Properties

Label 2671.2.a.b.1.39
Level $2671$
Weight $2$
Character 2671.1
Self dual yes
Analytic conductor $21.328$
Analytic rank $0$
Dimension $122$
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] = [2671,2,Mod(1,2671)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2671, 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("2671.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2671 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2671.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: \(21.3280423799\)
Analytic rank: \(0\)
Dimension: \(122\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.39
Character \(\chi\) \(=\) 2671.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.01100 q^{2} -0.165355 q^{3} -0.977888 q^{4} -2.31604 q^{5} +0.167173 q^{6} -1.01194 q^{7} +3.01063 q^{8} -2.97266 q^{9} +O(q^{10})\) \(q-1.01100 q^{2} -0.165355 q^{3} -0.977888 q^{4} -2.31604 q^{5} +0.167173 q^{6} -1.01194 q^{7} +3.01063 q^{8} -2.97266 q^{9} +2.34151 q^{10} -0.218595 q^{11} +0.161698 q^{12} +0.505652 q^{13} +1.02307 q^{14} +0.382968 q^{15} -1.08796 q^{16} -5.73669 q^{17} +3.00534 q^{18} -7.05039 q^{19} +2.26483 q^{20} +0.167330 q^{21} +0.220999 q^{22} +0.146062 q^{23} -0.497822 q^{24} +0.364049 q^{25} -0.511212 q^{26} +0.987607 q^{27} +0.989568 q^{28} -6.06175 q^{29} -0.387179 q^{30} +7.28560 q^{31} -4.92134 q^{32} +0.0361457 q^{33} +5.79977 q^{34} +2.34370 q^{35} +2.90693 q^{36} -6.84193 q^{37} +7.12791 q^{38} -0.0836119 q^{39} -6.97275 q^{40} -4.17529 q^{41} -0.169170 q^{42} -1.89201 q^{43} +0.213762 q^{44} +6.88480 q^{45} -0.147668 q^{46} +8.78285 q^{47} +0.179899 q^{48} -5.97597 q^{49} -0.368052 q^{50} +0.948588 q^{51} -0.494471 q^{52} +2.46364 q^{53} -0.998466 q^{54} +0.506276 q^{55} -3.04659 q^{56} +1.16581 q^{57} +6.12841 q^{58} -13.6770 q^{59} -0.374500 q^{60} -2.55026 q^{61} -7.36571 q^{62} +3.00816 q^{63} +7.15137 q^{64} -1.17111 q^{65} -0.0365432 q^{66} -12.7317 q^{67} +5.60984 q^{68} -0.0241521 q^{69} -2.36948 q^{70} +9.24961 q^{71} -8.94958 q^{72} -13.7175 q^{73} +6.91717 q^{74} -0.0601972 q^{75} +6.89449 q^{76} +0.221206 q^{77} +0.0845313 q^{78} -4.72867 q^{79} +2.51976 q^{80} +8.75467 q^{81} +4.22120 q^{82} +2.10913 q^{83} -0.163630 q^{84} +13.2864 q^{85} +1.91281 q^{86} +1.00234 q^{87} -0.658110 q^{88} +3.30801 q^{89} -6.96050 q^{90} -0.511692 q^{91} -0.142833 q^{92} -1.20471 q^{93} -8.87942 q^{94} +16.3290 q^{95} +0.813766 q^{96} -9.74610 q^{97} +6.04168 q^{98} +0.649809 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.01100 −0.714882 −0.357441 0.933936i \(-0.616351\pi\)
−0.357441 + 0.933936i \(0.616351\pi\)
\(3\) −0.165355 −0.0954675 −0.0477338 0.998860i \(-0.515200\pi\)
−0.0477338 + 0.998860i \(0.515200\pi\)
\(4\) −0.977888 −0.488944
\(5\) −2.31604 −1.03577 −0.517883 0.855452i \(-0.673280\pi\)
−0.517883 + 0.855452i \(0.673280\pi\)
\(6\) 0.167173 0.0682480
\(7\) −1.01194 −0.382479 −0.191239 0.981543i \(-0.561251\pi\)
−0.191239 + 0.981543i \(0.561251\pi\)
\(8\) 3.01063 1.06442
\(9\) −2.97266 −0.990886
\(10\) 2.34151 0.740450
\(11\) −0.218595 −0.0659089 −0.0329545 0.999457i \(-0.510492\pi\)
−0.0329545 + 0.999457i \(0.510492\pi\)
\(12\) 0.161698 0.0466783
\(13\) 0.505652 0.140243 0.0701213 0.997538i \(-0.477661\pi\)
0.0701213 + 0.997538i \(0.477661\pi\)
\(14\) 1.02307 0.273427
\(15\) 0.382968 0.0988820
\(16\) −1.08796 −0.271990
\(17\) −5.73669 −1.39135 −0.695675 0.718356i \(-0.744895\pi\)
−0.695675 + 0.718356i \(0.744895\pi\)
\(18\) 3.00534 0.708366
\(19\) −7.05039 −1.61747 −0.808735 0.588173i \(-0.799847\pi\)
−0.808735 + 0.588173i \(0.799847\pi\)
\(20\) 2.26483 0.506431
\(21\) 0.167330 0.0365143
\(22\) 0.220999 0.0471171
\(23\) 0.146062 0.0304561 0.0152281 0.999884i \(-0.495153\pi\)
0.0152281 + 0.999884i \(0.495153\pi\)
\(24\) −0.497822 −0.101617
\(25\) 0.364049 0.0728098
\(26\) −0.511212 −0.100257
\(27\) 0.987607 0.190065
\(28\) 0.989568 0.187011
\(29\) −6.06175 −1.12564 −0.562820 0.826580i \(-0.690283\pi\)
−0.562820 + 0.826580i \(0.690283\pi\)
\(30\) −0.387179 −0.0706889
\(31\) 7.28560 1.30853 0.654266 0.756264i \(-0.272978\pi\)
0.654266 + 0.756264i \(0.272978\pi\)
\(32\) −4.92134 −0.869978
\(33\) 0.0361457 0.00629216
\(34\) 5.79977 0.994652
\(35\) 2.34370 0.396158
\(36\) 2.90693 0.484488
\(37\) −6.84193 −1.12481 −0.562404 0.826863i \(-0.690123\pi\)
−0.562404 + 0.826863i \(0.690123\pi\)
\(38\) 7.12791 1.15630
\(39\) −0.0836119 −0.0133886
\(40\) −6.97275 −1.10249
\(41\) −4.17529 −0.652071 −0.326035 0.945358i \(-0.605713\pi\)
−0.326035 + 0.945358i \(0.605713\pi\)
\(42\) −0.169170 −0.0261034
\(43\) −1.89201 −0.288528 −0.144264 0.989539i \(-0.546081\pi\)
−0.144264 + 0.989539i \(0.546081\pi\)
\(44\) 0.213762 0.0322258
\(45\) 6.88480 1.02633
\(46\) −0.147668 −0.0217725
\(47\) 8.78285 1.28111 0.640555 0.767912i \(-0.278704\pi\)
0.640555 + 0.767912i \(0.278704\pi\)
\(48\) 0.179899 0.0259662
\(49\) −5.97597 −0.853710
\(50\) −0.368052 −0.0520504
\(51\) 0.948588 0.132829
\(52\) −0.494471 −0.0685708
\(53\) 2.46364 0.338406 0.169203 0.985581i \(-0.445881\pi\)
0.169203 + 0.985581i \(0.445881\pi\)
\(54\) −0.998466 −0.135874
\(55\) 0.506276 0.0682662
\(56\) −3.04659 −0.407118
\(57\) 1.16581 0.154416
\(58\) 6.12841 0.804699
\(59\) −13.6770 −1.78059 −0.890296 0.455383i \(-0.849502\pi\)
−0.890296 + 0.455383i \(0.849502\pi\)
\(60\) −0.374500 −0.0483477
\(61\) −2.55026 −0.326528 −0.163264 0.986582i \(-0.552202\pi\)
−0.163264 + 0.986582i \(0.552202\pi\)
\(62\) −7.36571 −0.935446
\(63\) 3.00816 0.378993
\(64\) 7.15137 0.893922
\(65\) −1.17111 −0.145258
\(66\) −0.0365432 −0.00449815
\(67\) −12.7317 −1.55543 −0.777714 0.628619i \(-0.783621\pi\)
−0.777714 + 0.628619i \(0.783621\pi\)
\(68\) 5.60984 0.680293
\(69\) −0.0241521 −0.00290757
\(70\) −2.36948 −0.283206
\(71\) 9.24961 1.09773 0.548863 0.835912i \(-0.315061\pi\)
0.548863 + 0.835912i \(0.315061\pi\)
\(72\) −8.94958 −1.05472
\(73\) −13.7175 −1.60551 −0.802757 0.596307i \(-0.796634\pi\)
−0.802757 + 0.596307i \(0.796634\pi\)
\(74\) 6.91717 0.804104
\(75\) −0.0601972 −0.00695097
\(76\) 6.89449 0.790852
\(77\) 0.221206 0.0252088
\(78\) 0.0845313 0.00957128
\(79\) −4.72867 −0.532017 −0.266008 0.963971i \(-0.585705\pi\)
−0.266008 + 0.963971i \(0.585705\pi\)
\(80\) 2.51976 0.281718
\(81\) 8.75467 0.972741
\(82\) 4.22120 0.466153
\(83\) 2.10913 0.231507 0.115754 0.993278i \(-0.463072\pi\)
0.115754 + 0.993278i \(0.463072\pi\)
\(84\) −0.163630 −0.0178535
\(85\) 13.2864 1.44111
\(86\) 1.91281 0.206264
\(87\) 1.00234 0.107462
\(88\) −0.658110 −0.0701547
\(89\) 3.30801 0.350648 0.175324 0.984511i \(-0.443903\pi\)
0.175324 + 0.984511i \(0.443903\pi\)
\(90\) −6.96050 −0.733701
\(91\) −0.511692 −0.0536398
\(92\) −0.142833 −0.0148913
\(93\) −1.20471 −0.124922
\(94\) −8.87942 −0.915842
\(95\) 16.3290 1.67532
\(96\) 0.813766 0.0830547
\(97\) −9.74610 −0.989567 −0.494783 0.869016i \(-0.664753\pi\)
−0.494783 + 0.869016i \(0.664753\pi\)
\(98\) 6.04168 0.610302
\(99\) 0.649809 0.0653082
\(100\) −0.355999 −0.0355999
\(101\) 1.32007 0.131352 0.0656758 0.997841i \(-0.479080\pi\)
0.0656758 + 0.997841i \(0.479080\pi\)
\(102\) −0.959018 −0.0949569
\(103\) 17.8613 1.75993 0.879964 0.475040i \(-0.157566\pi\)
0.879964 + 0.475040i \(0.157566\pi\)
\(104\) 1.52233 0.149277
\(105\) −0.387542 −0.0378203
\(106\) −2.49073 −0.241921
\(107\) −0.378696 −0.0366099 −0.0183050 0.999832i \(-0.505827\pi\)
−0.0183050 + 0.999832i \(0.505827\pi\)
\(108\) −0.965768 −0.0929311
\(109\) 6.23618 0.597317 0.298659 0.954360i \(-0.403461\pi\)
0.298659 + 0.954360i \(0.403461\pi\)
\(110\) −0.511842 −0.0488023
\(111\) 1.13135 0.107383
\(112\) 1.10095 0.104030
\(113\) −0.527570 −0.0496296 −0.0248148 0.999692i \(-0.507900\pi\)
−0.0248148 + 0.999692i \(0.507900\pi\)
\(114\) −1.17863 −0.110389
\(115\) −0.338287 −0.0315454
\(116\) 5.92771 0.550375
\(117\) −1.50313 −0.138964
\(118\) 13.8274 1.27291
\(119\) 5.80521 0.532162
\(120\) 1.15298 0.105252
\(121\) −10.9522 −0.995656
\(122\) 2.57831 0.233429
\(123\) 0.690403 0.0622516
\(124\) −7.12450 −0.639799
\(125\) 10.7371 0.960351
\(126\) −3.04124 −0.270935
\(127\) 18.9217 1.67903 0.839513 0.543340i \(-0.182841\pi\)
0.839513 + 0.543340i \(0.182841\pi\)
\(128\) 2.61267 0.230930
\(129\) 0.312852 0.0275451
\(130\) 1.18399 0.103843
\(131\) −18.1298 −1.58401 −0.792003 0.610517i \(-0.790962\pi\)
−0.792003 + 0.610517i \(0.790962\pi\)
\(132\) −0.0353465 −0.00307651
\(133\) 7.13460 0.618648
\(134\) 12.8717 1.11195
\(135\) −2.28734 −0.196863
\(136\) −17.2711 −1.48098
\(137\) 4.08860 0.349313 0.174656 0.984629i \(-0.444119\pi\)
0.174656 + 0.984629i \(0.444119\pi\)
\(138\) 0.0244177 0.00207857
\(139\) 17.9300 1.52080 0.760402 0.649453i \(-0.225002\pi\)
0.760402 + 0.649453i \(0.225002\pi\)
\(140\) −2.29188 −0.193699
\(141\) −1.45228 −0.122304
\(142\) −9.35131 −0.784745
\(143\) −0.110533 −0.00924324
\(144\) 3.23413 0.269511
\(145\) 14.0393 1.16590
\(146\) 13.8683 1.14775
\(147\) 0.988154 0.0815016
\(148\) 6.69064 0.549968
\(149\) −0.219919 −0.0180164 −0.00900821 0.999959i \(-0.502867\pi\)
−0.00900821 + 0.999959i \(0.502867\pi\)
\(150\) 0.0608591 0.00496912
\(151\) 6.00917 0.489019 0.244510 0.969647i \(-0.421373\pi\)
0.244510 + 0.969647i \(0.421373\pi\)
\(152\) −21.2261 −1.72167
\(153\) 17.0532 1.37867
\(154\) −0.223638 −0.0180213
\(155\) −16.8737 −1.35533
\(156\) 0.0817630 0.00654628
\(157\) 19.1751 1.53034 0.765171 0.643827i \(-0.222654\pi\)
0.765171 + 0.643827i \(0.222654\pi\)
\(158\) 4.78066 0.380329
\(159\) −0.407374 −0.0323068
\(160\) 11.3980 0.901093
\(161\) −0.147807 −0.0116488
\(162\) −8.85093 −0.695395
\(163\) 20.2337 1.58483 0.792413 0.609985i \(-0.208825\pi\)
0.792413 + 0.609985i \(0.208825\pi\)
\(164\) 4.08296 0.318826
\(165\) −0.0837150 −0.00651720
\(166\) −2.13232 −0.165500
\(167\) 6.88392 0.532694 0.266347 0.963877i \(-0.414183\pi\)
0.266347 + 0.963877i \(0.414183\pi\)
\(168\) 0.503768 0.0388665
\(169\) −12.7443 −0.980332
\(170\) −13.4325 −1.03023
\(171\) 20.9584 1.60273
\(172\) 1.85017 0.141074
\(173\) 9.99045 0.759560 0.379780 0.925077i \(-0.376000\pi\)
0.379780 + 0.925077i \(0.376000\pi\)
\(174\) −1.01336 −0.0768226
\(175\) −0.368397 −0.0278482
\(176\) 0.237823 0.0179266
\(177\) 2.26155 0.169989
\(178\) −3.34438 −0.250672
\(179\) −19.3231 −1.44428 −0.722139 0.691748i \(-0.756841\pi\)
−0.722139 + 0.691748i \(0.756841\pi\)
\(180\) −6.73256 −0.501816
\(181\) 6.13660 0.456130 0.228065 0.973646i \(-0.426760\pi\)
0.228065 + 0.973646i \(0.426760\pi\)
\(182\) 0.517318 0.0383462
\(183\) 0.421698 0.0311728
\(184\) 0.439740 0.0324181
\(185\) 15.8462 1.16504
\(186\) 1.21795 0.0893047
\(187\) 1.25401 0.0917024
\(188\) −8.58864 −0.626391
\(189\) −0.999403 −0.0726959
\(190\) −16.5085 −1.19766
\(191\) 16.5464 1.19725 0.598627 0.801028i \(-0.295713\pi\)
0.598627 + 0.801028i \(0.295713\pi\)
\(192\) −1.18251 −0.0853405
\(193\) −6.28569 −0.452454 −0.226227 0.974075i \(-0.572639\pi\)
−0.226227 + 0.974075i \(0.572639\pi\)
\(194\) 9.85327 0.707423
\(195\) 0.193649 0.0138675
\(196\) 5.84383 0.417416
\(197\) −11.6303 −0.828621 −0.414311 0.910136i \(-0.635977\pi\)
−0.414311 + 0.910136i \(0.635977\pi\)
\(198\) −0.656954 −0.0466877
\(199\) −12.9014 −0.914556 −0.457278 0.889324i \(-0.651176\pi\)
−0.457278 + 0.889324i \(0.651176\pi\)
\(200\) 1.09602 0.0775001
\(201\) 2.10525 0.148493
\(202\) −1.33458 −0.0939008
\(203\) 6.13416 0.430533
\(204\) −0.927612 −0.0649459
\(205\) 9.67014 0.675392
\(206\) −18.0577 −1.25814
\(207\) −0.434193 −0.0301785
\(208\) −0.550129 −0.0381446
\(209\) 1.54118 0.106606
\(210\) 0.391804 0.0270370
\(211\) −13.7094 −0.943797 −0.471898 0.881653i \(-0.656431\pi\)
−0.471898 + 0.881653i \(0.656431\pi\)
\(212\) −2.40916 −0.165462
\(213\) −1.52947 −0.104797
\(214\) 0.382860 0.0261718
\(215\) 4.38197 0.298848
\(216\) 2.97332 0.202309
\(217\) −7.37262 −0.500486
\(218\) −6.30475 −0.427011
\(219\) 2.26825 0.153274
\(220\) −0.495081 −0.0333783
\(221\) −2.90077 −0.195127
\(222\) −1.14379 −0.0767658
\(223\) −0.0515454 −0.00345174 −0.00172587 0.999999i \(-0.500549\pi\)
−0.00172587 + 0.999999i \(0.500549\pi\)
\(224\) 4.98012 0.332748
\(225\) −1.08219 −0.0721462
\(226\) 0.533371 0.0354793
\(227\) 17.4384 1.15743 0.578714 0.815530i \(-0.303555\pi\)
0.578714 + 0.815530i \(0.303555\pi\)
\(228\) −1.14004 −0.0755007
\(229\) −21.0706 −1.39238 −0.696192 0.717856i \(-0.745124\pi\)
−0.696192 + 0.717856i \(0.745124\pi\)
\(230\) 0.342006 0.0225512
\(231\) −0.0365775 −0.00240662
\(232\) −18.2497 −1.19815
\(233\) −0.718155 −0.0470479 −0.0235239 0.999723i \(-0.507489\pi\)
−0.0235239 + 0.999723i \(0.507489\pi\)
\(234\) 1.51966 0.0993432
\(235\) −20.3414 −1.32693
\(236\) 13.3746 0.870609
\(237\) 0.781907 0.0507903
\(238\) −5.86904 −0.380433
\(239\) 23.2198 1.50197 0.750984 0.660321i \(-0.229580\pi\)
0.750984 + 0.660321i \(0.229580\pi\)
\(240\) −0.416654 −0.0268949
\(241\) 19.1893 1.23609 0.618046 0.786142i \(-0.287925\pi\)
0.618046 + 0.786142i \(0.287925\pi\)
\(242\) 11.0726 0.711776
\(243\) −4.41044 −0.282930
\(244\) 2.49387 0.159654
\(245\) 13.8406 0.884243
\(246\) −0.697995 −0.0445025
\(247\) −3.56504 −0.226838
\(248\) 21.9343 1.39283
\(249\) −0.348754 −0.0221014
\(250\) −10.8551 −0.686538
\(251\) 19.3018 1.21832 0.609159 0.793048i \(-0.291507\pi\)
0.609159 + 0.793048i \(0.291507\pi\)
\(252\) −2.94165 −0.185306
\(253\) −0.0319285 −0.00200733
\(254\) −19.1297 −1.20030
\(255\) −2.19697 −0.137580
\(256\) −16.9441 −1.05901
\(257\) −2.01807 −0.125884 −0.0629418 0.998017i \(-0.520048\pi\)
−0.0629418 + 0.998017i \(0.520048\pi\)
\(258\) −0.316292 −0.0196915
\(259\) 6.92366 0.430215
\(260\) 1.14522 0.0710232
\(261\) 18.0195 1.11538
\(262\) 18.3291 1.13238
\(263\) −12.8064 −0.789677 −0.394838 0.918751i \(-0.629199\pi\)
−0.394838 + 0.918751i \(0.629199\pi\)
\(264\) 0.108821 0.00669750
\(265\) −5.70588 −0.350510
\(266\) −7.21305 −0.442260
\(267\) −0.546994 −0.0334755
\(268\) 12.4502 0.760517
\(269\) −25.0242 −1.52575 −0.762876 0.646544i \(-0.776214\pi\)
−0.762876 + 0.646544i \(0.776214\pi\)
\(270\) 2.31249 0.140734
\(271\) −16.7333 −1.01647 −0.508237 0.861217i \(-0.669703\pi\)
−0.508237 + 0.861217i \(0.669703\pi\)
\(272\) 6.24128 0.378433
\(273\) 0.0846106 0.00512086
\(274\) −4.13356 −0.249717
\(275\) −0.0795793 −0.00479881
\(276\) 0.0236180 0.00142164
\(277\) −18.9063 −1.13597 −0.567984 0.823040i \(-0.692276\pi\)
−0.567984 + 0.823040i \(0.692276\pi\)
\(278\) −18.1272 −1.08719
\(279\) −21.6576 −1.29661
\(280\) 7.05603 0.421679
\(281\) 31.9292 1.90474 0.952368 0.304950i \(-0.0986396\pi\)
0.952368 + 0.304950i \(0.0986396\pi\)
\(282\) 1.46825 0.0874332
\(283\) −12.5918 −0.748504 −0.374252 0.927327i \(-0.622101\pi\)
−0.374252 + 0.927327i \(0.622101\pi\)
\(284\) −9.04508 −0.536727
\(285\) −2.70007 −0.159939
\(286\) 0.111748 0.00660782
\(287\) 4.22516 0.249403
\(288\) 14.6295 0.862049
\(289\) 15.9096 0.935858
\(290\) −14.1936 −0.833479
\(291\) 1.61156 0.0944715
\(292\) 13.4142 0.785006
\(293\) 9.60465 0.561110 0.280555 0.959838i \(-0.409482\pi\)
0.280555 + 0.959838i \(0.409482\pi\)
\(294\) −0.999020 −0.0582640
\(295\) 31.6765 1.84427
\(296\) −20.5985 −1.19727
\(297\) −0.215886 −0.0125270
\(298\) 0.222337 0.0128796
\(299\) 0.0738567 0.00427124
\(300\) 0.0588661 0.00339863
\(301\) 1.91461 0.110356
\(302\) −6.07524 −0.349591
\(303\) −0.218279 −0.0125398
\(304\) 7.67054 0.439936
\(305\) 5.90652 0.338206
\(306\) −17.2407 −0.985586
\(307\) −0.309692 −0.0176751 −0.00883753 0.999961i \(-0.502813\pi\)
−0.00883753 + 0.999961i \(0.502813\pi\)
\(308\) −0.216315 −0.0123257
\(309\) −2.95345 −0.168016
\(310\) 17.0593 0.968902
\(311\) −26.7336 −1.51592 −0.757962 0.652299i \(-0.773805\pi\)
−0.757962 + 0.652299i \(0.773805\pi\)
\(312\) −0.251725 −0.0142511
\(313\) −24.9391 −1.40964 −0.704821 0.709385i \(-0.748973\pi\)
−0.704821 + 0.709385i \(0.748973\pi\)
\(314\) −19.3860 −1.09401
\(315\) −6.96703 −0.392548
\(316\) 4.62411 0.260126
\(317\) 30.1627 1.69411 0.847054 0.531507i \(-0.178374\pi\)
0.847054 + 0.531507i \(0.178374\pi\)
\(318\) 0.411853 0.0230956
\(319\) 1.32507 0.0741897
\(320\) −16.5629 −0.925893
\(321\) 0.0626191 0.00349506
\(322\) 0.149432 0.00832753
\(323\) 40.4459 2.25047
\(324\) −8.56108 −0.475616
\(325\) 0.184082 0.0102110
\(326\) −20.4562 −1.13296
\(327\) −1.03118 −0.0570244
\(328\) −12.5703 −0.694076
\(329\) −8.88775 −0.489998
\(330\) 0.0846355 0.00465903
\(331\) −13.1988 −0.725470 −0.362735 0.931892i \(-0.618157\pi\)
−0.362735 + 0.931892i \(0.618157\pi\)
\(332\) −2.06249 −0.113194
\(333\) 20.3387 1.11456
\(334\) −6.95962 −0.380813
\(335\) 29.4872 1.61106
\(336\) −0.182048 −0.00993153
\(337\) 14.5417 0.792138 0.396069 0.918221i \(-0.370374\pi\)
0.396069 + 0.918221i \(0.370374\pi\)
\(338\) 12.8844 0.700822
\(339\) 0.0872362 0.00473802
\(340\) −12.9926 −0.704623
\(341\) −1.59260 −0.0862439
\(342\) −21.1888 −1.14576
\(343\) 13.1310 0.709005
\(344\) −5.69613 −0.307115
\(345\) 0.0559372 0.00301156
\(346\) −10.1003 −0.542996
\(347\) 8.12988 0.436435 0.218217 0.975900i \(-0.429976\pi\)
0.218217 + 0.975900i \(0.429976\pi\)
\(348\) −0.980175 −0.0525429
\(349\) −2.82897 −0.151431 −0.0757157 0.997129i \(-0.524124\pi\)
−0.0757157 + 0.997129i \(0.524124\pi\)
\(350\) 0.372448 0.0199082
\(351\) 0.499385 0.0266552
\(352\) 1.07578 0.0573393
\(353\) −11.0300 −0.587069 −0.293535 0.955948i \(-0.594832\pi\)
−0.293535 + 0.955948i \(0.594832\pi\)
\(354\) −2.28642 −0.121522
\(355\) −21.4225 −1.13699
\(356\) −3.23486 −0.171447
\(357\) −0.959918 −0.0508042
\(358\) 19.5356 1.03249
\(359\) 4.24418 0.223999 0.112000 0.993708i \(-0.464274\pi\)
0.112000 + 0.993708i \(0.464274\pi\)
\(360\) 20.7276 1.09244
\(361\) 30.7080 1.61621
\(362\) −6.20408 −0.326079
\(363\) 1.81100 0.0950528
\(364\) 0.500377 0.0262269
\(365\) 31.7703 1.66294
\(366\) −0.426335 −0.0222849
\(367\) −11.3734 −0.593686 −0.296843 0.954926i \(-0.595934\pi\)
−0.296843 + 0.954926i \(0.595934\pi\)
\(368\) −0.158910 −0.00828376
\(369\) 12.4117 0.646128
\(370\) −16.0204 −0.832863
\(371\) −2.49306 −0.129433
\(372\) 1.17807 0.0610800
\(373\) −24.4613 −1.26656 −0.633278 0.773924i \(-0.718291\pi\)
−0.633278 + 0.773924i \(0.718291\pi\)
\(374\) −1.26780 −0.0655564
\(375\) −1.77542 −0.0916824
\(376\) 26.4419 1.36364
\(377\) −3.06514 −0.157863
\(378\) 1.01039 0.0519690
\(379\) −17.4839 −0.898085 −0.449043 0.893510i \(-0.648235\pi\)
−0.449043 + 0.893510i \(0.648235\pi\)
\(380\) −15.9679 −0.819137
\(381\) −3.12878 −0.160292
\(382\) −16.7283 −0.855894
\(383\) −32.2317 −1.64697 −0.823483 0.567342i \(-0.807972\pi\)
−0.823483 + 0.567342i \(0.807972\pi\)
\(384\) −0.432018 −0.0220463
\(385\) −0.512323 −0.0261104
\(386\) 6.35480 0.323451
\(387\) 5.62429 0.285899
\(388\) 9.53059 0.483843
\(389\) 9.76934 0.495325 0.247663 0.968846i \(-0.420338\pi\)
0.247663 + 0.968846i \(0.420338\pi\)
\(390\) −0.195778 −0.00991360
\(391\) −0.837914 −0.0423751
\(392\) −17.9914 −0.908705
\(393\) 2.99784 0.151221
\(394\) 11.7581 0.592366
\(395\) 10.9518 0.551045
\(396\) −0.635440 −0.0319321
\(397\) −29.0332 −1.45714 −0.728568 0.684974i \(-0.759814\pi\)
−0.728568 + 0.684974i \(0.759814\pi\)
\(398\) 13.0433 0.653800
\(399\) −1.17974 −0.0590608
\(400\) −0.396071 −0.0198035
\(401\) 28.8923 1.44281 0.721407 0.692511i \(-0.243496\pi\)
0.721407 + 0.692511i \(0.243496\pi\)
\(402\) −2.12840 −0.106155
\(403\) 3.68398 0.183512
\(404\) −1.29088 −0.0642235
\(405\) −20.2762 −1.00753
\(406\) −6.20161 −0.307781
\(407\) 1.49561 0.0741348
\(408\) 2.85585 0.141386
\(409\) 35.7645 1.76844 0.884219 0.467072i \(-0.154691\pi\)
0.884219 + 0.467072i \(0.154691\pi\)
\(410\) −9.77647 −0.482826
\(411\) −0.676069 −0.0333480
\(412\) −17.4664 −0.860507
\(413\) 13.8403 0.681039
\(414\) 0.438968 0.0215741
\(415\) −4.88483 −0.239787
\(416\) −2.48849 −0.122008
\(417\) −2.96481 −0.145187
\(418\) −1.55813 −0.0762105
\(419\) 35.0002 1.70987 0.854936 0.518734i \(-0.173596\pi\)
0.854936 + 0.518734i \(0.173596\pi\)
\(420\) 0.378973 0.0184920
\(421\) −35.1477 −1.71300 −0.856498 0.516151i \(-0.827364\pi\)
−0.856498 + 0.516151i \(0.827364\pi\)
\(422\) 13.8602 0.674703
\(423\) −26.1084 −1.26943
\(424\) 7.41710 0.360206
\(425\) −2.08843 −0.101304
\(426\) 1.54628 0.0749177
\(427\) 2.58073 0.124890
\(428\) 0.370322 0.0179002
\(429\) 0.0182772 0.000882429 0
\(430\) −4.43015 −0.213641
\(431\) −2.20728 −0.106321 −0.0531604 0.998586i \(-0.516929\pi\)
−0.0531604 + 0.998586i \(0.516929\pi\)
\(432\) −1.07448 −0.0516958
\(433\) −21.5181 −1.03409 −0.517047 0.855957i \(-0.672969\pi\)
−0.517047 + 0.855957i \(0.672969\pi\)
\(434\) 7.45369 0.357788
\(435\) −2.32146 −0.111305
\(436\) −6.09828 −0.292055
\(437\) −1.02980 −0.0492618
\(438\) −2.29320 −0.109573
\(439\) 15.8230 0.755188 0.377594 0.925971i \(-0.376751\pi\)
0.377594 + 0.925971i \(0.376751\pi\)
\(440\) 1.52421 0.0726638
\(441\) 17.7645 0.845929
\(442\) 2.93266 0.139493
\(443\) −22.0597 −1.04809 −0.524044 0.851691i \(-0.675577\pi\)
−0.524044 + 0.851691i \(0.675577\pi\)
\(444\) −1.10633 −0.0525040
\(445\) −7.66148 −0.363189
\(446\) 0.0521122 0.00246758
\(447\) 0.0363645 0.00171998
\(448\) −7.23679 −0.341906
\(449\) −9.46744 −0.446796 −0.223398 0.974727i \(-0.571715\pi\)
−0.223398 + 0.974727i \(0.571715\pi\)
\(450\) 1.09409 0.0515760
\(451\) 0.912698 0.0429773
\(452\) 0.515905 0.0242661
\(453\) −0.993644 −0.0466855
\(454\) −17.6302 −0.827425
\(455\) 1.18510 0.0555583
\(456\) 3.50984 0.164363
\(457\) −21.9256 −1.02564 −0.512819 0.858497i \(-0.671399\pi\)
−0.512819 + 0.858497i \(0.671399\pi\)
\(458\) 21.3023 0.995390
\(459\) −5.66559 −0.264447
\(460\) 0.330806 0.0154239
\(461\) 12.4927 0.581841 0.290921 0.956747i \(-0.406038\pi\)
0.290921 + 0.956747i \(0.406038\pi\)
\(462\) 0.0369797 0.00172045
\(463\) −1.81679 −0.0844333 −0.0422166 0.999108i \(-0.513442\pi\)
−0.0422166 + 0.999108i \(0.513442\pi\)
\(464\) 6.59494 0.306163
\(465\) 2.79015 0.129390
\(466\) 0.726051 0.0336337
\(467\) −6.90171 −0.319373 −0.159687 0.987168i \(-0.551048\pi\)
−0.159687 + 0.987168i \(0.551048\pi\)
\(468\) 1.46989 0.0679458
\(469\) 12.8838 0.594918
\(470\) 20.5651 0.948598
\(471\) −3.17070 −0.146098
\(472\) −41.1764 −1.89530
\(473\) 0.413584 0.0190166
\(474\) −0.790505 −0.0363091
\(475\) −2.56669 −0.117768
\(476\) −5.67684 −0.260198
\(477\) −7.32355 −0.335322
\(478\) −23.4752 −1.07373
\(479\) −27.0104 −1.23414 −0.617068 0.786910i \(-0.711680\pi\)
−0.617068 + 0.786910i \(0.711680\pi\)
\(480\) −1.88472 −0.0860252
\(481\) −3.45964 −0.157746
\(482\) −19.4003 −0.883660
\(483\) 0.0244406 0.00111208
\(484\) 10.7100 0.486820
\(485\) 22.5724 1.02496
\(486\) 4.45894 0.202262
\(487\) −8.59437 −0.389448 −0.194724 0.980858i \(-0.562381\pi\)
−0.194724 + 0.980858i \(0.562381\pi\)
\(488\) −7.67791 −0.347563
\(489\) −3.34574 −0.151299
\(490\) −13.9928 −0.632129
\(491\) 11.5260 0.520161 0.260080 0.965587i \(-0.416251\pi\)
0.260080 + 0.965587i \(0.416251\pi\)
\(492\) −0.675137 −0.0304375
\(493\) 34.7744 1.56616
\(494\) 3.60424 0.162163
\(495\) −1.50498 −0.0676440
\(496\) −7.92644 −0.355908
\(497\) −9.36009 −0.419857
\(498\) 0.352589 0.0157999
\(499\) −3.95509 −0.177054 −0.0885270 0.996074i \(-0.528216\pi\)
−0.0885270 + 0.996074i \(0.528216\pi\)
\(500\) −10.4996 −0.469558
\(501\) −1.13829 −0.0508550
\(502\) −19.5140 −0.870954
\(503\) 26.3194 1.17352 0.586761 0.809760i \(-0.300403\pi\)
0.586761 + 0.809760i \(0.300403\pi\)
\(504\) 9.05647 0.403407
\(505\) −3.05733 −0.136049
\(506\) 0.0322796 0.00143500
\(507\) 2.10733 0.0935899
\(508\) −18.5033 −0.820949
\(509\) −4.11736 −0.182499 −0.0912493 0.995828i \(-0.529086\pi\)
−0.0912493 + 0.995828i \(0.529086\pi\)
\(510\) 2.22113 0.0983531
\(511\) 13.8814 0.614075
\(512\) 11.9051 0.526137
\(513\) −6.96301 −0.307424
\(514\) 2.04026 0.0899920
\(515\) −41.3676 −1.82287
\(516\) −0.305934 −0.0134680
\(517\) −1.91989 −0.0844366
\(518\) −6.99979 −0.307553
\(519\) −1.65197 −0.0725133
\(520\) −3.52578 −0.154616
\(521\) −9.91059 −0.434191 −0.217095 0.976150i \(-0.569658\pi\)
−0.217095 + 0.976150i \(0.569658\pi\)
\(522\) −18.2177 −0.797365
\(523\) −6.25084 −0.273330 −0.136665 0.990617i \(-0.543638\pi\)
−0.136665 + 0.990617i \(0.543638\pi\)
\(524\) 17.7289 0.774491
\(525\) 0.0609162 0.00265860
\(526\) 12.9472 0.564525
\(527\) −41.7952 −1.82063
\(528\) −0.0393251 −0.00171141
\(529\) −22.9787 −0.999072
\(530\) 5.76862 0.250573
\(531\) 40.6570 1.76436
\(532\) −6.97684 −0.302484
\(533\) −2.11124 −0.0914481
\(534\) 0.553009 0.0239310
\(535\) 0.877076 0.0379193
\(536\) −38.3305 −1.65563
\(537\) 3.19517 0.137882
\(538\) 25.2994 1.09073
\(539\) 1.30632 0.0562671
\(540\) 2.23676 0.0962548
\(541\) −45.8569 −1.97154 −0.985770 0.168098i \(-0.946237\pi\)
−0.985770 + 0.168098i \(0.946237\pi\)
\(542\) 16.9173 0.726659
\(543\) −1.01472 −0.0435456
\(544\) 28.2322 1.21045
\(545\) −14.4432 −0.618681
\(546\) −0.0855409 −0.00366081
\(547\) 39.9554 1.70837 0.854185 0.519969i \(-0.174056\pi\)
0.854185 + 0.519969i \(0.174056\pi\)
\(548\) −3.99819 −0.170794
\(549\) 7.58106 0.323552
\(550\) 0.0804544 0.00343059
\(551\) 42.7377 1.82069
\(552\) −0.0727130 −0.00309487
\(553\) 4.78515 0.203485
\(554\) 19.1141 0.812082
\(555\) −2.62024 −0.111223
\(556\) −17.5335 −0.743588
\(557\) 25.9730 1.10051 0.550256 0.834996i \(-0.314530\pi\)
0.550256 + 0.834996i \(0.314530\pi\)
\(558\) 21.8957 0.926920
\(559\) −0.956697 −0.0404640
\(560\) −2.54986 −0.107751
\(561\) −0.207357 −0.00875461
\(562\) −32.2803 −1.36166
\(563\) 16.2957 0.686783 0.343392 0.939192i \(-0.388424\pi\)
0.343392 + 0.939192i \(0.388424\pi\)
\(564\) 1.42017 0.0598000
\(565\) 1.22187 0.0514047
\(566\) 12.7302 0.535092
\(567\) −8.85924 −0.372053
\(568\) 27.8472 1.16844
\(569\) 15.4272 0.646744 0.323372 0.946272i \(-0.395184\pi\)
0.323372 + 0.946272i \(0.395184\pi\)
\(570\) 2.72976 0.114337
\(571\) 36.6907 1.53546 0.767729 0.640775i \(-0.221387\pi\)
0.767729 + 0.640775i \(0.221387\pi\)
\(572\) 0.108089 0.00451943
\(573\) −2.73602 −0.114299
\(574\) −4.27162 −0.178294
\(575\) 0.0531738 0.00221750
\(576\) −21.2586 −0.885774
\(577\) 19.2897 0.803041 0.401520 0.915850i \(-0.368482\pi\)
0.401520 + 0.915850i \(0.368482\pi\)
\(578\) −16.0845 −0.669028
\(579\) 1.03937 0.0431947
\(580\) −13.7288 −0.570059
\(581\) −2.13432 −0.0885466
\(582\) −1.62928 −0.0675360
\(583\) −0.538539 −0.0223040
\(584\) −41.2984 −1.70894
\(585\) 3.48131 0.143935
\(586\) −9.71026 −0.401127
\(587\) 43.5333 1.79681 0.898405 0.439168i \(-0.144727\pi\)
0.898405 + 0.439168i \(0.144727\pi\)
\(588\) −0.966304 −0.0398497
\(589\) −51.3663 −2.11651
\(590\) −32.0248 −1.31844
\(591\) 1.92312 0.0791064
\(592\) 7.44375 0.305936
\(593\) 2.94911 0.121105 0.0605527 0.998165i \(-0.480714\pi\)
0.0605527 + 0.998165i \(0.480714\pi\)
\(594\) 0.218260 0.00895531
\(595\) −13.4451 −0.551195
\(596\) 0.215056 0.00880902
\(597\) 2.13331 0.0873104
\(598\) −0.0746688 −0.00305344
\(599\) 40.0061 1.63461 0.817303 0.576208i \(-0.195468\pi\)
0.817303 + 0.576208i \(0.195468\pi\)
\(600\) −0.181232 −0.00739875
\(601\) 4.70362 0.191864 0.0959322 0.995388i \(-0.469417\pi\)
0.0959322 + 0.995388i \(0.469417\pi\)
\(602\) −1.93566 −0.0788915
\(603\) 37.8470 1.54125
\(604\) −5.87629 −0.239103
\(605\) 25.3658 1.03127
\(606\) 0.220679 0.00896448
\(607\) 25.6662 1.04176 0.520879 0.853631i \(-0.325604\pi\)
0.520879 + 0.853631i \(0.325604\pi\)
\(608\) 34.6974 1.40716
\(609\) −1.01431 −0.0411020
\(610\) −5.97147 −0.241778
\(611\) 4.44106 0.179666
\(612\) −16.6761 −0.674092
\(613\) −27.6866 −1.11825 −0.559126 0.829082i \(-0.688863\pi\)
−0.559126 + 0.829082i \(0.688863\pi\)
\(614\) 0.313097 0.0126356
\(615\) −1.59900 −0.0644780
\(616\) 0.665970 0.0268327
\(617\) −23.7340 −0.955493 −0.477747 0.878498i \(-0.658546\pi\)
−0.477747 + 0.878498i \(0.658546\pi\)
\(618\) 2.98593 0.120112
\(619\) 10.1068 0.406228 0.203114 0.979155i \(-0.434894\pi\)
0.203114 + 0.979155i \(0.434894\pi\)
\(620\) 16.5006 0.662681
\(621\) 0.144252 0.00578864
\(622\) 27.0276 1.08371
\(623\) −3.34752 −0.134115
\(624\) 0.0909664 0.00364157
\(625\) −26.6877 −1.06751
\(626\) 25.2133 1.00773
\(627\) −0.254841 −0.0101774
\(628\) −18.7511 −0.748251
\(629\) 39.2500 1.56500
\(630\) 7.04364 0.280625
\(631\) −28.8533 −1.14863 −0.574316 0.818634i \(-0.694732\pi\)
−0.574316 + 0.818634i \(0.694732\pi\)
\(632\) −14.2363 −0.566289
\(633\) 2.26692 0.0901020
\(634\) −30.4944 −1.21109
\(635\) −43.8233 −1.73908
\(636\) 0.398366 0.0157962
\(637\) −3.02176 −0.119726
\(638\) −1.33964 −0.0530369
\(639\) −27.4959 −1.08772
\(640\) −6.05106 −0.239189
\(641\) 15.2099 0.600756 0.300378 0.953820i \(-0.402887\pi\)
0.300378 + 0.953820i \(0.402887\pi\)
\(642\) −0.0633077 −0.00249855
\(643\) 1.63211 0.0643640 0.0321820 0.999482i \(-0.489754\pi\)
0.0321820 + 0.999482i \(0.489754\pi\)
\(644\) 0.144539 0.00569562
\(645\) −0.724578 −0.0285302
\(646\) −40.8906 −1.60882
\(647\) −42.1264 −1.65616 −0.828080 0.560610i \(-0.810567\pi\)
−0.828080 + 0.560610i \(0.810567\pi\)
\(648\) 26.3571 1.03540
\(649\) 2.98972 0.117357
\(650\) −0.186106 −0.00729968
\(651\) 1.21910 0.0477802
\(652\) −19.7863 −0.774891
\(653\) −28.1328 −1.10092 −0.550460 0.834862i \(-0.685548\pi\)
−0.550460 + 0.834862i \(0.685548\pi\)
\(654\) 1.04252 0.0407657
\(655\) 41.9893 1.64066
\(656\) 4.54255 0.177357
\(657\) 40.7775 1.59088
\(658\) 8.98548 0.350290
\(659\) −48.1661 −1.87629 −0.938143 0.346248i \(-0.887455\pi\)
−0.938143 + 0.346248i \(0.887455\pi\)
\(660\) 0.0818639 0.00318655
\(661\) −25.2043 −0.980335 −0.490168 0.871628i \(-0.663064\pi\)
−0.490168 + 0.871628i \(0.663064\pi\)
\(662\) 13.3439 0.518625
\(663\) 0.479655 0.0186283
\(664\) 6.34981 0.246420
\(665\) −16.5240 −0.640774
\(666\) −20.5624 −0.796776
\(667\) −0.885394 −0.0342826
\(668\) −6.73170 −0.260457
\(669\) 0.00852328 0.000329529 0
\(670\) −29.8114 −1.15172
\(671\) 0.557476 0.0215211
\(672\) −0.823486 −0.0317667
\(673\) −32.2595 −1.24351 −0.621757 0.783210i \(-0.713581\pi\)
−0.621757 + 0.783210i \(0.713581\pi\)
\(674\) −14.7016 −0.566285
\(675\) 0.359537 0.0138386
\(676\) 12.4625 0.479327
\(677\) −6.15792 −0.236668 −0.118334 0.992974i \(-0.537755\pi\)
−0.118334 + 0.992974i \(0.537755\pi\)
\(678\) −0.0881954 −0.00338712
\(679\) 9.86251 0.378488
\(680\) 40.0005 1.53395
\(681\) −2.88352 −0.110497
\(682\) 1.61011 0.0616542
\(683\) −32.7408 −1.25279 −0.626396 0.779505i \(-0.715471\pi\)
−0.626396 + 0.779505i \(0.715471\pi\)
\(684\) −20.4950 −0.783644
\(685\) −9.46937 −0.361806
\(686\) −13.2753 −0.506855
\(687\) 3.48412 0.132927
\(688\) 2.05843 0.0784768
\(689\) 1.24574 0.0474590
\(690\) −0.0565523 −0.00215291
\(691\) −50.9047 −1.93651 −0.968253 0.249974i \(-0.919578\pi\)
−0.968253 + 0.249974i \(0.919578\pi\)
\(692\) −9.76954 −0.371382
\(693\) −0.657570 −0.0249790
\(694\) −8.21927 −0.311999
\(695\) −41.5267 −1.57520
\(696\) 3.01767 0.114385
\(697\) 23.9523 0.907259
\(698\) 2.86008 0.108256
\(699\) 0.118750 0.00449154
\(700\) 0.360251 0.0136162
\(701\) 37.8577 1.42987 0.714933 0.699193i \(-0.246457\pi\)
0.714933 + 0.699193i \(0.246457\pi\)
\(702\) −0.504876 −0.0190553
\(703\) 48.2383 1.81934
\(704\) −1.56326 −0.0589174
\(705\) 3.36355 0.126679
\(706\) 11.1513 0.419685
\(707\) −1.33583 −0.0502392
\(708\) −2.21154 −0.0831149
\(709\) −37.9785 −1.42631 −0.713156 0.701005i \(-0.752735\pi\)
−0.713156 + 0.701005i \(0.752735\pi\)
\(710\) 21.6580 0.812811
\(711\) 14.0567 0.527168
\(712\) 9.95919 0.373236
\(713\) 1.06415 0.0398528
\(714\) 0.970473 0.0363190
\(715\) 0.255999 0.00957383
\(716\) 18.8958 0.706171
\(717\) −3.83951 −0.143389
\(718\) −4.29085 −0.160133
\(719\) 7.41758 0.276629 0.138315 0.990388i \(-0.455832\pi\)
0.138315 + 0.990388i \(0.455832\pi\)
\(720\) −7.49038 −0.279150
\(721\) −18.0747 −0.673136
\(722\) −31.0456 −1.15540
\(723\) −3.17304 −0.118007
\(724\) −6.00091 −0.223022
\(725\) −2.20677 −0.0819576
\(726\) −1.83091 −0.0679515
\(727\) −9.45230 −0.350566 −0.175283 0.984518i \(-0.556084\pi\)
−0.175283 + 0.984518i \(0.556084\pi\)
\(728\) −1.54051 −0.0570953
\(729\) −25.5347 −0.945730
\(730\) −32.1197 −1.18880
\(731\) 10.8538 0.401444
\(732\) −0.412373 −0.0152418
\(733\) −7.51009 −0.277391 −0.138696 0.990335i \(-0.544291\pi\)
−0.138696 + 0.990335i \(0.544291\pi\)
\(734\) 11.4984 0.424415
\(735\) −2.28861 −0.0844165
\(736\) −0.718823 −0.0264962
\(737\) 2.78309 0.102517
\(738\) −12.5482 −0.461905
\(739\) 25.4681 0.936859 0.468430 0.883501i \(-0.344820\pi\)
0.468430 + 0.883501i \(0.344820\pi\)
\(740\) −15.4958 −0.569637
\(741\) 0.589496 0.0216557
\(742\) 2.52047 0.0925295
\(743\) −34.4841 −1.26510 −0.632550 0.774519i \(-0.717992\pi\)
−0.632550 + 0.774519i \(0.717992\pi\)
\(744\) −3.62693 −0.132970
\(745\) 0.509340 0.0186608
\(746\) 24.7302 0.905438
\(747\) −6.26972 −0.229397
\(748\) −1.22628 −0.0448374
\(749\) 0.383219 0.0140025
\(750\) 1.79494 0.0655421
\(751\) −14.7004 −0.536426 −0.268213 0.963360i \(-0.586433\pi\)
−0.268213 + 0.963360i \(0.586433\pi\)
\(752\) −9.55539 −0.348449
\(753\) −3.19164 −0.116310
\(754\) 3.09884 0.112853
\(755\) −13.9175 −0.506509
\(756\) 0.977304 0.0355442
\(757\) 44.5642 1.61971 0.809856 0.586628i \(-0.199545\pi\)
0.809856 + 0.586628i \(0.199545\pi\)
\(758\) 17.6761 0.642025
\(759\) 0.00527953 0.000191635 0
\(760\) 49.1606 1.78324
\(761\) −31.1285 −1.12841 −0.564203 0.825636i \(-0.690817\pi\)
−0.564203 + 0.825636i \(0.690817\pi\)
\(762\) 3.16319 0.114590
\(763\) −6.31066 −0.228461
\(764\) −16.1805 −0.585390
\(765\) −39.4959 −1.42798
\(766\) 32.5862 1.17739
\(767\) −6.91579 −0.249715
\(768\) 2.80179 0.101101
\(769\) 16.6611 0.600813 0.300406 0.953811i \(-0.402878\pi\)
0.300406 + 0.953811i \(0.402878\pi\)
\(770\) 0.517956 0.0186658
\(771\) 0.333697 0.0120178
\(772\) 6.14670 0.221225
\(773\) −47.4838 −1.70787 −0.853937 0.520376i \(-0.825792\pi\)
−0.853937 + 0.520376i \(0.825792\pi\)
\(774\) −5.68613 −0.204384
\(775\) 2.65231 0.0952739
\(776\) −29.3419 −1.05331
\(777\) −1.14486 −0.0410716
\(778\) −9.87676 −0.354099
\(779\) 29.4374 1.05470
\(780\) −0.189367 −0.00678041
\(781\) −2.02192 −0.0723500
\(782\) 0.847128 0.0302932
\(783\) −5.98663 −0.213945
\(784\) 6.50161 0.232200
\(785\) −44.4104 −1.58507
\(786\) −3.03081 −0.108105
\(787\) −7.35369 −0.262131 −0.131065 0.991374i \(-0.541840\pi\)
−0.131065 + 0.991374i \(0.541840\pi\)
\(788\) 11.3731 0.405149
\(789\) 2.11760 0.0753885
\(790\) −11.0722 −0.393932
\(791\) 0.533872 0.0189823
\(792\) 1.95633 0.0695153
\(793\) −1.28955 −0.0457931
\(794\) 29.3525 1.04168
\(795\) 0.943494 0.0334623
\(796\) 12.6161 0.447167
\(797\) 13.2563 0.469563 0.234782 0.972048i \(-0.424563\pi\)
0.234782 + 0.972048i \(0.424563\pi\)
\(798\) 1.19271 0.0422215
\(799\) −50.3845 −1.78247
\(800\) −1.79161 −0.0633429
\(801\) −9.83357 −0.347452
\(802\) −29.2100 −1.03144
\(803\) 2.99858 0.105818
\(804\) −2.05870 −0.0726046
\(805\) 0.342327 0.0120654
\(806\) −3.72448 −0.131189
\(807\) 4.13787 0.145660
\(808\) 3.97423 0.139813
\(809\) −17.1489 −0.602923 −0.301461 0.953478i \(-0.597474\pi\)
−0.301461 + 0.953478i \(0.597474\pi\)
\(810\) 20.4991 0.720266
\(811\) −53.2000 −1.86810 −0.934052 0.357136i \(-0.883753\pi\)
−0.934052 + 0.357136i \(0.883753\pi\)
\(812\) −5.99852 −0.210507
\(813\) 2.76692 0.0970403
\(814\) −1.51206 −0.0529976
\(815\) −46.8621 −1.64151
\(816\) −1.03203 −0.0361281
\(817\) 13.3394 0.466686
\(818\) −36.1577 −1.26422
\(819\) 1.52108 0.0531510
\(820\) −9.45632 −0.330229
\(821\) 42.7850 1.49321 0.746604 0.665269i \(-0.231683\pi\)
0.746604 + 0.665269i \(0.231683\pi\)
\(822\) 0.683503 0.0238399
\(823\) 41.9401 1.46194 0.730969 0.682411i \(-0.239068\pi\)
0.730969 + 0.682411i \(0.239068\pi\)
\(824\) 53.7739 1.87330
\(825\) 0.0131588 0.000458131 0
\(826\) −13.9925 −0.486862
\(827\) −17.6450 −0.613578 −0.306789 0.951778i \(-0.599255\pi\)
−0.306789 + 0.951778i \(0.599255\pi\)
\(828\) 0.424592 0.0147556
\(829\) 6.52471 0.226613 0.113306 0.993560i \(-0.463856\pi\)
0.113306 + 0.993560i \(0.463856\pi\)
\(830\) 4.93854 0.171419
\(831\) 3.12624 0.108448
\(832\) 3.61611 0.125366
\(833\) 34.2823 1.18781
\(834\) 2.99741 0.103792
\(835\) −15.9435 −0.551746
\(836\) −1.50710 −0.0521242
\(837\) 7.19531 0.248706
\(838\) −35.3851 −1.22236
\(839\) 18.7574 0.647578 0.323789 0.946129i \(-0.395043\pi\)
0.323789 + 0.946129i \(0.395043\pi\)
\(840\) −1.16675 −0.0402566
\(841\) 7.74485 0.267064
\(842\) 35.5342 1.22459
\(843\) −5.27964 −0.181841
\(844\) 13.4063 0.461464
\(845\) 29.5164 1.01539
\(846\) 26.3955 0.907495
\(847\) 11.0830 0.380817
\(848\) −2.68034 −0.0920431
\(849\) 2.08211 0.0714579
\(850\) 2.11140 0.0724204
\(851\) −0.999349 −0.0342572
\(852\) 1.49565 0.0512400
\(853\) 3.72327 0.127482 0.0637411 0.997966i \(-0.479697\pi\)
0.0637411 + 0.997966i \(0.479697\pi\)
\(854\) −2.60910 −0.0892817
\(855\) −48.5405 −1.66005
\(856\) −1.14011 −0.0389683
\(857\) 5.36052 0.183112 0.0915559 0.995800i \(-0.470816\pi\)
0.0915559 + 0.995800i \(0.470816\pi\)
\(858\) −0.0184781 −0.000630833 0
\(859\) 5.70168 0.194539 0.0972695 0.995258i \(-0.468989\pi\)
0.0972695 + 0.995258i \(0.468989\pi\)
\(860\) −4.28507 −0.146120
\(861\) −0.698650 −0.0238099
\(862\) 2.23155 0.0760068
\(863\) −23.3086 −0.793434 −0.396717 0.917941i \(-0.629851\pi\)
−0.396717 + 0.917941i \(0.629851\pi\)
\(864\) −4.86035 −0.165352
\(865\) −23.1383 −0.786726
\(866\) 21.7547 0.739255
\(867\) −2.63072 −0.0893440
\(868\) 7.20959 0.244710
\(869\) 1.03366 0.0350647
\(870\) 2.34698 0.0795702
\(871\) −6.43782 −0.218137
\(872\) 18.7748 0.635796
\(873\) 28.9718 0.980548
\(874\) 1.04112 0.0352164
\(875\) −10.8653 −0.367314
\(876\) −2.21810 −0.0749426
\(877\) 25.2049 0.851109 0.425555 0.904933i \(-0.360079\pi\)
0.425555 + 0.904933i \(0.360079\pi\)
\(878\) −15.9969 −0.539870
\(879\) −1.58817 −0.0535677
\(880\) −0.550807 −0.0185677
\(881\) 26.8752 0.905450 0.452725 0.891650i \(-0.350452\pi\)
0.452725 + 0.891650i \(0.350452\pi\)
\(882\) −17.9598 −0.604739
\(883\) −19.4627 −0.654973 −0.327487 0.944856i \(-0.606202\pi\)
−0.327487 + 0.944856i \(0.606202\pi\)
\(884\) 2.83662 0.0954060
\(885\) −5.23785 −0.176068
\(886\) 22.3023 0.749259
\(887\) 3.16833 0.106382 0.0531910 0.998584i \(-0.483061\pi\)
0.0531910 + 0.998584i \(0.483061\pi\)
\(888\) 3.40606 0.114300
\(889\) −19.1477 −0.642192
\(890\) 7.74572 0.259637
\(891\) −1.91373 −0.0641123
\(892\) 0.0504057 0.00168771
\(893\) −61.9225 −2.07216
\(894\) −0.0367644 −0.00122959
\(895\) 44.7532 1.49593
\(896\) −2.64388 −0.0883258
\(897\) −0.0122126 −0.000407765 0
\(898\) 9.57154 0.319407
\(899\) −44.1635 −1.47294
\(900\) 1.05826 0.0352754
\(901\) −14.1331 −0.470842
\(902\) −0.922734 −0.0307237
\(903\) −0.316589 −0.0105354
\(904\) −1.58832 −0.0528267
\(905\) −14.2126 −0.472444
\(906\) 1.00457 0.0333746
\(907\) −12.2670 −0.407320 −0.203660 0.979042i \(-0.565284\pi\)
−0.203660 + 0.979042i \(0.565284\pi\)
\(908\) −17.0528 −0.565918
\(909\) −3.92411 −0.130154
\(910\) −1.19813 −0.0397176
\(911\) −48.4249 −1.60439 −0.802193 0.597064i \(-0.796334\pi\)
−0.802193 + 0.597064i \(0.796334\pi\)
\(912\) −1.26836 −0.0419996
\(913\) −0.461046 −0.0152584
\(914\) 22.1667 0.733210
\(915\) −0.976670 −0.0322877
\(916\) 20.6047 0.680798
\(917\) 18.3463 0.605849
\(918\) 5.72789 0.189048
\(919\) −22.8781 −0.754678 −0.377339 0.926075i \(-0.623161\pi\)
−0.377339 + 0.926075i \(0.623161\pi\)
\(920\) −1.01846 −0.0335775
\(921\) 0.0512090 0.00168739
\(922\) −12.6300 −0.415948
\(923\) 4.67708 0.153948
\(924\) 0.0357687 0.00117670
\(925\) −2.49080 −0.0818970
\(926\) 1.83676 0.0603598
\(927\) −53.0956 −1.74389
\(928\) 29.8320 0.979282
\(929\) 45.1914 1.48268 0.741341 0.671128i \(-0.234190\pi\)
0.741341 + 0.671128i \(0.234190\pi\)
\(930\) −2.82083 −0.0924987
\(931\) 42.1329 1.38085
\(932\) 0.702275 0.0230038
\(933\) 4.42053 0.144721
\(934\) 6.97760 0.228314
\(935\) −2.90434 −0.0949822
\(936\) −4.52537 −0.147916
\(937\) −5.19362 −0.169668 −0.0848341 0.996395i \(-0.527036\pi\)
−0.0848341 + 0.996395i \(0.527036\pi\)
\(938\) −13.0255 −0.425296
\(939\) 4.12380 0.134575
\(940\) 19.8917 0.648794
\(941\) 49.6383 1.61816 0.809081 0.587697i \(-0.199965\pi\)
0.809081 + 0.587697i \(0.199965\pi\)
\(942\) 3.20556 0.104443
\(943\) −0.609853 −0.0198595
\(944\) 14.8800 0.484303
\(945\) 2.31466 0.0752958
\(946\) −0.418131 −0.0135946
\(947\) −28.6531 −0.931099 −0.465550 0.885022i \(-0.654143\pi\)
−0.465550 + 0.885022i \(0.654143\pi\)
\(948\) −0.764618 −0.0248336
\(949\) −6.93629 −0.225161
\(950\) 2.59491 0.0841899
\(951\) −4.98755 −0.161732
\(952\) 17.4773 0.566444
\(953\) 15.2516 0.494048 0.247024 0.969009i \(-0.420547\pi\)
0.247024 + 0.969009i \(0.420547\pi\)
\(954\) 7.40407 0.239716
\(955\) −38.3221 −1.24007
\(956\) −22.7064 −0.734378
\(957\) −0.219106 −0.00708271
\(958\) 27.3074 0.882262
\(959\) −4.13744 −0.133605
\(960\) 2.73875 0.0883927
\(961\) 22.0799 0.712256
\(962\) 3.49768 0.112770
\(963\) 1.12573 0.0362763
\(964\) −18.7650 −0.604380
\(965\) 14.5579 0.468636
\(966\) −0.0247093 −0.000795009 0
\(967\) −18.3538 −0.590220 −0.295110 0.955463i \(-0.595356\pi\)
−0.295110 + 0.955463i \(0.595356\pi\)
\(968\) −32.9731 −1.05980
\(969\) −6.68791 −0.214847
\(970\) −22.8206 −0.732725
\(971\) 3.48125 0.111719 0.0558593 0.998439i \(-0.482210\pi\)
0.0558593 + 0.998439i \(0.482210\pi\)
\(972\) 4.31292 0.138337
\(973\) −18.1442 −0.581675
\(974\) 8.68887 0.278409
\(975\) −0.0304388 −0.000974822 0
\(976\) 2.77459 0.0888123
\(977\) −18.6386 −0.596302 −0.298151 0.954519i \(-0.596370\pi\)
−0.298151 + 0.954519i \(0.596370\pi\)
\(978\) 3.38252 0.108161
\(979\) −0.723114 −0.0231108
\(980\) −13.5345 −0.432345
\(981\) −18.5380 −0.591873
\(982\) −11.6527 −0.371853
\(983\) 45.3085 1.44512 0.722559 0.691310i \(-0.242966\pi\)
0.722559 + 0.691310i \(0.242966\pi\)
\(984\) 2.07855 0.0662618
\(985\) 26.9362 0.858257
\(986\) −35.1567 −1.11962
\(987\) 1.46963 0.0467789
\(988\) 3.48621 0.110911
\(989\) −0.276351 −0.00878745
\(990\) 1.52153 0.0483575
\(991\) 6.74006 0.214105 0.107053 0.994253i \(-0.465859\pi\)
0.107053 + 0.994253i \(0.465859\pi\)
\(992\) −35.8549 −1.13839
\(993\) 2.18248 0.0692588
\(994\) 9.46301 0.300148
\(995\) 29.8802 0.947266
\(996\) 0.341043 0.0108063
\(997\) 25.0811 0.794327 0.397164 0.917748i \(-0.369995\pi\)
0.397164 + 0.917748i \(0.369995\pi\)
\(998\) 3.99857 0.126573
\(999\) −6.75714 −0.213786
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 2671.2.a.b.1.39 122
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2671.2.a.b.1.39 122 1.1 even 1 trivial