Properties

Label 6014.2.a.j.1.10
Level $6014$
Weight $2$
Character 6014.1
Self dual yes
Analytic conductor $48.022$
Analytic rank $0$
Dimension $32$
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] = [6014,2,Mod(1,6014)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6014, 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("6014.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6014 = 2 \cdot 31 \cdot 97 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6014.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: \(48.0220317756\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Character \(\chi\) \(=\) 6014.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{2} -1.52309 q^{3} +1.00000 q^{4} -0.0721797 q^{5} +1.52309 q^{6} +3.89998 q^{7} -1.00000 q^{8} -0.680188 q^{9} +O(q^{10})\) \(q-1.00000 q^{2} -1.52309 q^{3} +1.00000 q^{4} -0.0721797 q^{5} +1.52309 q^{6} +3.89998 q^{7} -1.00000 q^{8} -0.680188 q^{9} +0.0721797 q^{10} +1.26492 q^{11} -1.52309 q^{12} +3.78887 q^{13} -3.89998 q^{14} +0.109936 q^{15} +1.00000 q^{16} -7.52558 q^{17} +0.680188 q^{18} +2.59237 q^{19} -0.0721797 q^{20} -5.94003 q^{21} -1.26492 q^{22} +1.46163 q^{23} +1.52309 q^{24} -4.99479 q^{25} -3.78887 q^{26} +5.60527 q^{27} +3.89998 q^{28} +5.05456 q^{29} -0.109936 q^{30} -1.00000 q^{31} -1.00000 q^{32} -1.92660 q^{33} +7.52558 q^{34} -0.281500 q^{35} -0.680188 q^{36} -3.19836 q^{37} -2.59237 q^{38} -5.77080 q^{39} +0.0721797 q^{40} +6.54873 q^{41} +5.94003 q^{42} +4.82172 q^{43} +1.26492 q^{44} +0.0490958 q^{45} -1.46163 q^{46} -7.18513 q^{47} -1.52309 q^{48} +8.20984 q^{49} +4.99479 q^{50} +11.4622 q^{51} +3.78887 q^{52} -6.50668 q^{53} -5.60527 q^{54} -0.0913019 q^{55} -3.89998 q^{56} -3.94842 q^{57} -5.05456 q^{58} +7.31482 q^{59} +0.109936 q^{60} +4.13851 q^{61} +1.00000 q^{62} -2.65272 q^{63} +1.00000 q^{64} -0.273480 q^{65} +1.92660 q^{66} +9.24848 q^{67} -7.52558 q^{68} -2.22619 q^{69} +0.281500 q^{70} -0.0717312 q^{71} +0.680188 q^{72} -6.45943 q^{73} +3.19836 q^{74} +7.60753 q^{75} +2.59237 q^{76} +4.93318 q^{77} +5.77080 q^{78} +12.4804 q^{79} -0.0721797 q^{80} -6.49678 q^{81} -6.54873 q^{82} +0.0614961 q^{83} -5.94003 q^{84} +0.543194 q^{85} -4.82172 q^{86} -7.69857 q^{87} -1.26492 q^{88} +5.60595 q^{89} -0.0490958 q^{90} +14.7765 q^{91} +1.46163 q^{92} +1.52309 q^{93} +7.18513 q^{94} -0.187117 q^{95} +1.52309 q^{96} +1.00000 q^{97} -8.20984 q^{98} -0.860387 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.52309 −0.879358 −0.439679 0.898155i \(-0.644908\pi\)
−0.439679 + 0.898155i \(0.644908\pi\)
\(4\) 1.00000 0.500000
\(5\) −0.0721797 −0.0322798 −0.0161399 0.999870i \(-0.505138\pi\)
−0.0161399 + 0.999870i \(0.505138\pi\)
\(6\) 1.52309 0.621800
\(7\) 3.89998 1.47405 0.737027 0.675863i \(-0.236229\pi\)
0.737027 + 0.675863i \(0.236229\pi\)
\(8\) −1.00000 −0.353553
\(9\) −0.680188 −0.226729
\(10\) 0.0721797 0.0228252
\(11\) 1.26492 0.381389 0.190695 0.981649i \(-0.438926\pi\)
0.190695 + 0.981649i \(0.438926\pi\)
\(12\) −1.52309 −0.439679
\(13\) 3.78887 1.05084 0.525422 0.850842i \(-0.323908\pi\)
0.525422 + 0.850842i \(0.323908\pi\)
\(14\) −3.89998 −1.04231
\(15\) 0.109936 0.0283855
\(16\) 1.00000 0.250000
\(17\) −7.52558 −1.82522 −0.912611 0.408830i \(-0.865937\pi\)
−0.912611 + 0.408830i \(0.865937\pi\)
\(18\) 0.680188 0.160322
\(19\) 2.59237 0.594730 0.297365 0.954764i \(-0.403892\pi\)
0.297365 + 0.954764i \(0.403892\pi\)
\(20\) −0.0721797 −0.0161399
\(21\) −5.94003 −1.29622
\(22\) −1.26492 −0.269683
\(23\) 1.46163 0.304770 0.152385 0.988321i \(-0.451305\pi\)
0.152385 + 0.988321i \(0.451305\pi\)
\(24\) 1.52309 0.310900
\(25\) −4.99479 −0.998958
\(26\) −3.78887 −0.743059
\(27\) 5.60527 1.07873
\(28\) 3.89998 0.737027
\(29\) 5.05456 0.938609 0.469305 0.883036i \(-0.344505\pi\)
0.469305 + 0.883036i \(0.344505\pi\)
\(30\) −0.109936 −0.0200716
\(31\) −1.00000 −0.179605
\(32\) −1.00000 −0.176777
\(33\) −1.92660 −0.335378
\(34\) 7.52558 1.29063
\(35\) −0.281500 −0.0475821
\(36\) −0.680188 −0.113365
\(37\) −3.19836 −0.525808 −0.262904 0.964822i \(-0.584680\pi\)
−0.262904 + 0.964822i \(0.584680\pi\)
\(38\) −2.59237 −0.420538
\(39\) −5.77080 −0.924068
\(40\) 0.0721797 0.0114126
\(41\) 6.54873 1.02274 0.511370 0.859361i \(-0.329138\pi\)
0.511370 + 0.859361i \(0.329138\pi\)
\(42\) 5.94003 0.916567
\(43\) 4.82172 0.735305 0.367653 0.929963i \(-0.380162\pi\)
0.367653 + 0.929963i \(0.380162\pi\)
\(44\) 1.26492 0.190695
\(45\) 0.0490958 0.00731877
\(46\) −1.46163 −0.215505
\(47\) −7.18513 −1.04806 −0.524030 0.851700i \(-0.675572\pi\)
−0.524030 + 0.851700i \(0.675572\pi\)
\(48\) −1.52309 −0.219840
\(49\) 8.20984 1.17283
\(50\) 4.99479 0.706370
\(51\) 11.4622 1.60502
\(52\) 3.78887 0.525422
\(53\) −6.50668 −0.893761 −0.446880 0.894594i \(-0.647465\pi\)
−0.446880 + 0.894594i \(0.647465\pi\)
\(54\) −5.60527 −0.762780
\(55\) −0.0913019 −0.0123111
\(56\) −3.89998 −0.521157
\(57\) −3.94842 −0.522981
\(58\) −5.05456 −0.663697
\(59\) 7.31482 0.952309 0.476154 0.879362i \(-0.342030\pi\)
0.476154 + 0.879362i \(0.342030\pi\)
\(60\) 0.109936 0.0141927
\(61\) 4.13851 0.529882 0.264941 0.964265i \(-0.414648\pi\)
0.264941 + 0.964265i \(0.414648\pi\)
\(62\) 1.00000 0.127000
\(63\) −2.65272 −0.334211
\(64\) 1.00000 0.125000
\(65\) −0.273480 −0.0339210
\(66\) 1.92660 0.237148
\(67\) 9.24848 1.12988 0.564941 0.825132i \(-0.308899\pi\)
0.564941 + 0.825132i \(0.308899\pi\)
\(68\) −7.52558 −0.912611
\(69\) −2.22619 −0.268002
\(70\) 0.281500 0.0336456
\(71\) −0.0717312 −0.00851293 −0.00425646 0.999991i \(-0.501355\pi\)
−0.00425646 + 0.999991i \(0.501355\pi\)
\(72\) 0.680188 0.0801610
\(73\) −6.45943 −0.756019 −0.378009 0.925802i \(-0.623391\pi\)
−0.378009 + 0.925802i \(0.623391\pi\)
\(74\) 3.19836 0.371802
\(75\) 7.60753 0.878442
\(76\) 2.59237 0.297365
\(77\) 4.93318 0.562188
\(78\) 5.77080 0.653415
\(79\) 12.4804 1.40415 0.702075 0.712103i \(-0.252257\pi\)
0.702075 + 0.712103i \(0.252257\pi\)
\(80\) −0.0721797 −0.00806994
\(81\) −6.49678 −0.721864
\(82\) −6.54873 −0.723186
\(83\) 0.0614961 0.00675007 0.00337504 0.999994i \(-0.498926\pi\)
0.00337504 + 0.999994i \(0.498926\pi\)
\(84\) −5.94003 −0.648110
\(85\) 0.543194 0.0589177
\(86\) −4.82172 −0.519939
\(87\) −7.69857 −0.825373
\(88\) −1.26492 −0.134841
\(89\) 5.60595 0.594230 0.297115 0.954842i \(-0.403976\pi\)
0.297115 + 0.954842i \(0.403976\pi\)
\(90\) −0.0490958 −0.00517515
\(91\) 14.7765 1.54900
\(92\) 1.46163 0.152385
\(93\) 1.52309 0.157937
\(94\) 7.18513 0.741090
\(95\) −0.187117 −0.0191978
\(96\) 1.52309 0.155450
\(97\) 1.00000 0.101535
\(98\) −8.20984 −0.829319
\(99\) −0.860387 −0.0864721
\(100\) −4.99479 −0.499479
\(101\) −11.6500 −1.15922 −0.579610 0.814894i \(-0.696795\pi\)
−0.579610 + 0.814894i \(0.696795\pi\)
\(102\) −11.4622 −1.13492
\(103\) 11.3568 1.11902 0.559510 0.828824i \(-0.310989\pi\)
0.559510 + 0.828824i \(0.310989\pi\)
\(104\) −3.78887 −0.371529
\(105\) 0.428750 0.0418417
\(106\) 6.50668 0.631984
\(107\) 17.5759 1.69913 0.849563 0.527487i \(-0.176866\pi\)
0.849563 + 0.527487i \(0.176866\pi\)
\(108\) 5.60527 0.539367
\(109\) 8.70260 0.833557 0.416779 0.909008i \(-0.363159\pi\)
0.416779 + 0.909008i \(0.363159\pi\)
\(110\) 0.0913019 0.00870530
\(111\) 4.87141 0.462373
\(112\) 3.89998 0.368513
\(113\) −2.35657 −0.221687 −0.110844 0.993838i \(-0.535355\pi\)
−0.110844 + 0.993838i \(0.535355\pi\)
\(114\) 3.94842 0.369803
\(115\) −0.105500 −0.00983792
\(116\) 5.05456 0.469305
\(117\) −2.57715 −0.238257
\(118\) −7.31482 −0.673384
\(119\) −29.3496 −2.69047
\(120\) −0.109936 −0.0100358
\(121\) −9.39997 −0.854542
\(122\) −4.13851 −0.374683
\(123\) −9.97432 −0.899355
\(124\) −1.00000 −0.0898027
\(125\) 0.721421 0.0645259
\(126\) 2.65272 0.236323
\(127\) −8.40371 −0.745709 −0.372855 0.927890i \(-0.621621\pi\)
−0.372855 + 0.927890i \(0.621621\pi\)
\(128\) −1.00000 −0.0883883
\(129\) −7.34392 −0.646596
\(130\) 0.273480 0.0239858
\(131\) −4.72359 −0.412702 −0.206351 0.978478i \(-0.566159\pi\)
−0.206351 + 0.978478i \(0.566159\pi\)
\(132\) −1.92660 −0.167689
\(133\) 10.1102 0.876665
\(134\) −9.24848 −0.798947
\(135\) −0.404587 −0.0348213
\(136\) 7.52558 0.645313
\(137\) 7.39319 0.631643 0.315821 0.948819i \(-0.397720\pi\)
0.315821 + 0.948819i \(0.397720\pi\)
\(138\) 2.22619 0.189506
\(139\) 4.04853 0.343392 0.171696 0.985150i \(-0.445075\pi\)
0.171696 + 0.985150i \(0.445075\pi\)
\(140\) −0.281500 −0.0237911
\(141\) 10.9436 0.921620
\(142\) 0.0717312 0.00601955
\(143\) 4.79264 0.400780
\(144\) −0.680188 −0.0566824
\(145\) −0.364837 −0.0302981
\(146\) 6.45943 0.534586
\(147\) −12.5043 −1.03134
\(148\) −3.19836 −0.262904
\(149\) −20.2864 −1.66193 −0.830963 0.556327i \(-0.812210\pi\)
−0.830963 + 0.556327i \(0.812210\pi\)
\(150\) −7.60753 −0.621152
\(151\) −12.6915 −1.03282 −0.516411 0.856341i \(-0.672732\pi\)
−0.516411 + 0.856341i \(0.672732\pi\)
\(152\) −2.59237 −0.210269
\(153\) 5.11881 0.413831
\(154\) −4.93318 −0.397527
\(155\) 0.0721797 0.00579762
\(156\) −5.77080 −0.462034
\(157\) −10.4383 −0.833067 −0.416533 0.909120i \(-0.636755\pi\)
−0.416533 + 0.909120i \(0.636755\pi\)
\(158\) −12.4804 −0.992884
\(159\) 9.91027 0.785936
\(160\) 0.0721797 0.00570631
\(161\) 5.70032 0.449248
\(162\) 6.49678 0.510435
\(163\) 3.32897 0.260745 0.130373 0.991465i \(-0.458383\pi\)
0.130373 + 0.991465i \(0.458383\pi\)
\(164\) 6.54873 0.511370
\(165\) 0.139061 0.0108259
\(166\) −0.0614961 −0.00477302
\(167\) −6.53936 −0.506031 −0.253015 0.967462i \(-0.581422\pi\)
−0.253015 + 0.967462i \(0.581422\pi\)
\(168\) 5.94003 0.458283
\(169\) 1.35554 0.104272
\(170\) −0.543194 −0.0416611
\(171\) −1.76330 −0.134843
\(172\) 4.82172 0.367653
\(173\) 8.69790 0.661289 0.330645 0.943755i \(-0.392734\pi\)
0.330645 + 0.943755i \(0.392734\pi\)
\(174\) 7.69857 0.583627
\(175\) −19.4796 −1.47252
\(176\) 1.26492 0.0953473
\(177\) −11.1412 −0.837420
\(178\) −5.60595 −0.420184
\(179\) 2.43635 0.182101 0.0910506 0.995846i \(-0.470977\pi\)
0.0910506 + 0.995846i \(0.470977\pi\)
\(180\) 0.0490958 0.00365939
\(181\) 6.44436 0.479006 0.239503 0.970896i \(-0.423016\pi\)
0.239503 + 0.970896i \(0.423016\pi\)
\(182\) −14.7765 −1.09531
\(183\) −6.30333 −0.465956
\(184\) −1.46163 −0.107753
\(185\) 0.230857 0.0169730
\(186\) −1.52309 −0.111679
\(187\) −9.51929 −0.696119
\(188\) −7.18513 −0.524030
\(189\) 21.8604 1.59011
\(190\) 0.187117 0.0135749
\(191\) −1.00262 −0.0725472 −0.0362736 0.999342i \(-0.511549\pi\)
−0.0362736 + 0.999342i \(0.511549\pi\)
\(192\) −1.52309 −0.109920
\(193\) 5.49049 0.395214 0.197607 0.980281i \(-0.436683\pi\)
0.197607 + 0.980281i \(0.436683\pi\)
\(194\) −1.00000 −0.0717958
\(195\) 0.416535 0.0298287
\(196\) 8.20984 0.586417
\(197\) 3.29099 0.234473 0.117237 0.993104i \(-0.462596\pi\)
0.117237 + 0.993104i \(0.462596\pi\)
\(198\) 0.860387 0.0611450
\(199\) −20.0998 −1.42484 −0.712419 0.701754i \(-0.752401\pi\)
−0.712419 + 0.701754i \(0.752401\pi\)
\(200\) 4.99479 0.353185
\(201\) −14.0863 −0.993570
\(202\) 11.6500 0.819693
\(203\) 19.7127 1.38356
\(204\) 11.4622 0.802512
\(205\) −0.472686 −0.0330138
\(206\) −11.3568 −0.791266
\(207\) −0.994182 −0.0691004
\(208\) 3.78887 0.262711
\(209\) 3.27915 0.226824
\(210\) −0.428750 −0.0295866
\(211\) 12.2752 0.845059 0.422529 0.906349i \(-0.361142\pi\)
0.422529 + 0.906349i \(0.361142\pi\)
\(212\) −6.50668 −0.446880
\(213\) 0.109253 0.00748591
\(214\) −17.5759 −1.20146
\(215\) −0.348030 −0.0237355
\(216\) −5.60527 −0.381390
\(217\) −3.89998 −0.264748
\(218\) −8.70260 −0.589414
\(219\) 9.83831 0.664811
\(220\) −0.0913019 −0.00615557
\(221\) −28.5135 −1.91802
\(222\) −4.87141 −0.326947
\(223\) 19.9653 1.33697 0.668487 0.743724i \(-0.266942\pi\)
0.668487 + 0.743724i \(0.266942\pi\)
\(224\) −3.89998 −0.260578
\(225\) 3.39740 0.226493
\(226\) 2.35657 0.156757
\(227\) −9.62939 −0.639125 −0.319563 0.947565i \(-0.603536\pi\)
−0.319563 + 0.947565i \(0.603536\pi\)
\(228\) −3.94842 −0.261490
\(229\) 12.8718 0.850590 0.425295 0.905055i \(-0.360170\pi\)
0.425295 + 0.905055i \(0.360170\pi\)
\(230\) 0.105500 0.00695646
\(231\) −7.51369 −0.494364
\(232\) −5.05456 −0.331848
\(233\) −16.1117 −1.05551 −0.527755 0.849396i \(-0.676966\pi\)
−0.527755 + 0.849396i \(0.676966\pi\)
\(234\) 2.57715 0.168473
\(235\) 0.518621 0.0338311
\(236\) 7.31482 0.476154
\(237\) −19.0087 −1.23475
\(238\) 29.3496 1.90245
\(239\) −7.28439 −0.471188 −0.235594 0.971852i \(-0.575704\pi\)
−0.235594 + 0.971852i \(0.575704\pi\)
\(240\) 0.109936 0.00709637
\(241\) 15.8406 1.02038 0.510191 0.860061i \(-0.329575\pi\)
0.510191 + 0.860061i \(0.329575\pi\)
\(242\) 9.39997 0.604253
\(243\) −6.92061 −0.443957
\(244\) 4.13851 0.264941
\(245\) −0.592584 −0.0378588
\(246\) 9.97432 0.635940
\(247\) 9.82215 0.624969
\(248\) 1.00000 0.0635001
\(249\) −0.0936643 −0.00593573
\(250\) −0.721421 −0.0456267
\(251\) 23.3857 1.47609 0.738047 0.674749i \(-0.235748\pi\)
0.738047 + 0.674749i \(0.235748\pi\)
\(252\) −2.65272 −0.167106
\(253\) 1.84885 0.116236
\(254\) 8.40371 0.527296
\(255\) −0.827336 −0.0518098
\(256\) 1.00000 0.0625000
\(257\) −12.2262 −0.762652 −0.381326 0.924441i \(-0.624532\pi\)
−0.381326 + 0.924441i \(0.624532\pi\)
\(258\) 7.34392 0.457213
\(259\) −12.4736 −0.775069
\(260\) −0.273480 −0.0169605
\(261\) −3.43806 −0.212810
\(262\) 4.72359 0.291824
\(263\) 17.1286 1.05619 0.528097 0.849184i \(-0.322906\pi\)
0.528097 + 0.849184i \(0.322906\pi\)
\(264\) 1.92660 0.118574
\(265\) 0.469650 0.0288504
\(266\) −10.1102 −0.619895
\(267\) −8.53839 −0.522541
\(268\) 9.24848 0.564941
\(269\) −5.93482 −0.361852 −0.180926 0.983497i \(-0.557910\pi\)
−0.180926 + 0.983497i \(0.557910\pi\)
\(270\) 0.404587 0.0246224
\(271\) 29.9704 1.82057 0.910286 0.413980i \(-0.135862\pi\)
0.910286 + 0.413980i \(0.135862\pi\)
\(272\) −7.52558 −0.456305
\(273\) −22.5060 −1.36213
\(274\) −7.39319 −0.446639
\(275\) −6.31803 −0.380992
\(276\) −2.22619 −0.134001
\(277\) −3.95743 −0.237779 −0.118889 0.992908i \(-0.537933\pi\)
−0.118889 + 0.992908i \(0.537933\pi\)
\(278\) −4.04853 −0.242814
\(279\) 0.680188 0.0407218
\(280\) 0.281500 0.0168228
\(281\) −16.3944 −0.978010 −0.489005 0.872281i \(-0.662640\pi\)
−0.489005 + 0.872281i \(0.662640\pi\)
\(282\) −10.9436 −0.651683
\(283\) −12.3852 −0.736225 −0.368113 0.929781i \(-0.619996\pi\)
−0.368113 + 0.929781i \(0.619996\pi\)
\(284\) −0.0717312 −0.00425646
\(285\) 0.284996 0.0168817
\(286\) −4.79264 −0.283394
\(287\) 25.5399 1.50757
\(288\) 0.680188 0.0400805
\(289\) 39.6344 2.33143
\(290\) 0.364837 0.0214240
\(291\) −1.52309 −0.0892853
\(292\) −6.45943 −0.378009
\(293\) −8.57860 −0.501167 −0.250584 0.968095i \(-0.580623\pi\)
−0.250584 + 0.968095i \(0.580623\pi\)
\(294\) 12.5043 0.729268
\(295\) −0.527982 −0.0307403
\(296\) 3.19836 0.185901
\(297\) 7.09024 0.411417
\(298\) 20.2864 1.17516
\(299\) 5.53792 0.320266
\(300\) 7.60753 0.439221
\(301\) 18.8046 1.08388
\(302\) 12.6915 0.730316
\(303\) 17.7441 1.01937
\(304\) 2.59237 0.148683
\(305\) −0.298716 −0.0171045
\(306\) −5.11881 −0.292623
\(307\) 27.5872 1.57449 0.787243 0.616643i \(-0.211508\pi\)
0.787243 + 0.616643i \(0.211508\pi\)
\(308\) 4.93318 0.281094
\(309\) −17.2975 −0.984019
\(310\) −0.0721797 −0.00409953
\(311\) −20.4691 −1.16069 −0.580347 0.814369i \(-0.697083\pi\)
−0.580347 + 0.814369i \(0.697083\pi\)
\(312\) 5.77080 0.326707
\(313\) 13.7204 0.775522 0.387761 0.921760i \(-0.373249\pi\)
0.387761 + 0.921760i \(0.373249\pi\)
\(314\) 10.4383 0.589067
\(315\) 0.191473 0.0107883
\(316\) 12.4804 0.702075
\(317\) 23.4019 1.31438 0.657191 0.753724i \(-0.271744\pi\)
0.657191 + 0.753724i \(0.271744\pi\)
\(318\) −9.91027 −0.555740
\(319\) 6.39364 0.357975
\(320\) −0.0721797 −0.00403497
\(321\) −26.7697 −1.49414
\(322\) −5.70032 −0.317666
\(323\) −19.5091 −1.08551
\(324\) −6.49678 −0.360932
\(325\) −18.9246 −1.04975
\(326\) −3.32897 −0.184375
\(327\) −13.2549 −0.732995
\(328\) −6.54873 −0.361593
\(329\) −28.0219 −1.54490
\(330\) −0.139061 −0.00765507
\(331\) 13.8521 0.761383 0.380691 0.924702i \(-0.375686\pi\)
0.380691 + 0.924702i \(0.375686\pi\)
\(332\) 0.0614961 0.00337504
\(333\) 2.17549 0.119216
\(334\) 6.53936 0.357818
\(335\) −0.667553 −0.0364723
\(336\) −5.94003 −0.324055
\(337\) 29.5301 1.60861 0.804304 0.594218i \(-0.202539\pi\)
0.804304 + 0.594218i \(0.202539\pi\)
\(338\) −1.35554 −0.0737317
\(339\) 3.58927 0.194942
\(340\) 0.543194 0.0294589
\(341\) −1.26492 −0.0684995
\(342\) 1.76330 0.0953483
\(343\) 4.71835 0.254767
\(344\) −4.82172 −0.259970
\(345\) 0.160686 0.00865105
\(346\) −8.69790 −0.467602
\(347\) −7.62554 −0.409360 −0.204680 0.978829i \(-0.565615\pi\)
−0.204680 + 0.978829i \(0.565615\pi\)
\(348\) −7.69857 −0.412687
\(349\) 33.1412 1.77401 0.887004 0.461761i \(-0.152782\pi\)
0.887004 + 0.461761i \(0.152782\pi\)
\(350\) 19.4796 1.04123
\(351\) 21.2376 1.13358
\(352\) −1.26492 −0.0674207
\(353\) −4.72300 −0.251380 −0.125690 0.992070i \(-0.540114\pi\)
−0.125690 + 0.992070i \(0.540114\pi\)
\(354\) 11.1412 0.592146
\(355\) 0.00517754 0.000274795 0
\(356\) 5.60595 0.297115
\(357\) 44.7022 2.36589
\(358\) −2.43635 −0.128765
\(359\) 30.3409 1.60133 0.800667 0.599110i \(-0.204479\pi\)
0.800667 + 0.599110i \(0.204479\pi\)
\(360\) −0.0490958 −0.00258758
\(361\) −12.2796 −0.646296
\(362\) −6.44436 −0.338708
\(363\) 14.3170 0.751449
\(364\) 14.7765 0.774500
\(365\) 0.466240 0.0244041
\(366\) 6.30333 0.329480
\(367\) −12.5646 −0.655869 −0.327934 0.944701i \(-0.606352\pi\)
−0.327934 + 0.944701i \(0.606352\pi\)
\(368\) 1.46163 0.0761926
\(369\) −4.45437 −0.231885
\(370\) −0.230857 −0.0120017
\(371\) −25.3759 −1.31745
\(372\) 1.52309 0.0789687
\(373\) −16.2479 −0.841284 −0.420642 0.907227i \(-0.638195\pi\)
−0.420642 + 0.907227i \(0.638195\pi\)
\(374\) 9.51929 0.492231
\(375\) −1.09879 −0.0567414
\(376\) 7.18513 0.370545
\(377\) 19.1511 0.986331
\(378\) −21.8604 −1.12438
\(379\) 2.07245 0.106455 0.0532273 0.998582i \(-0.483049\pi\)
0.0532273 + 0.998582i \(0.483049\pi\)
\(380\) −0.187117 −0.00959888
\(381\) 12.7996 0.655745
\(382\) 1.00262 0.0512987
\(383\) −15.6530 −0.799833 −0.399917 0.916551i \(-0.630961\pi\)
−0.399917 + 0.916551i \(0.630961\pi\)
\(384\) 1.52309 0.0777250
\(385\) −0.356076 −0.0181473
\(386\) −5.49049 −0.279459
\(387\) −3.27968 −0.166715
\(388\) 1.00000 0.0507673
\(389\) 0.655386 0.0332294 0.0166147 0.999862i \(-0.494711\pi\)
0.0166147 + 0.999862i \(0.494711\pi\)
\(390\) −0.416535 −0.0210921
\(391\) −10.9996 −0.556273
\(392\) −8.20984 −0.414660
\(393\) 7.19447 0.362913
\(394\) −3.29099 −0.165797
\(395\) −0.900829 −0.0453256
\(396\) −0.860387 −0.0432361
\(397\) 18.2764 0.917264 0.458632 0.888626i \(-0.348340\pi\)
0.458632 + 0.888626i \(0.348340\pi\)
\(398\) 20.0998 1.00751
\(399\) −15.3988 −0.770902
\(400\) −4.99479 −0.249740
\(401\) 13.3275 0.665545 0.332772 0.943007i \(-0.392016\pi\)
0.332772 + 0.943007i \(0.392016\pi\)
\(402\) 14.0863 0.702560
\(403\) −3.78887 −0.188737
\(404\) −11.6500 −0.579610
\(405\) 0.468936 0.0233016
\(406\) −19.7127 −0.978325
\(407\) −4.04569 −0.200537
\(408\) −11.4622 −0.567461
\(409\) 35.4803 1.75439 0.877194 0.480137i \(-0.159413\pi\)
0.877194 + 0.480137i \(0.159413\pi\)
\(410\) 0.472686 0.0233443
\(411\) −11.2605 −0.555440
\(412\) 11.3568 0.559510
\(413\) 28.5277 1.40375
\(414\) 0.994182 0.0488614
\(415\) −0.00443877 −0.000217891 0
\(416\) −3.78887 −0.185765
\(417\) −6.16628 −0.301964
\(418\) −3.27915 −0.160389
\(419\) 29.6289 1.44747 0.723733 0.690080i \(-0.242425\pi\)
0.723733 + 0.690080i \(0.242425\pi\)
\(420\) 0.428750 0.0209209
\(421\) −15.7535 −0.767778 −0.383889 0.923379i \(-0.625415\pi\)
−0.383889 + 0.923379i \(0.625415\pi\)
\(422\) −12.2752 −0.597547
\(423\) 4.88725 0.237626
\(424\) 6.50668 0.315992
\(425\) 37.5887 1.82332
\(426\) −0.109253 −0.00529334
\(427\) 16.1401 0.781074
\(428\) 17.5759 0.849563
\(429\) −7.29963 −0.352429
\(430\) 0.348030 0.0167835
\(431\) 10.2828 0.495307 0.247653 0.968849i \(-0.420341\pi\)
0.247653 + 0.968849i \(0.420341\pi\)
\(432\) 5.60527 0.269684
\(433\) −3.49173 −0.167802 −0.0839009 0.996474i \(-0.526738\pi\)
−0.0839009 + 0.996474i \(0.526738\pi\)
\(434\) 3.89998 0.187205
\(435\) 0.555681 0.0266429
\(436\) 8.70260 0.416779
\(437\) 3.78908 0.181256
\(438\) −9.83831 −0.470092
\(439\) 1.97908 0.0944563 0.0472281 0.998884i \(-0.484961\pi\)
0.0472281 + 0.998884i \(0.484961\pi\)
\(440\) 0.0913019 0.00435265
\(441\) −5.58424 −0.265916
\(442\) 28.5135 1.35625
\(443\) −14.2391 −0.676520 −0.338260 0.941053i \(-0.609838\pi\)
−0.338260 + 0.941053i \(0.609838\pi\)
\(444\) 4.87141 0.231187
\(445\) −0.404636 −0.0191816
\(446\) −19.9653 −0.945383
\(447\) 30.8981 1.46143
\(448\) 3.89998 0.184257
\(449\) −16.6508 −0.785800 −0.392900 0.919581i \(-0.628528\pi\)
−0.392900 + 0.919581i \(0.628528\pi\)
\(450\) −3.39740 −0.160155
\(451\) 8.28365 0.390062
\(452\) −2.35657 −0.110844
\(453\) 19.3304 0.908221
\(454\) 9.62939 0.451930
\(455\) −1.06657 −0.0500014
\(456\) 3.94842 0.184902
\(457\) 32.8349 1.53595 0.767975 0.640480i \(-0.221265\pi\)
0.767975 + 0.640480i \(0.221265\pi\)
\(458\) −12.8718 −0.601458
\(459\) −42.1829 −1.96893
\(460\) −0.105500 −0.00491896
\(461\) −6.69769 −0.311942 −0.155971 0.987762i \(-0.549851\pi\)
−0.155971 + 0.987762i \(0.549851\pi\)
\(462\) 7.51369 0.349568
\(463\) −27.6004 −1.28270 −0.641350 0.767248i \(-0.721625\pi\)
−0.641350 + 0.767248i \(0.721625\pi\)
\(464\) 5.05456 0.234652
\(465\) −0.109936 −0.00509818
\(466\) 16.1117 0.746359
\(467\) −17.6138 −0.815071 −0.407535 0.913189i \(-0.633612\pi\)
−0.407535 + 0.913189i \(0.633612\pi\)
\(468\) −2.57715 −0.119129
\(469\) 36.0689 1.66551
\(470\) −0.518621 −0.0239222
\(471\) 15.8985 0.732564
\(472\) −7.31482 −0.336692
\(473\) 6.09911 0.280437
\(474\) 19.0087 0.873100
\(475\) −12.9483 −0.594111
\(476\) −29.3496 −1.34524
\(477\) 4.42577 0.202642
\(478\) 7.28439 0.333180
\(479\) 35.7829 1.63496 0.817482 0.575954i \(-0.195369\pi\)
0.817482 + 0.575954i \(0.195369\pi\)
\(480\) −0.109936 −0.00501789
\(481\) −12.1182 −0.552542
\(482\) −15.8406 −0.721520
\(483\) −8.68211 −0.395050
\(484\) −9.39997 −0.427271
\(485\) −0.0721797 −0.00327751
\(486\) 6.92061 0.313925
\(487\) −4.91312 −0.222635 −0.111317 0.993785i \(-0.535507\pi\)
−0.111317 + 0.993785i \(0.535507\pi\)
\(488\) −4.13851 −0.187341
\(489\) −5.07033 −0.229288
\(490\) 0.592584 0.0267702
\(491\) 1.21826 0.0549795 0.0274897 0.999622i \(-0.491249\pi\)
0.0274897 + 0.999622i \(0.491249\pi\)
\(492\) −9.97432 −0.449677
\(493\) −38.0385 −1.71317
\(494\) −9.82215 −0.441920
\(495\) 0.0621025 0.00279130
\(496\) −1.00000 −0.0449013
\(497\) −0.279750 −0.0125485
\(498\) 0.0936643 0.00419720
\(499\) −40.6275 −1.81874 −0.909369 0.415991i \(-0.863435\pi\)
−0.909369 + 0.415991i \(0.863435\pi\)
\(500\) 0.721421 0.0322629
\(501\) 9.96005 0.444982
\(502\) −23.3857 −1.04376
\(503\) −0.804360 −0.0358646 −0.0179323 0.999839i \(-0.505708\pi\)
−0.0179323 + 0.999839i \(0.505708\pi\)
\(504\) 2.65272 0.118162
\(505\) 0.840896 0.0374194
\(506\) −1.84885 −0.0821913
\(507\) −2.06462 −0.0916928
\(508\) −8.40371 −0.372855
\(509\) 20.4784 0.907691 0.453845 0.891080i \(-0.350052\pi\)
0.453845 + 0.891080i \(0.350052\pi\)
\(510\) 0.827336 0.0366350
\(511\) −25.1916 −1.11441
\(512\) −1.00000 −0.0441942
\(513\) 14.5309 0.641556
\(514\) 12.2262 0.539276
\(515\) −0.819732 −0.0361217
\(516\) −7.34392 −0.323298
\(517\) −9.08865 −0.399718
\(518\) 12.4736 0.548057
\(519\) −13.2477 −0.581510
\(520\) 0.273480 0.0119929
\(521\) −7.42604 −0.325341 −0.162670 0.986680i \(-0.552011\pi\)
−0.162670 + 0.986680i \(0.552011\pi\)
\(522\) 3.43806 0.150480
\(523\) −5.87234 −0.256779 −0.128390 0.991724i \(-0.540981\pi\)
−0.128390 + 0.991724i \(0.540981\pi\)
\(524\) −4.72359 −0.206351
\(525\) 29.6692 1.29487
\(526\) −17.1286 −0.746842
\(527\) 7.52558 0.327819
\(528\) −1.92660 −0.0838444
\(529\) −20.8636 −0.907115
\(530\) −0.469650 −0.0204003
\(531\) −4.97546 −0.215916
\(532\) 10.1102 0.438332
\(533\) 24.8123 1.07474
\(534\) 8.53839 0.369492
\(535\) −1.26862 −0.0548474
\(536\) −9.24848 −0.399473
\(537\) −3.71078 −0.160132
\(538\) 5.93482 0.255868
\(539\) 10.3848 0.447306
\(540\) −0.404587 −0.0174106
\(541\) 41.0196 1.76357 0.881784 0.471653i \(-0.156342\pi\)
0.881784 + 0.471653i \(0.156342\pi\)
\(542\) −29.9704 −1.28734
\(543\) −9.81536 −0.421217
\(544\) 7.52558 0.322657
\(545\) −0.628151 −0.0269070
\(546\) 22.5060 0.963168
\(547\) 7.59911 0.324914 0.162457 0.986716i \(-0.448058\pi\)
0.162457 + 0.986716i \(0.448058\pi\)
\(548\) 7.39319 0.315821
\(549\) −2.81497 −0.120140
\(550\) 6.31803 0.269402
\(551\) 13.1033 0.558219
\(552\) 2.22619 0.0947531
\(553\) 48.6731 2.06979
\(554\) 3.95743 0.168135
\(555\) −0.351617 −0.0149253
\(556\) 4.04853 0.171696
\(557\) 10.0402 0.425416 0.212708 0.977116i \(-0.431772\pi\)
0.212708 + 0.977116i \(0.431772\pi\)
\(558\) −0.680188 −0.0287947
\(559\) 18.2689 0.772691
\(560\) −0.281500 −0.0118955
\(561\) 14.4988 0.612138
\(562\) 16.3944 0.691557
\(563\) 36.4540 1.53635 0.768176 0.640238i \(-0.221164\pi\)
0.768176 + 0.640238i \(0.221164\pi\)
\(564\) 10.9436 0.460810
\(565\) 0.170096 0.00715601
\(566\) 12.3852 0.520590
\(567\) −25.3373 −1.06407
\(568\) 0.0717312 0.00300977
\(569\) 1.42838 0.0598808 0.0299404 0.999552i \(-0.490468\pi\)
0.0299404 + 0.999552i \(0.490468\pi\)
\(570\) −0.284996 −0.0119372
\(571\) 45.0446 1.88506 0.942528 0.334126i \(-0.108441\pi\)
0.942528 + 0.334126i \(0.108441\pi\)
\(572\) 4.79264 0.200390
\(573\) 1.52709 0.0637950
\(574\) −25.5399 −1.06602
\(575\) −7.30052 −0.304453
\(576\) −0.680188 −0.0283412
\(577\) 9.06730 0.377477 0.188738 0.982027i \(-0.439560\pi\)
0.188738 + 0.982027i \(0.439560\pi\)
\(578\) −39.6344 −1.64857
\(579\) −8.36252 −0.347535
\(580\) −0.364837 −0.0151490
\(581\) 0.239834 0.00994997
\(582\) 1.52309 0.0631342
\(583\) −8.23045 −0.340871
\(584\) 6.45943 0.267293
\(585\) 0.186018 0.00769089
\(586\) 8.57860 0.354379
\(587\) 11.9782 0.494391 0.247196 0.968966i \(-0.420491\pi\)
0.247196 + 0.968966i \(0.420491\pi\)
\(588\) −12.5043 −0.515671
\(589\) −2.59237 −0.106817
\(590\) 0.527982 0.0217367
\(591\) −5.01248 −0.206186
\(592\) −3.19836 −0.131452
\(593\) 29.6574 1.21789 0.608943 0.793214i \(-0.291594\pi\)
0.608943 + 0.793214i \(0.291594\pi\)
\(594\) −7.09024 −0.290916
\(595\) 2.11845 0.0868479
\(596\) −20.2864 −0.830963
\(597\) 30.6139 1.25294
\(598\) −5.53792 −0.226462
\(599\) 16.8699 0.689284 0.344642 0.938734i \(-0.388000\pi\)
0.344642 + 0.938734i \(0.388000\pi\)
\(600\) −7.60753 −0.310576
\(601\) 18.1570 0.740638 0.370319 0.928905i \(-0.379248\pi\)
0.370319 + 0.928905i \(0.379248\pi\)
\(602\) −18.8046 −0.766418
\(603\) −6.29071 −0.256177
\(604\) −12.6915 −0.516411
\(605\) 0.678487 0.0275844
\(606\) −17.7441 −0.720804
\(607\) −5.14842 −0.208968 −0.104484 0.994527i \(-0.533319\pi\)
−0.104484 + 0.994527i \(0.533319\pi\)
\(608\) −2.59237 −0.105134
\(609\) −30.0243 −1.21664
\(610\) 0.298716 0.0120947
\(611\) −27.2235 −1.10135
\(612\) 5.11881 0.206916
\(613\) 16.8775 0.681676 0.340838 0.940122i \(-0.389289\pi\)
0.340838 + 0.940122i \(0.389289\pi\)
\(614\) −27.5872 −1.11333
\(615\) 0.719944 0.0290310
\(616\) −4.93318 −0.198763
\(617\) 45.9380 1.84939 0.924696 0.380705i \(-0.124319\pi\)
0.924696 + 0.380705i \(0.124319\pi\)
\(618\) 17.2975 0.695807
\(619\) −2.57732 −0.103591 −0.0517957 0.998658i \(-0.516494\pi\)
−0.0517957 + 0.998658i \(0.516494\pi\)
\(620\) 0.0721797 0.00289881
\(621\) 8.19282 0.328766
\(622\) 20.4691 0.820735
\(623\) 21.8631 0.875927
\(624\) −5.77080 −0.231017
\(625\) 24.9219 0.996875
\(626\) −13.7204 −0.548377
\(627\) −4.99445 −0.199459
\(628\) −10.4383 −0.416533
\(629\) 24.0695 0.959716
\(630\) −0.191473 −0.00762846
\(631\) 23.4076 0.931843 0.465922 0.884826i \(-0.345723\pi\)
0.465922 + 0.884826i \(0.345723\pi\)
\(632\) −12.4804 −0.496442
\(633\) −18.6962 −0.743109
\(634\) −23.4019 −0.929408
\(635\) 0.606578 0.0240713
\(636\) 9.91027 0.392968
\(637\) 31.1060 1.23247
\(638\) −6.39364 −0.253127
\(639\) 0.0487907 0.00193013
\(640\) 0.0721797 0.00285316
\(641\) 13.1966 0.521235 0.260618 0.965442i \(-0.416074\pi\)
0.260618 + 0.965442i \(0.416074\pi\)
\(642\) 26.7697 1.05652
\(643\) 39.6538 1.56379 0.781897 0.623408i \(-0.214252\pi\)
0.781897 + 0.623408i \(0.214252\pi\)
\(644\) 5.70032 0.224624
\(645\) 0.530083 0.0208720
\(646\) 19.5091 0.767575
\(647\) 5.80527 0.228229 0.114114 0.993468i \(-0.463597\pi\)
0.114114 + 0.993468i \(0.463597\pi\)
\(648\) 6.49678 0.255218
\(649\) 9.25270 0.363200
\(650\) 18.9246 0.742284
\(651\) 5.94003 0.232808
\(652\) 3.32897 0.130373
\(653\) −2.88821 −0.113024 −0.0565122 0.998402i \(-0.517998\pi\)
−0.0565122 + 0.998402i \(0.517998\pi\)
\(654\) 13.2549 0.518306
\(655\) 0.340948 0.0133219
\(656\) 6.54873 0.255685
\(657\) 4.39363 0.171412
\(658\) 28.0219 1.09241
\(659\) −0.478385 −0.0186352 −0.00931761 0.999957i \(-0.502966\pi\)
−0.00931761 + 0.999957i \(0.502966\pi\)
\(660\) 0.139061 0.00541295
\(661\) −12.5627 −0.488632 −0.244316 0.969696i \(-0.578563\pi\)
−0.244316 + 0.969696i \(0.578563\pi\)
\(662\) −13.8521 −0.538379
\(663\) 43.4286 1.68663
\(664\) −0.0614961 −0.00238651
\(665\) −0.729751 −0.0282985
\(666\) −2.17549 −0.0842985
\(667\) 7.38789 0.286060
\(668\) −6.53936 −0.253015
\(669\) −30.4090 −1.17568
\(670\) 0.667553 0.0257898
\(671\) 5.23490 0.202091
\(672\) 5.94003 0.229142
\(673\) −8.32713 −0.320987 −0.160494 0.987037i \(-0.551309\pi\)
−0.160494 + 0.987037i \(0.551309\pi\)
\(674\) −29.5301 −1.13746
\(675\) −27.9971 −1.07761
\(676\) 1.35554 0.0521362
\(677\) 46.0135 1.76844 0.884221 0.467068i \(-0.154690\pi\)
0.884221 + 0.467068i \(0.154690\pi\)
\(678\) −3.58927 −0.137845
\(679\) 3.89998 0.149667
\(680\) −0.543194 −0.0208306
\(681\) 14.6665 0.562020
\(682\) 1.26492 0.0484365
\(683\) −13.1792 −0.504287 −0.252143 0.967690i \(-0.581135\pi\)
−0.252143 + 0.967690i \(0.581135\pi\)
\(684\) −1.76330 −0.0674215
\(685\) −0.533639 −0.0203893
\(686\) −4.71835 −0.180148
\(687\) −19.6049 −0.747973
\(688\) 4.82172 0.183826
\(689\) −24.6530 −0.939203
\(690\) −0.160686 −0.00611722
\(691\) −46.2645 −1.75998 −0.879991 0.474990i \(-0.842452\pi\)
−0.879991 + 0.474990i \(0.842452\pi\)
\(692\) 8.69790 0.330645
\(693\) −3.35549 −0.127465
\(694\) 7.62554 0.289461
\(695\) −0.292222 −0.0110846
\(696\) 7.69857 0.291814
\(697\) −49.2830 −1.86673
\(698\) −33.1412 −1.25441
\(699\) 24.5396 0.928172
\(700\) −19.4796 −0.736259
\(701\) 31.8234 1.20195 0.600976 0.799267i \(-0.294779\pi\)
0.600976 + 0.799267i \(0.294779\pi\)
\(702\) −21.2376 −0.801563
\(703\) −8.29134 −0.312714
\(704\) 1.26492 0.0476736
\(705\) −0.789908 −0.0297497
\(706\) 4.72300 0.177753
\(707\) −45.4349 −1.70875
\(708\) −11.1412 −0.418710
\(709\) 28.0995 1.05530 0.527649 0.849462i \(-0.323073\pi\)
0.527649 + 0.849462i \(0.323073\pi\)
\(710\) −0.00517754 −0.000194310 0
\(711\) −8.48899 −0.318362
\(712\) −5.60595 −0.210092
\(713\) −1.46163 −0.0547384
\(714\) −44.7022 −1.67294
\(715\) −0.345931 −0.0129371
\(716\) 2.43635 0.0910506
\(717\) 11.0948 0.414343
\(718\) −30.3409 −1.13231
\(719\) −14.9996 −0.559392 −0.279696 0.960089i \(-0.590234\pi\)
−0.279696 + 0.960089i \(0.590234\pi\)
\(720\) 0.0490958 0.00182969
\(721\) 44.2913 1.64950
\(722\) 12.2796 0.457000
\(723\) −24.1267 −0.897282
\(724\) 6.44436 0.239503
\(725\) −25.2465 −0.937631
\(726\) −14.3170 −0.531354
\(727\) −9.74867 −0.361558 −0.180779 0.983524i \(-0.557862\pi\)
−0.180779 + 0.983524i \(0.557862\pi\)
\(728\) −14.7765 −0.547654
\(729\) 30.0311 1.11226
\(730\) −0.466240 −0.0172563
\(731\) −36.2862 −1.34209
\(732\) −6.30333 −0.232978
\(733\) −42.3700 −1.56497 −0.782486 0.622668i \(-0.786049\pi\)
−0.782486 + 0.622668i \(0.786049\pi\)
\(734\) 12.5646 0.463769
\(735\) 0.902561 0.0332915
\(736\) −1.46163 −0.0538763
\(737\) 11.6986 0.430924
\(738\) 4.45437 0.163968
\(739\) −48.5373 −1.78547 −0.892737 0.450578i \(-0.851218\pi\)
−0.892737 + 0.450578i \(0.851218\pi\)
\(740\) 0.230857 0.00848648
\(741\) −14.9601 −0.549571
\(742\) 25.3759 0.931579
\(743\) −24.2013 −0.887860 −0.443930 0.896061i \(-0.646416\pi\)
−0.443930 + 0.896061i \(0.646416\pi\)
\(744\) −1.52309 −0.0558393
\(745\) 1.46427 0.0536466
\(746\) 16.2479 0.594878
\(747\) −0.0418289 −0.00153044
\(748\) −9.51929 −0.348060
\(749\) 68.5456 2.50460
\(750\) 1.09879 0.0401222
\(751\) 43.2325 1.57757 0.788787 0.614666i \(-0.210709\pi\)
0.788787 + 0.614666i \(0.210709\pi\)
\(752\) −7.18513 −0.262015
\(753\) −35.6186 −1.29801
\(754\) −19.1511 −0.697442
\(755\) 0.916072 0.0333393
\(756\) 21.8604 0.795056
\(757\) 44.9322 1.63309 0.816544 0.577283i \(-0.195887\pi\)
0.816544 + 0.577283i \(0.195887\pi\)
\(758\) −2.07245 −0.0752748
\(759\) −2.81597 −0.102213
\(760\) 0.187117 0.00678743
\(761\) −42.8925 −1.55485 −0.777425 0.628976i \(-0.783475\pi\)
−0.777425 + 0.628976i \(0.783475\pi\)
\(762\) −12.7996 −0.463682
\(763\) 33.9399 1.22871
\(764\) −1.00262 −0.0362736
\(765\) −0.369475 −0.0133584
\(766\) 15.6530 0.565568
\(767\) 27.7149 1.00073
\(768\) −1.52309 −0.0549599
\(769\) −24.1125 −0.869521 −0.434760 0.900546i \(-0.643167\pi\)
−0.434760 + 0.900546i \(0.643167\pi\)
\(770\) 0.356076 0.0128321
\(771\) 18.6217 0.670644
\(772\) 5.49049 0.197607
\(773\) 51.7220 1.86031 0.930155 0.367166i \(-0.119672\pi\)
0.930155 + 0.367166i \(0.119672\pi\)
\(774\) 3.27968 0.117886
\(775\) 4.99479 0.179418
\(776\) −1.00000 −0.0358979
\(777\) 18.9984 0.681563
\(778\) −0.655386 −0.0234967
\(779\) 16.9767 0.608255
\(780\) 0.416535 0.0149143
\(781\) −0.0907346 −0.00324674
\(782\) 10.9996 0.393345
\(783\) 28.3322 1.01251
\(784\) 8.20984 0.293209
\(785\) 0.753433 0.0268912
\(786\) −7.19447 −0.256618
\(787\) −27.9081 −0.994815 −0.497408 0.867517i \(-0.665715\pi\)
−0.497408 + 0.867517i \(0.665715\pi\)
\(788\) 3.29099 0.117237
\(789\) −26.0884 −0.928773
\(790\) 0.900829 0.0320501
\(791\) −9.19057 −0.326779
\(792\) 0.860387 0.0305725
\(793\) 15.6803 0.556823
\(794\) −18.2764 −0.648604
\(795\) −0.715321 −0.0253698
\(796\) −20.0998 −0.712419
\(797\) −26.9757 −0.955529 −0.477765 0.878488i \(-0.658553\pi\)
−0.477765 + 0.878488i \(0.658553\pi\)
\(798\) 15.3988 0.545110
\(799\) 54.0723 1.91294
\(800\) 4.99479 0.176592
\(801\) −3.81311 −0.134729
\(802\) −13.3275 −0.470611
\(803\) −8.17069 −0.288337
\(804\) −14.0863 −0.496785
\(805\) −0.411448 −0.0145016
\(806\) 3.78887 0.133457
\(807\) 9.03928 0.318198
\(808\) 11.6500 0.409846
\(809\) 14.0554 0.494162 0.247081 0.968995i \(-0.420529\pi\)
0.247081 + 0.968995i \(0.420529\pi\)
\(810\) −0.468936 −0.0164767
\(811\) −26.7527 −0.939416 −0.469708 0.882822i \(-0.655641\pi\)
−0.469708 + 0.882822i \(0.655641\pi\)
\(812\) 19.7127 0.691780
\(813\) −45.6477 −1.60093
\(814\) 4.04569 0.141801
\(815\) −0.240284 −0.00841679
\(816\) 11.4622 0.401256
\(817\) 12.4997 0.437308
\(818\) −35.4803 −1.24054
\(819\) −10.0508 −0.351204
\(820\) −0.472686 −0.0165069
\(821\) 8.98723 0.313656 0.156828 0.987626i \(-0.449873\pi\)
0.156828 + 0.987626i \(0.449873\pi\)
\(822\) 11.2605 0.392755
\(823\) 5.86772 0.204536 0.102268 0.994757i \(-0.467390\pi\)
0.102268 + 0.994757i \(0.467390\pi\)
\(824\) −11.3568 −0.395633
\(825\) 9.62295 0.335028
\(826\) −28.5277 −0.992604
\(827\) 1.30007 0.0452080 0.0226040 0.999744i \(-0.492804\pi\)
0.0226040 + 0.999744i \(0.492804\pi\)
\(828\) −0.994182 −0.0345502
\(829\) −45.0904 −1.56605 −0.783026 0.621989i \(-0.786325\pi\)
−0.783026 + 0.621989i \(0.786325\pi\)
\(830\) 0.00443877 0.000154072 0
\(831\) 6.02753 0.209093
\(832\) 3.78887 0.131355
\(833\) −61.7838 −2.14068
\(834\) 6.16628 0.213521
\(835\) 0.472009 0.0163345
\(836\) 3.27915 0.113412
\(837\) −5.60527 −0.193746
\(838\) −29.6289 −1.02351
\(839\) 1.74493 0.0602417 0.0301208 0.999546i \(-0.490411\pi\)
0.0301208 + 0.999546i \(0.490411\pi\)
\(840\) −0.428750 −0.0147933
\(841\) −3.45137 −0.119013
\(842\) 15.7535 0.542901
\(843\) 24.9702 0.860021
\(844\) 12.2752 0.422529
\(845\) −0.0978426 −0.00336589
\(846\) −4.88725 −0.168027
\(847\) −36.6597 −1.25964
\(848\) −6.50668 −0.223440
\(849\) 18.8638 0.647405
\(850\) −37.5887 −1.28928
\(851\) −4.67482 −0.160251
\(852\) 0.109253 0.00374296
\(853\) 6.32932 0.216712 0.108356 0.994112i \(-0.465441\pi\)
0.108356 + 0.994112i \(0.465441\pi\)
\(854\) −16.1401 −0.552303
\(855\) 0.127275 0.00435270
\(856\) −17.5759 −0.600732
\(857\) −7.72730 −0.263959 −0.131980 0.991252i \(-0.542133\pi\)
−0.131980 + 0.991252i \(0.542133\pi\)
\(858\) 7.29963 0.249205
\(859\) −45.6097 −1.55618 −0.778091 0.628151i \(-0.783812\pi\)
−0.778091 + 0.628151i \(0.783812\pi\)
\(860\) −0.348030 −0.0118677
\(861\) −38.8997 −1.32570
\(862\) −10.2828 −0.350235
\(863\) −56.3762 −1.91907 −0.959533 0.281595i \(-0.909137\pi\)
−0.959533 + 0.281595i \(0.909137\pi\)
\(864\) −5.60527 −0.190695
\(865\) −0.627812 −0.0213463
\(866\) 3.49173 0.118654
\(867\) −60.3668 −2.05016
\(868\) −3.89998 −0.132374
\(869\) 15.7867 0.535527
\(870\) −0.555681 −0.0188393
\(871\) 35.0413 1.18733
\(872\) −8.70260 −0.294707
\(873\) −0.680188 −0.0230209
\(874\) −3.78908 −0.128168
\(875\) 2.81353 0.0951146
\(876\) 9.83831 0.332406
\(877\) 9.34976 0.315719 0.157860 0.987462i \(-0.449541\pi\)
0.157860 + 0.987462i \(0.449541\pi\)
\(878\) −1.97908 −0.0667907
\(879\) 13.0660 0.440705
\(880\) −0.0913019 −0.00307779
\(881\) 1.16486 0.0392450 0.0196225 0.999807i \(-0.493754\pi\)
0.0196225 + 0.999807i \(0.493754\pi\)
\(882\) 5.58424 0.188031
\(883\) −28.2285 −0.949964 −0.474982 0.879996i \(-0.657545\pi\)
−0.474982 + 0.879996i \(0.657545\pi\)
\(884\) −28.5135 −0.959011
\(885\) 0.804166 0.0270317
\(886\) 14.2391 0.478372
\(887\) 31.5848 1.06051 0.530256 0.847837i \(-0.322096\pi\)
0.530256 + 0.847837i \(0.322096\pi\)
\(888\) −4.87141 −0.163474
\(889\) −32.7743 −1.09922
\(890\) 0.404636 0.0135634
\(891\) −8.21793 −0.275311
\(892\) 19.9653 0.668487
\(893\) −18.6265 −0.623313
\(894\) −30.8981 −1.03339
\(895\) −0.175855 −0.00587818
\(896\) −3.89998 −0.130289
\(897\) −8.43476 −0.281629
\(898\) 16.6508 0.555644
\(899\) −5.05456 −0.168579
\(900\) 3.39740 0.113247
\(901\) 48.9665 1.63131
\(902\) −8.28365 −0.275815
\(903\) −28.6412 −0.953118
\(904\) 2.35657 0.0783783
\(905\) −0.465152 −0.0154622
\(906\) −19.3304 −0.642209
\(907\) 38.3482 1.27333 0.636666 0.771140i \(-0.280313\pi\)
0.636666 + 0.771140i \(0.280313\pi\)
\(908\) −9.62939 −0.319563
\(909\) 7.92421 0.262830
\(910\) 1.06657 0.0353563
\(911\) 12.2582 0.406132 0.203066 0.979165i \(-0.434909\pi\)
0.203066 + 0.979165i \(0.434909\pi\)
\(912\) −3.94842 −0.130745
\(913\) 0.0777879 0.00257440
\(914\) −32.8349 −1.08608
\(915\) 0.454973 0.0150409
\(916\) 12.8718 0.425295
\(917\) −18.4219 −0.608345
\(918\) 42.1829 1.39224
\(919\) −31.2508 −1.03087 −0.515434 0.856929i \(-0.672369\pi\)
−0.515434 + 0.856929i \(0.672369\pi\)
\(920\) 0.105500 0.00347823
\(921\) −42.0179 −1.38454
\(922\) 6.69769 0.220577
\(923\) −0.271780 −0.00894576
\(924\) −7.51369 −0.247182
\(925\) 15.9752 0.525260
\(926\) 27.6004 0.907006
\(927\) −7.72477 −0.253715
\(928\) −5.05456 −0.165924
\(929\) 41.9899 1.37764 0.688822 0.724931i \(-0.258128\pi\)
0.688822 + 0.724931i \(0.258128\pi\)
\(930\) 0.109936 0.00360496
\(931\) 21.2829 0.697520
\(932\) −16.1117 −0.527755
\(933\) 31.1763 1.02067
\(934\) 17.6138 0.576342
\(935\) 0.687100 0.0224706
\(936\) 2.57715 0.0842367
\(937\) −38.5166 −1.25828 −0.629141 0.777291i \(-0.716593\pi\)
−0.629141 + 0.777291i \(0.716593\pi\)
\(938\) −36.0689 −1.17769
\(939\) −20.8974 −0.681961
\(940\) 0.518621 0.0169156
\(941\) 40.9593 1.33524 0.667618 0.744504i \(-0.267314\pi\)
0.667618 + 0.744504i \(0.267314\pi\)
\(942\) −15.8985 −0.518001
\(943\) 9.57181 0.311701
\(944\) 7.31482 0.238077
\(945\) −1.57788 −0.0513285
\(946\) −6.09911 −0.198299
\(947\) −25.3440 −0.823570 −0.411785 0.911281i \(-0.635095\pi\)
−0.411785 + 0.911281i \(0.635095\pi\)
\(948\) −19.0087 −0.617375
\(949\) −24.4739 −0.794458
\(950\) 12.9483 0.420100
\(951\) −35.6433 −1.15581
\(952\) 29.3496 0.951226
\(953\) 45.2715 1.46649 0.733244 0.679965i \(-0.238005\pi\)
0.733244 + 0.679965i \(0.238005\pi\)
\(954\) −4.42577 −0.143289
\(955\) 0.0723691 0.00234181
\(956\) −7.28439 −0.235594
\(957\) −9.73811 −0.314788
\(958\) −35.7829 −1.15609
\(959\) 28.8333 0.931075
\(960\) 0.109936 0.00354818
\(961\) 1.00000 0.0322581
\(962\) 12.1182 0.390706
\(963\) −11.9549 −0.385242
\(964\) 15.8406 0.510191
\(965\) −0.396302 −0.0127574
\(966\) 8.68211 0.279342
\(967\) −53.6869 −1.72645 −0.863227 0.504816i \(-0.831560\pi\)
−0.863227 + 0.504816i \(0.831560\pi\)
\(968\) 9.39997 0.302126
\(969\) 29.7141 0.954556
\(970\) 0.0721797 0.00231755
\(971\) −16.5124 −0.529907 −0.264954 0.964261i \(-0.585357\pi\)
−0.264954 + 0.964261i \(0.585357\pi\)
\(972\) −6.92061 −0.221979
\(973\) 15.7892 0.506178
\(974\) 4.91312 0.157426
\(975\) 28.8239 0.923105
\(976\) 4.13851 0.132470
\(977\) −21.2877 −0.681055 −0.340528 0.940235i \(-0.610606\pi\)
−0.340528 + 0.940235i \(0.610606\pi\)
\(978\) 5.07033 0.162131
\(979\) 7.09111 0.226633
\(980\) −0.592584 −0.0189294
\(981\) −5.91940 −0.188992
\(982\) −1.21826 −0.0388764
\(983\) 27.4940 0.876923 0.438461 0.898750i \(-0.355524\pi\)
0.438461 + 0.898750i \(0.355524\pi\)
\(984\) 9.97432 0.317970
\(985\) −0.237543 −0.00756873
\(986\) 38.0385 1.21139
\(987\) 42.6799 1.35852
\(988\) 9.82215 0.312484
\(989\) 7.04756 0.224099
\(990\) −0.0621025 −0.00197375
\(991\) 48.3298 1.53525 0.767623 0.640901i \(-0.221439\pi\)
0.767623 + 0.640901i \(0.221439\pi\)
\(992\) 1.00000 0.0317500
\(993\) −21.0981 −0.669528
\(994\) 0.279750 0.00887314
\(995\) 1.45080 0.0459935
\(996\) −0.0936643 −0.00296787
\(997\) −8.32851 −0.263766 −0.131883 0.991265i \(-0.542102\pi\)
−0.131883 + 0.991265i \(0.542102\pi\)
\(998\) 40.6275 1.28604
\(999\) −17.9277 −0.567207
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 6014.2.a.j.1.10 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6014.2.a.j.1.10 32 1.1 even 1 trivial