0107867 0.999942i \(-0.503434\pi\)
−0.0107867 + 0.999942i \(0.503434\pi\)
\(608\) 2.91550 0.118239
\(609\) −11.3555 −0.460148
\(610\) −0.00860838 −0.000348543 0
\(611\) −11.7544 −0.475532
\(612\) −1.72444 −0.0697062
\(613\) 46.2746 1.86901 0.934506 0.355947i \(-0.115842\pi\)
0.934506 + 0.355947i \(0.115842\pi\)
\(614\) −10.0006 −0.403593
\(615\) 0.0271669 0.00109548
\(616\) −52.4932 −2.11501
\(617\) 1.35818 0.0546784 0.0273392 0.999626i \(-0.491297\pi\)
0.0273392 + 0.999626i \(0.491297\pi\)
\(618\) −5.15258 −0.207267
\(619\) −28.6878 −1.15306 −0.576530 0.817076i \(-0.695594\pi\)
−0.576530 + 0.817076i \(0.695594\pi\)
\(620\) −0.246461 −0.00989810
\(621\) 2.44586 0.0981489
\(622\) 0.0755439 0.00302903
\(623\) −39.0200 −1.56330
\(624\) 3.61489 0.144712
\(625\) 24.9856 0.999426
\(626\) 14.8817 0.594793
\(627\) 3.33385 0.133141
\(628\) 1.72444 0.0688125
\(629\) 6.57170 0.262031
\(630\) 0.0735946 0.00293208
\(631\) −37.8397 −1.50637 −0.753187 0.657806i \(-0.771485\pi\)
−0.753187 + 0.657806i \(0.771485\pi\)
\(632\) −0.875286 −0.0348170
\(633\) −20.8553 −0.828924
\(634\) 4.80899 0.190990
\(635\) −0.244529 −0.00970385
\(636\) −0.605885 −0.0240249
\(637\) 20.1911 0.800000
\(638\) −7.79532 −0.308620
\(639\) 1.53716 0.0608091
\(640\) −0.355175 −0.0140395
\(641\) −11.5380 −0.455724 −0.227862 0.973693i \(-0.573174\pi\)
−0.227862 + 0.973693i \(0.573174\pi\)
\(642\) 3.56399 0.140660
\(643\) −35.5281 −1.40109 −0.700547 0.713607i \(-0.747060\pi\)
−0.700547 + 0.713607i \(0.747060\pi\)
\(644\) −19.1111 −0.753083
\(645\) 0.332126 0.0130774
\(646\) 0.295347 0.0116203
\(647\) −17.4723 −0.686908 −0.343454 0.939170i \(-0.611597\pi\)
−0.343454 + 0.939170i \(0.611597\pi\)
\(648\) 1.95511 0.0768040
\(649\) 58.2573 2.28680
\(650\) 3.91580 0.153590
\(651\) −20.9306 −0.820333
\(652\) 1.42311 0.0557333
\(653\) −17.9820 −0.703689 −0.351844 0.936059i \(-0.614445\pi\)
−0.351844 + 0.936059i \(0.614445\pi\)
\(654\) −3.04578 −0.119100
\(655\) 0.0140515 0.000549039 0
\(656\) −2.12709 −0.0830491
\(657\) −6.42822 −0.250789
\(658\) 18.7368 0.730438
\(659\) −28.2993 −1.10238 −0.551192 0.834379i \(-0.685827\pi\)
−0.551192 + 0.834379i \(0.685827\pi\)
\(660\) −0.316154 −0.0123063
\(661\) −10.0576 −0.391194 −0.195597 0.980684i \(-0.562665\pi\)
−0.195597 + 0.980684i \(0.562665\pi\)
\(662\) −11.2984 −0.439123
\(663\) 1.49218 0.0579516
\(664\) 8.12436 0.315286
\(665\) 0.0788782 0.00305877
\(666\) −3.44976 −0.133675
\(667\) −6.12957 −0.237338
\(668\) 35.9412 1.39061
\(669\) −5.38829 −0.208323
\(670\) 0.0248823 0.000961289 0
\(671\) 3.14056 0.121240
\(672\) −23.4800 −0.905761
\(673\) −5.54678 −0.213813 −0.106906 0.994269i \(-0.534094\pi\)
−0.106906 + 0.994269i \(0.534094\pi\)
\(674\) 11.7614 0.453034
\(675\) −4.99904 −0.192413
\(676\) 18.5780 0.714539
\(677\) −19.3559 −0.743907 −0.371953 0.928251i \(-0.621312\pi\)
−0.371953 + 0.928251i \(0.621312\pi\)
\(678\) 3.36398 0.129193
\(679\) −62.3924 −2.39440
\(680\) −0.0604922 −0.00231977
\(681\) 15.8982 0.609220
\(682\) −14.3684 −0.550195
\(683\) 31.7896 1.21640 0.608198 0.793785i \(-0.291893\pi\)
0.608198 + 0.793785i \(0.291893\pi\)
\(684\) 0.970218 0.0370972
\(685\) −0.306357 −0.0117053
\(686\) −15.5351 −0.593132
\(687\) 15.6755 0.598059
\(688\) −26.0045 −0.991412
\(689\) 0.524282 0.0199736
\(690\) 0.0397255 0.00151233
\(691\) 47.2811 1.79866 0.899329 0.437273i \(-0.144056\pi\)
0.899329 + 0.437273i \(0.144056\pi\)
\(692\) 13.1172 0.498639
\(693\) −26.8492 −1.01992
\(694\) −12.2299 −0.464241
\(695\) −0.350679 −0.0133020
\(696\) −4.89971 −0.185723
\(697\) −0.878038 −0.0332581
\(698\) 8.10611 0.306821
\(699\) −17.1629 −0.649161
\(700\) 39.0608 1.47636
\(701\) −31.4591 −1.18819 −0.594096 0.804394i \(-0.702490\pi\)
−0.594096 + 0.804394i \(0.702490\pi\)
\(702\) −0.783310 −0.0295641
\(703\) −3.69743 −0.139451
\(704\) 12.5911 0.474543
\(705\) 0.243728 0.00917932
\(706\) −5.54144 −0.208555
\(707\) −36.6204 −1.37725
\(708\) 16.9541 0.637172
\(709\) −22.0195 −0.826961 −0.413480 0.910513i \(-0.635687\pi\)
−0.413480 + 0.910513i \(0.635687\pi\)
\(710\) 0.0249665 0.000936975 0
\(711\) −0.447691 −0.0167897
\(712\) −16.8365 −0.630974
\(713\) −11.2981 −0.423116
\(714\) −2.37858 −0.0890163
\(715\) 0.273573 0.0102311
\(716\) −14.2353 −0.532000
\(717\) −11.7555 −0.439016
\(718\) 18.0635 0.674124
\(719\) −21.6422 −0.807119 −0.403560 0.914953i \(-0.632227\pi\)
−0.403560 + 0.914953i \(0.632227\pi\)
\(720\) −0.0749550 −0.00279341
\(721\) 44.4755 1.65635
\(722\) 9.80772 0.365006
\(723\) 27.8965 1.03748
\(724\) 22.1686 0.823889
\(725\) 12.5281 0.465283
\(726\) −12.6571 −0.469749
\(727\) −14.8127 −0.549374 −0.274687 0.961534i \(-0.588574\pi\)
−0.274687 + 0.961534i \(0.588574\pi\)
\(728\) 13.2191 0.489932
\(729\) 1.00000 0.0370370
\(730\) −0.104407 −0.00386428
\(731\) −10.7343 −0.397024
\(732\) 0.913967 0.0337812
\(733\) 39.1731 1.44689 0.723446 0.690381i \(-0.242557\pi\)
0.723446 + 0.690381i \(0.242557\pi\)
\(734\) 17.6185 0.650312
\(735\) −0.418663 −0.0154426
\(736\) −12.6742 −0.467179
\(737\) −9.07772 −0.334382
\(738\) 0.460919 0.0169667
\(739\) 43.5631 1.60250 0.801248 0.598332i \(-0.204170\pi\)
0.801248 + 0.598332i \(0.204170\pi\)
\(740\) 0.350633 0.0128895
\(741\) −0.839546 −0.0308415
\(742\) −0.835721 −0.0306803
\(743\) 34.4910 1.26535 0.632676 0.774416i \(-0.281956\pi\)
0.632676 + 0.774416i \(0.281956\pi\)
\(744\) −9.03119 −0.331099
\(745\) 0.491787 0.0180177
\(746\) 0.368369 0.0134870
\(747\) 4.15544 0.152040
\(748\) 10.2181 0.373612
\(749\) −30.7633 −1.12407
\(750\) −0.162404 −0.00593016
\(751\) −50.4142 −1.83964 −0.919820 0.392341i \(-0.871665\pi\)
−0.919820 + 0.392341i \(0.871665\pi\)
\(752\) −19.0832 −0.695892
\(753\) 4.10976 0.149768
\(754\) 1.96305 0.0714902
\(755\) −0.368277 −0.0134030
\(756\) −7.81366 −0.284180
\(757\) 0.908233 0.0330103 0.0165052 0.999864i \(-0.494746\pi\)
0.0165052 + 0.999864i \(0.494746\pi\)
\(758\) 7.60003 0.276045
\(759\) −14.4929 −0.526059
\(760\) 0.0340346 0.00123457
\(761\) −12.5656 −0.455503 −0.227752 0.973719i \(-0.573137\pi\)
−0.227752 + 0.973719i \(0.573137\pi\)
\(762\) −4.14873 −0.150292
\(763\) 26.2903 0.951773
\(764\) 31.8374 1.15184
\(765\) −0.0309405 −0.00111866
\(766\) −5.77569 −0.208684
\(767\) −14.6706 −0.529726
\(768\) −1.77616 −0.0640918
\(769\) 41.0157 1.47906 0.739532 0.673121i \(-0.235047\pi\)
0.739532 + 0.673121i \(0.235047\pi\)
\(770\) −0.436084 −0.0157154
\(771\) 6.27533 0.226001
\(772\) 32.2168 1.15951
\(773\) 11.9536 0.429941 0.214971 0.976621i \(-0.431034\pi\)
0.214971 + 0.976621i \(0.431034\pi\)
\(774\) 5.63490 0.202542
\(775\) 23.0919 0.829486
\(776\) −26.9213 −0.966418
\(777\) 29.7773 1.06825
\(778\) 10.5830 0.379417
\(779\) 0.494010 0.0176997
\(780\) 0.0796154 0.00285069
\(781\) −9.10842 −0.325925
\(782\) −1.28393 −0.0459133
\(783\) −2.50610 −0.0895608
\(784\) 32.7801 1.17072
\(785\) 0.0309405 0.00110431
\(786\) 0.238401 0.00850347
\(787\) 10.3129 0.367613 0.183807 0.982962i \(-0.441158\pi\)
0.183807 + 0.982962i \(0.441158\pi\)
\(788\) −24.8451 −0.885070
\(789\) 17.8354 0.634957
\(790\) −0.00727138 −0.000258704 0
\(791\) −29.0368 −1.03243
\(792\) −11.5850 −0.411655
\(793\) −0.790871 −0.0280846
\(794\) −10.2672 −0.364369
\(795\) −0.0108710 −0.000385555 0
\(796\) −8.00025 −0.283561
\(797\) 43.0865 1.52620 0.763102 0.646278i \(-0.223675\pi\)
0.763102 + 0.646278i \(0.223675\pi\)
\(798\) 1.33826 0.0473739
\(799\) −7.87731 −0.278679
\(800\) 25.9047 0.915868
\(801\) −8.61151 −0.304273
\(802\) −12.8135 −0.452461
\(803\) 38.0904 1.34418
\(804\) −2.64180 −0.0931691
\(805\) −0.342899 −0.0120856
\(806\) 3.61832 0.127450
\(807\) 22.4357 0.789775
\(808\) −15.8011 −0.555880
\(809\) −2.33890 −0.0822312 −0.0411156 0.999154i \(-0.513091\pi\)
−0.0411156 + 0.999154i \(0.513091\pi\)
\(810\) 0.0162420 0.000570684 0
\(811\) −24.1108 −0.846645 −0.423323 0.905979i \(-0.639136\pi\)
−0.423323 + 0.905979i \(0.639136\pi\)
\(812\) 19.5818 0.687188
\(813\) 14.1161 0.495075
\(814\) 20.4415 0.716475
\(815\) 0.0255340 0.000894417 0
\(816\) 2.42255 0.0848063
\(817\) 6.03945 0.211294
\(818\) −0.414219 −0.0144828
\(819\) 6.76130 0.236259
\(820\) −0.0468477 −0.00163599
\(821\) −16.7806 −0.585647 −0.292823 0.956167i \(-0.594595\pi\)
−0.292823 + 0.956167i \(0.594595\pi\)
\(822\) −5.19770 −0.181291
\(823\) 44.7104 1.55851 0.779253 0.626710i \(-0.215599\pi\)
0.779253 + 0.626710i \(0.215599\pi\)
\(824\) 19.1904 0.668531
\(825\) 29.6218 1.03130
\(826\) 23.3854 0.813683
\(827\) 26.2729 0.913597 0.456798 0.889570i \(-0.348996\pi\)
0.456798 + 0.889570i \(0.348996\pi\)
\(828\) −4.21773 −0.146576
\(829\) 2.93255 0.101852 0.0509258 0.998702i \(-0.483783\pi\)
0.0509258 + 0.998702i \(0.483783\pi\)
\(830\) 0.0674926 0.00234270
\(831\) 17.8122 0.617900
\(832\) −3.17074 −0.109926
\(833\) 13.5312 0.468829
\(834\) −5.94967 −0.206020
\(835\) 0.644871 0.0223167
\(836\) −5.74901 −0.198834
\(837\) −4.61927 −0.159665
\(838\) −20.2104 −0.698158
\(839\) −34.5744 −1.19364 −0.596821 0.802374i \(-0.703570\pi\)
−0.596821 + 0.802374i \(0.703570\pi\)
\(840\) −0.274098 −0.00945729
\(841\) −22.7194 −0.783429
\(842\) 4.10323 0.141407
\(843\) −16.7597 −0.577236
\(844\) 35.9637 1.23792
\(845\) 0.333334 0.0114670
\(846\) 4.13513 0.142169
\(847\) 109.252 3.75395
\(848\) 0.851170 0.0292293
\(849\) 12.2689 0.421068
\(850\) 2.62421 0.0900095
\(851\) 16.0734 0.550991
\(852\) −2.65073 −0.0908126
\(853\) −53.6615 −1.83734 −0.918668 0.395032i \(-0.870734\pi\)
−0.918668 + 0.395032i \(0.870734\pi\)
\(854\) 1.26067 0.0431393
\(855\) 0.0174080 0.000595342 0
\(856\) −13.2739 −0.453691
\(857\) −14.4224 −0.492660 −0.246330 0.969186i \(-0.579225\pi\)
−0.246330 + 0.969186i \(0.579225\pi\)
\(858\) 4.64149 0.158458
\(859\) −13.3074 −0.454043 −0.227021 0.973890i \(-0.572899\pi\)
−0.227021 + 0.973890i \(0.572899\pi\)
\(860\) −0.572730 −0.0195299
\(861\) −3.97851 −0.135587
\(862\) 5.65572 0.192634
\(863\) 18.4520 0.628113 0.314056 0.949404i \(-0.398312\pi\)
0.314056 + 0.949404i \(0.398312\pi\)
\(864\) −5.18192 −0.176293
\(865\) 0.235353 0.00800224
\(866\) 6.59448 0.224089
\(867\) 1.00000 0.0339618
\(868\) 36.0934 1.22509
\(869\) 2.65279 0.0899897
\(870\) −0.0407040 −0.00138000
\(871\) 2.28599 0.0774580
\(872\) 11.3438 0.384151
\(873\) −13.7697 −0.466034
\(874\) 0.722378 0.0244348
\(875\) 1.40182 0.0473903
\(876\) 11.0851 0.374530
\(877\) −16.1852 −0.546536 −0.273268 0.961938i \(-0.588105\pi\)
−0.273268 + 0.961938i \(0.588105\pi\)
\(878\) −0.355973 −0.0120135
\(879\) −20.0852 −0.677458
\(880\) 0.444145 0.0149721
\(881\) 1.87050 0.0630187 0.0315093 0.999503i \(-0.489969\pi\)
0.0315093 + 0.999503i \(0.489969\pi\)
\(882\) −7.10311 −0.239174
\(883\) 25.7461 0.866426 0.433213 0.901291i \(-0.357380\pi\)
0.433213 + 0.901291i \(0.357380\pi\)
\(884\) −2.57318 −0.0865453
\(885\) 0.304196 0.0102254
\(886\) −2.02986 −0.0681946
\(887\) −9.15777 −0.307488 −0.153744 0.988111i \(-0.549133\pi\)
−0.153744 + 0.988111i \(0.549133\pi\)
\(888\) 12.8484 0.431164
\(889\) 35.8106 1.20105
\(890\) −0.139868 −0.00468838
\(891\) −5.92549 −0.198511
\(892\) 9.29176 0.311111
\(893\) 4.43200 0.148311
\(894\) 8.34374 0.279056
\(895\) −0.255416 −0.00853762
\(896\) 52.0143 1.73768
\(897\) 3.64967 0.121859
\(898\) 21.1410 0.705486
\(899\) 11.5764 0.386093
\(900\) 8.62053 0.287351
\(901\) 0.351352 0.0117052
\(902\) −2.73117 −0.0909380
\(903\) −48.6388 −1.61860
\(904\) −12.5289 −0.416705
\(905\) 0.397758 0.0132219
\(906\) −6.24824 −0.207584
\(907\) 30.9045 1.02617 0.513083 0.858339i \(-0.328503\pi\)
0.513083 + 0.858339i \(0.328503\pi\)
\(908\) −27.4154 −0.909813
\(909\) −8.08193 −0.268061
\(910\) 0.109817 0.00364039
\(911\) −34.3041 −1.13655 −0.568274 0.822840i \(-0.692388\pi\)
−0.568274 + 0.822840i \(0.692388\pi\)
\(912\) −1.36300 −0.0451334
\(913\) −24.6230 −0.814904
\(914\) −0.153959 −0.00509252
\(915\) 0.0163987 0.000542126 0
\(916\) −27.0314 −0.893144
\(917\) −2.05780 −0.0679546
\(918\) −0.524942 −0.0173257
\(919\) 11.9896 0.395502 0.197751 0.980252i \(-0.436636\pi\)
0.197751 + 0.980252i \(0.436636\pi\)
\(920\) −0.147955 −0.00487794
\(921\) 19.0510 0.627750
\(922\) 2.02973 0.0668456
\(923\) 2.29372 0.0754988
\(924\) 46.2998 1.52315
\(925\) −32.8522 −1.08017
\(926\) −1.80803 −0.0594155
\(927\) 9.81552 0.322384
\(928\) 12.9864 0.426301
\(929\) 0.926931 0.0304116 0.0152058 0.999884i \(-0.495160\pi\)
0.0152058 + 0.999884i \(0.495160\pi\)
\(930\) −0.0750260 −0.00246020
\(931\) −7.61306 −0.249508
\(932\) 29.5964 0.969461
\(933\) −0.143909 −0.00471137
\(934\) 14.7832 0.483721
\(935\) 0.183338 0.00599578
\(936\) 2.91739 0.0953578
\(937\) 27.0705 0.884355 0.442177 0.896928i \(-0.354206\pi\)
0.442177 + 0.896928i \(0.354206\pi\)
\(938\) −3.64394 −0.118979
\(939\) −28.3493 −0.925143
\(940\) −0.420293 −0.0137085
\(941\) −51.3099 −1.67266 −0.836328 0.548230i \(-0.815302\pi\)
−0.836328 + 0.548230i \(0.815302\pi\)
\(942\) 0.524942 0.0171035
\(943\) −2.14756 −0.0699341
\(944\) −23.8177 −0.775200
\(945\) −0.140196 −0.00456057
\(946\) −33.3895 −1.08559
\(947\) −35.4696 −1.15261 −0.576303 0.817236i \(-0.695505\pi\)
−0.576303 + 0.817236i \(0.695505\pi\)
\(948\) 0.772015 0.0250739
\(949\) −9.59209 −0.311373
\(950\) −1.47645 −0.0479025
\(951\) −9.16101 −0.297066
\(952\) 8.85889 0.287118
\(953\) −2.18539 −0.0707916 −0.0353958 0.999373i \(-0.511269\pi\)
−0.0353958 + 0.999373i \(0.511269\pi\)
\(954\) −0.184440 −0.00597145
\(955\) 0.571238 0.0184848
\(956\) 20.2716 0.655629
\(957\) 14.8499 0.480029
\(958\) 11.1367 0.359809
\(959\) 44.8650 1.44877
\(960\) 0.0657454 0.00212192
\(961\) −9.66235 −0.311689
\(962\) −5.14768 −0.165968
\(963\) −6.78931 −0.218782
\(964\) −48.1057 −1.54938
\(965\) 0.578047 0.0186080
\(966\) −5.81768 −0.187181
\(967\) 51.2189 1.64709 0.823544 0.567253i \(-0.191994\pi\)
0.823544 + 0.567253i \(0.191994\pi\)
\(968\) 47.1405 1.51515
\(969\) −0.562629 −0.0180742
\(970\) −0.223647 −0.00718087
\(971\) 58.8245 1.88777 0.943884 0.330277i \(-0.107142\pi\)
0.943884 + 0.330277i \(0.107142\pi\)
\(972\) −1.72444 −0.0553113
\(973\) 51.3558 1.64639
\(974\) 2.23410 0.0715853
\(975\) −7.45949 −0.238895
\(976\) −1.28397 −0.0410990
\(977\) −50.9504 −1.63005 −0.815025 0.579426i \(-0.803277\pi\)
−0.815025 + 0.579426i \(0.803277\pi\)
\(978\) 0.433214 0.0138526
\(979\) 51.0274 1.63084
\(980\) 0.721958 0.0230621
\(981\) 5.80214 0.185248
\(982\) 3.55383 0.113407
\(983\) 16.1742 0.515877 0.257938 0.966161i \(-0.416957\pi\)
0.257938 + 0.966161i \(0.416957\pi\)
\(984\) −1.71666 −0.0547252
\(985\) −0.445780 −0.0142037
\(986\) 1.31556 0.0418959
\(987\) −35.6932 −1.13613
\(988\) 1.44774 0.0460589
\(989\) −26.2547 −0.834850
\(990\) −0.0962416 −0.00305876
\(991\) 34.6195 1.09973 0.549863 0.835255i \(-0.314680\pi\)
0.549863 + 0.835255i \(0.314680\pi\)
\(992\) 23.9367 0.759991
\(993\) 21.5231 0.683014
\(994\) −3.65626 −0.115970
\(995\) −0.143544 −0.00455064
\(996\) −7.16580 −0.227057
\(997\) 35.7180 1.13120 0.565600 0.824680i \(-0.308645\pi\)
0.565600 + 0.824680i \(0.308645\pi\)
\(998\) −0.212816 −0.00673658
\(999\) 6.57170 0.207919
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 8007.2.a.d.1.18 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
8007.2.a.d.1.18 40 1.1 even 1 trivial