Properties

Label 4006.2.a.i.1.1
Level $4006$
Weight $2$
Character 4006.1
Self dual yes
Analytic conductor $31.988$
Analytic rank $0$
Dimension $46$
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] = [4006,2,Mod(1,4006)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4006, 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("4006.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4006 = 2 \cdot 2003 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4006.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: \(31.9880710497\)
Analytic rank: \(0\)
Dimension: \(46\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 4006.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -3.34123 q^{3} +1.00000 q^{4} -1.21966 q^{5} -3.34123 q^{6} +1.21220 q^{7} +1.00000 q^{8} +8.16382 q^{9} +O(q^{10})\) \(q+1.00000 q^{2} -3.34123 q^{3} +1.00000 q^{4} -1.21966 q^{5} -3.34123 q^{6} +1.21220 q^{7} +1.00000 q^{8} +8.16382 q^{9} -1.21966 q^{10} -1.48208 q^{11} -3.34123 q^{12} -2.69785 q^{13} +1.21220 q^{14} +4.07517 q^{15} +1.00000 q^{16} +2.46441 q^{17} +8.16382 q^{18} +6.34284 q^{19} -1.21966 q^{20} -4.05023 q^{21} -1.48208 q^{22} -0.258764 q^{23} -3.34123 q^{24} -3.51243 q^{25} -2.69785 q^{26} -17.2535 q^{27} +1.21220 q^{28} -0.940582 q^{29} +4.07517 q^{30} +5.09661 q^{31} +1.00000 q^{32} +4.95196 q^{33} +2.46441 q^{34} -1.47847 q^{35} +8.16382 q^{36} +0.621932 q^{37} +6.34284 q^{38} +9.01416 q^{39} -1.21966 q^{40} +2.70955 q^{41} -4.05023 q^{42} -0.396684 q^{43} -1.48208 q^{44} -9.95710 q^{45} -0.258764 q^{46} -6.14729 q^{47} -3.34123 q^{48} -5.53058 q^{49} -3.51243 q^{50} -8.23415 q^{51} -2.69785 q^{52} -10.2505 q^{53} -17.2535 q^{54} +1.80763 q^{55} +1.21220 q^{56} -21.1929 q^{57} -0.940582 q^{58} +2.37335 q^{59} +4.07517 q^{60} -0.765657 q^{61} +5.09661 q^{62} +9.89616 q^{63} +1.00000 q^{64} +3.29047 q^{65} +4.95196 q^{66} -6.41950 q^{67} +2.46441 q^{68} +0.864591 q^{69} -1.47847 q^{70} +10.3122 q^{71} +8.16382 q^{72} +10.5627 q^{73} +0.621932 q^{74} +11.7358 q^{75} +6.34284 q^{76} -1.79657 q^{77} +9.01416 q^{78} -8.44573 q^{79} -1.21966 q^{80} +33.1566 q^{81} +2.70955 q^{82} +10.3832 q^{83} -4.05023 q^{84} -3.00574 q^{85} -0.396684 q^{86} +3.14270 q^{87} -1.48208 q^{88} +17.4152 q^{89} -9.95710 q^{90} -3.27033 q^{91} -0.258764 q^{92} -17.0289 q^{93} -6.14729 q^{94} -7.73611 q^{95} -3.34123 q^{96} +4.34938 q^{97} -5.53058 q^{98} -12.0994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 46 q + 46 q^{2} + 21 q^{3} + 46 q^{4} + 23 q^{5} + 21 q^{6} + 26 q^{7} + 46 q^{8} + 59 q^{9} + 23 q^{10} + 39 q^{11} + 21 q^{12} + 8 q^{13} + 26 q^{14} + 14 q^{15} + 46 q^{16} + 36 q^{17} + 59 q^{18} + 37 q^{19} + 23 q^{20} + 20 q^{21} + 39 q^{22} + 38 q^{23} + 21 q^{24} + 57 q^{25} + 8 q^{26} + 63 q^{27} + 26 q^{28} + 23 q^{29} + 14 q^{30} + 44 q^{31} + 46 q^{32} + 25 q^{33} + 36 q^{34} + 26 q^{35} + 59 q^{36} + 9 q^{37} + 37 q^{38} - 2 q^{39} + 23 q^{40} + 50 q^{41} + 20 q^{42} + 46 q^{43} + 39 q^{44} + 30 q^{45} + 38 q^{46} + 57 q^{47} + 21 q^{48} + 62 q^{49} + 57 q^{50} + 5 q^{51} + 8 q^{52} + 21 q^{53} + 63 q^{54} + 40 q^{55} + 26 q^{56} + 3 q^{57} + 23 q^{58} + 68 q^{59} + 14 q^{60} - q^{61} + 44 q^{62} + 40 q^{63} + 46 q^{64} + 18 q^{65} + 25 q^{66} + 42 q^{67} + 36 q^{68} - 7 q^{69} + 26 q^{70} + 67 q^{71} + 59 q^{72} + 48 q^{73} + 9 q^{74} + 71 q^{75} + 37 q^{76} - 5 q^{77} - 2 q^{78} + 40 q^{79} + 23 q^{80} + 82 q^{81} + 50 q^{82} + 48 q^{83} + 20 q^{84} - 68 q^{85} + 46 q^{86} + 18 q^{87} + 39 q^{88} + 90 q^{89} + 30 q^{90} + 9 q^{91} + 38 q^{92} - 42 q^{93} + 57 q^{94} + 6 q^{95} + 21 q^{96} + 46 q^{97} + 62 q^{98} + 61 q^{99}+O(q^{100}) \) 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
\(3\) −3.34123 −1.92906 −0.964530 0.263972i \(-0.914967\pi\)
−0.964530 + 0.263972i \(0.914967\pi\)
\(4\) 1.00000 0.500000
\(5\) −1.21966 −0.545449 −0.272724 0.962092i \(-0.587925\pi\)
−0.272724 + 0.962092i \(0.587925\pi\)
\(6\) −3.34123 −1.36405
\(7\) 1.21220 0.458167 0.229084 0.973407i \(-0.426427\pi\)
0.229084 + 0.973407i \(0.426427\pi\)
\(8\) 1.00000 0.353553
\(9\) 8.16382 2.72127
\(10\) −1.21966 −0.385691
\(11\) −1.48208 −0.446863 −0.223432 0.974720i \(-0.571726\pi\)
−0.223432 + 0.974720i \(0.571726\pi\)
\(12\) −3.34123 −0.964530
\(13\) −2.69785 −0.748250 −0.374125 0.927378i \(-0.622057\pi\)
−0.374125 + 0.927378i \(0.622057\pi\)
\(14\) 1.21220 0.323973
\(15\) 4.07517 1.05220
\(16\) 1.00000 0.250000
\(17\) 2.46441 0.597706 0.298853 0.954299i \(-0.403396\pi\)
0.298853 + 0.954299i \(0.403396\pi\)
\(18\) 8.16382 1.92423
\(19\) 6.34284 1.45515 0.727574 0.686030i \(-0.240648\pi\)
0.727574 + 0.686030i \(0.240648\pi\)
\(20\) −1.21966 −0.272724
\(21\) −4.05023 −0.883833
\(22\) −1.48208 −0.315980
\(23\) −0.258764 −0.0539561 −0.0269780 0.999636i \(-0.508588\pi\)
−0.0269780 + 0.999636i \(0.508588\pi\)
\(24\) −3.34123 −0.682026
\(25\) −3.51243 −0.702485
\(26\) −2.69785 −0.529093
\(27\) −17.2535 −3.32044
\(28\) 1.21220 0.229084
\(29\) −0.940582 −0.174662 −0.0873309 0.996179i \(-0.527834\pi\)
−0.0873309 + 0.996179i \(0.527834\pi\)
\(30\) 4.07517 0.744021
\(31\) 5.09661 0.915378 0.457689 0.889112i \(-0.348677\pi\)
0.457689 + 0.889112i \(0.348677\pi\)
\(32\) 1.00000 0.176777
\(33\) 4.95196 0.862026
\(34\) 2.46441 0.422642
\(35\) −1.47847 −0.249907
\(36\) 8.16382 1.36064
\(37\) 0.621932 0.102245 0.0511225 0.998692i \(-0.483720\pi\)
0.0511225 + 0.998692i \(0.483720\pi\)
\(38\) 6.34284 1.02894
\(39\) 9.01416 1.44342
\(40\) −1.21966 −0.192845
\(41\) 2.70955 0.423160 0.211580 0.977361i \(-0.432139\pi\)
0.211580 + 0.977361i \(0.432139\pi\)
\(42\) −4.05023 −0.624964
\(43\) −0.396684 −0.0604937 −0.0302469 0.999542i \(-0.509629\pi\)
−0.0302469 + 0.999542i \(0.509629\pi\)
\(44\) −1.48208 −0.223432
\(45\) −9.95710 −1.48432
\(46\) −0.258764 −0.0381527
\(47\) −6.14729 −0.896674 −0.448337 0.893865i \(-0.647984\pi\)
−0.448337 + 0.893865i \(0.647984\pi\)
\(48\) −3.34123 −0.482265
\(49\) −5.53058 −0.790083
\(50\) −3.51243 −0.496732
\(51\) −8.23415 −1.15301
\(52\) −2.69785 −0.374125
\(53\) −10.2505 −1.40801 −0.704005 0.710195i \(-0.748607\pi\)
−0.704005 + 0.710195i \(0.748607\pi\)
\(54\) −17.2535 −2.34791
\(55\) 1.80763 0.243741
\(56\) 1.21220 0.161987
\(57\) −21.1929 −2.80707
\(58\) −0.940582 −0.123505
\(59\) 2.37335 0.308984 0.154492 0.987994i \(-0.450626\pi\)
0.154492 + 0.987994i \(0.450626\pi\)
\(60\) 4.07517 0.526102
\(61\) −0.765657 −0.0980324 −0.0490162 0.998798i \(-0.515609\pi\)
−0.0490162 + 0.998798i \(0.515609\pi\)
\(62\) 5.09661 0.647270
\(63\) 9.89616 1.24680
\(64\) 1.00000 0.125000
\(65\) 3.29047 0.408132
\(66\) 4.95196 0.609545
\(67\) −6.41950 −0.784267 −0.392134 0.919908i \(-0.628263\pi\)
−0.392134 + 0.919908i \(0.628263\pi\)
\(68\) 2.46441 0.298853
\(69\) 0.864591 0.104085
\(70\) −1.47847 −0.176711
\(71\) 10.3122 1.22383 0.611915 0.790924i \(-0.290400\pi\)
0.611915 + 0.790924i \(0.290400\pi\)
\(72\) 8.16382 0.962116
\(73\) 10.5627 1.23627 0.618137 0.786070i \(-0.287888\pi\)
0.618137 + 0.786070i \(0.287888\pi\)
\(74\) 0.621932 0.0722981
\(75\) 11.7358 1.35514
\(76\) 6.34284 0.727574
\(77\) −1.79657 −0.204738
\(78\) 9.01416 1.02065
\(79\) −8.44573 −0.950219 −0.475110 0.879927i \(-0.657592\pi\)
−0.475110 + 0.879927i \(0.657592\pi\)
\(80\) −1.21966 −0.136362
\(81\) 33.1566 3.68406
\(82\) 2.70955 0.299219
\(83\) 10.3832 1.13970 0.569851 0.821748i \(-0.307001\pi\)
0.569851 + 0.821748i \(0.307001\pi\)
\(84\) −4.05023 −0.441916
\(85\) −3.00574 −0.326018
\(86\) −0.396684 −0.0427755
\(87\) 3.14270 0.336933
\(88\) −1.48208 −0.157990
\(89\) 17.4152 1.84601 0.923005 0.384787i \(-0.125725\pi\)
0.923005 + 0.384787i \(0.125725\pi\)
\(90\) −9.95710 −1.04957
\(91\) −3.27033 −0.342824
\(92\) −0.258764 −0.0269780
\(93\) −17.0289 −1.76582
\(94\) −6.14729 −0.634045
\(95\) −7.73611 −0.793709
\(96\) −3.34123 −0.341013
\(97\) 4.34938 0.441613 0.220806 0.975318i \(-0.429131\pi\)
0.220806 + 0.975318i \(0.429131\pi\)
\(98\) −5.53058 −0.558673
\(99\) −12.0994 −1.21604
\(100\) −3.51243 −0.351243
\(101\) 4.89335 0.486906 0.243453 0.969913i \(-0.421720\pi\)
0.243453 + 0.969913i \(0.421720\pi\)
\(102\) −8.23415 −0.815302
\(103\) −16.7617 −1.65158 −0.825789 0.563979i \(-0.809270\pi\)
−0.825789 + 0.563979i \(0.809270\pi\)
\(104\) −2.69785 −0.264546
\(105\) 4.93991 0.482086
\(106\) −10.2505 −0.995613
\(107\) 12.3674 1.19560 0.597800 0.801646i \(-0.296042\pi\)
0.597800 + 0.801646i \(0.296042\pi\)
\(108\) −17.2535 −1.66022
\(109\) −15.2467 −1.46037 −0.730183 0.683251i \(-0.760565\pi\)
−0.730183 + 0.683251i \(0.760565\pi\)
\(110\) 1.80763 0.172351
\(111\) −2.07802 −0.197237
\(112\) 1.21220 0.114542
\(113\) 4.39295 0.413254 0.206627 0.978420i \(-0.433751\pi\)
0.206627 + 0.978420i \(0.433751\pi\)
\(114\) −21.1929 −1.98490
\(115\) 0.315605 0.0294303
\(116\) −0.940582 −0.0873309
\(117\) −22.0248 −2.03619
\(118\) 2.37335 0.218484
\(119\) 2.98735 0.273850
\(120\) 4.07517 0.372010
\(121\) −8.80345 −0.800313
\(122\) −0.765657 −0.0693194
\(123\) −9.05322 −0.816301
\(124\) 5.09661 0.457689
\(125\) 10.3823 0.928619
\(126\) 9.89616 0.881620
\(127\) 9.72778 0.863201 0.431600 0.902065i \(-0.357949\pi\)
0.431600 + 0.902065i \(0.357949\pi\)
\(128\) 1.00000 0.0883883
\(129\) 1.32541 0.116696
\(130\) 3.29047 0.288593
\(131\) 12.3774 1.08142 0.540711 0.841209i \(-0.318155\pi\)
0.540711 + 0.841209i \(0.318155\pi\)
\(132\) 4.95196 0.431013
\(133\) 7.68877 0.666701
\(134\) −6.41950 −0.554561
\(135\) 21.0435 1.81113
\(136\) 2.46441 0.211321
\(137\) −0.763945 −0.0652682 −0.0326341 0.999467i \(-0.510390\pi\)
−0.0326341 + 0.999467i \(0.510390\pi\)
\(138\) 0.864591 0.0735989
\(139\) 5.36732 0.455250 0.227625 0.973749i \(-0.426904\pi\)
0.227625 + 0.973749i \(0.426904\pi\)
\(140\) −1.47847 −0.124953
\(141\) 20.5395 1.72974
\(142\) 10.3122 0.865378
\(143\) 3.99843 0.334366
\(144\) 8.16382 0.680319
\(145\) 1.14719 0.0952691
\(146\) 10.5627 0.874178
\(147\) 18.4789 1.52412
\(148\) 0.621932 0.0511225
\(149\) −18.6843 −1.53068 −0.765339 0.643628i \(-0.777429\pi\)
−0.765339 + 0.643628i \(0.777429\pi\)
\(150\) 11.7358 0.958227
\(151\) 16.3982 1.33447 0.667234 0.744848i \(-0.267478\pi\)
0.667234 + 0.744848i \(0.267478\pi\)
\(152\) 6.34284 0.514472
\(153\) 20.1190 1.62652
\(154\) −1.79657 −0.144772
\(155\) −6.21613 −0.499292
\(156\) 9.01416 0.721710
\(157\) 11.5783 0.924046 0.462023 0.886868i \(-0.347124\pi\)
0.462023 + 0.886868i \(0.347124\pi\)
\(158\) −8.44573 −0.671907
\(159\) 34.2492 2.71614
\(160\) −1.21966 −0.0964227
\(161\) −0.313673 −0.0247209
\(162\) 33.1566 2.60502
\(163\) 2.77315 0.217210 0.108605 0.994085i \(-0.465362\pi\)
0.108605 + 0.994085i \(0.465362\pi\)
\(164\) 2.70955 0.211580
\(165\) −6.03972 −0.470191
\(166\) 10.3832 0.805891
\(167\) 13.3818 1.03551 0.517756 0.855529i \(-0.326768\pi\)
0.517756 + 0.855529i \(0.326768\pi\)
\(168\) −4.05023 −0.312482
\(169\) −5.72158 −0.440121
\(170\) −3.00574 −0.230530
\(171\) 51.7818 3.95986
\(172\) −0.396684 −0.0302469
\(173\) −11.2336 −0.854072 −0.427036 0.904235i \(-0.640442\pi\)
−0.427036 + 0.904235i \(0.640442\pi\)
\(174\) 3.14270 0.238248
\(175\) −4.25775 −0.321856
\(176\) −1.48208 −0.111716
\(177\) −7.92990 −0.596048
\(178\) 17.4152 1.30533
\(179\) 4.85748 0.363065 0.181533 0.983385i \(-0.441894\pi\)
0.181533 + 0.983385i \(0.441894\pi\)
\(180\) −9.95710 −0.742158
\(181\) 11.3297 0.842127 0.421064 0.907031i \(-0.361657\pi\)
0.421064 + 0.907031i \(0.361657\pi\)
\(182\) −3.27033 −0.242413
\(183\) 2.55824 0.189110
\(184\) −0.258764 −0.0190764
\(185\) −0.758546 −0.0557694
\(186\) −17.0289 −1.24862
\(187\) −3.65244 −0.267093
\(188\) −6.14729 −0.448337
\(189\) −20.9147 −1.52132
\(190\) −7.73611 −0.561237
\(191\) 18.9452 1.37082 0.685412 0.728155i \(-0.259622\pi\)
0.685412 + 0.728155i \(0.259622\pi\)
\(192\) −3.34123 −0.241133
\(193\) −8.34283 −0.600530 −0.300265 0.953856i \(-0.597075\pi\)
−0.300265 + 0.953856i \(0.597075\pi\)
\(194\) 4.34938 0.312267
\(195\) −10.9942 −0.787312
\(196\) −5.53058 −0.395041
\(197\) 11.5578 0.823456 0.411728 0.911307i \(-0.364925\pi\)
0.411728 + 0.911307i \(0.364925\pi\)
\(198\) −12.0994 −0.859869
\(199\) 18.1935 1.28970 0.644851 0.764308i \(-0.276919\pi\)
0.644851 + 0.764308i \(0.276919\pi\)
\(200\) −3.51243 −0.248366
\(201\) 21.4490 1.51290
\(202\) 4.89335 0.344295
\(203\) −1.14017 −0.0800243
\(204\) −8.23415 −0.576506
\(205\) −3.30473 −0.230812
\(206\) −16.7617 −1.16784
\(207\) −2.11251 −0.146829
\(208\) −2.69785 −0.187063
\(209\) −9.40058 −0.650252
\(210\) 4.93991 0.340886
\(211\) 16.2521 1.11884 0.559420 0.828885i \(-0.311024\pi\)
0.559420 + 0.828885i \(0.311024\pi\)
\(212\) −10.2505 −0.704005
\(213\) −34.4553 −2.36084
\(214\) 12.3674 0.845416
\(215\) 0.483820 0.0329962
\(216\) −17.2535 −1.17395
\(217\) 6.17809 0.419396
\(218\) −15.2467 −1.03263
\(219\) −35.2925 −2.38485
\(220\) 1.80763 0.121871
\(221\) −6.64861 −0.447234
\(222\) −2.07802 −0.139467
\(223\) 25.1112 1.68157 0.840784 0.541371i \(-0.182095\pi\)
0.840784 + 0.541371i \(0.182095\pi\)
\(224\) 1.21220 0.0809933
\(225\) −28.6748 −1.91166
\(226\) 4.39295 0.292215
\(227\) −7.01735 −0.465758 −0.232879 0.972506i \(-0.574815\pi\)
−0.232879 + 0.972506i \(0.574815\pi\)
\(228\) −21.1929 −1.40353
\(229\) 1.11907 0.0739500 0.0369750 0.999316i \(-0.488228\pi\)
0.0369750 + 0.999316i \(0.488228\pi\)
\(230\) 0.315605 0.0208104
\(231\) 6.00276 0.394952
\(232\) −0.940582 −0.0617523
\(233\) 12.2990 0.805737 0.402868 0.915258i \(-0.368013\pi\)
0.402868 + 0.915258i \(0.368013\pi\)
\(234\) −22.0248 −1.43981
\(235\) 7.49761 0.489090
\(236\) 2.37335 0.154492
\(237\) 28.2191 1.83303
\(238\) 2.98735 0.193641
\(239\) 25.8095 1.66948 0.834739 0.550646i \(-0.185619\pi\)
0.834739 + 0.550646i \(0.185619\pi\)
\(240\) 4.07517 0.263051
\(241\) 14.9085 0.960342 0.480171 0.877175i \(-0.340575\pi\)
0.480171 + 0.877175i \(0.340575\pi\)
\(242\) −8.80345 −0.565907
\(243\) −59.0231 −3.78633
\(244\) −0.765657 −0.0490162
\(245\) 6.74543 0.430950
\(246\) −9.05322 −0.577212
\(247\) −17.1121 −1.08881
\(248\) 5.09661 0.323635
\(249\) −34.6926 −2.19856
\(250\) 10.3823 0.656633
\(251\) 19.2015 1.21199 0.605993 0.795470i \(-0.292776\pi\)
0.605993 + 0.795470i \(0.292776\pi\)
\(252\) 9.89616 0.623400
\(253\) 0.383509 0.0241110
\(254\) 9.72778 0.610375
\(255\) 10.0429 0.628909
\(256\) 1.00000 0.0625000
\(257\) 4.60640 0.287340 0.143670 0.989626i \(-0.454110\pi\)
0.143670 + 0.989626i \(0.454110\pi\)
\(258\) 1.32541 0.0825166
\(259\) 0.753903 0.0468453
\(260\) 3.29047 0.204066
\(261\) −7.67875 −0.475303
\(262\) 12.3774 0.764680
\(263\) 9.92093 0.611751 0.305875 0.952072i \(-0.401051\pi\)
0.305875 + 0.952072i \(0.401051\pi\)
\(264\) 4.95196 0.304772
\(265\) 12.5021 0.767997
\(266\) 7.68877 0.471429
\(267\) −58.1883 −3.56107
\(268\) −6.41950 −0.392134
\(269\) −1.01115 −0.0616510 −0.0308255 0.999525i \(-0.509814\pi\)
−0.0308255 + 0.999525i \(0.509814\pi\)
\(270\) 21.0435 1.28066
\(271\) −4.03444 −0.245075 −0.122537 0.992464i \(-0.539103\pi\)
−0.122537 + 0.992464i \(0.539103\pi\)
\(272\) 2.46441 0.149427
\(273\) 10.9269 0.661328
\(274\) −0.763945 −0.0461516
\(275\) 5.20569 0.313915
\(276\) 0.864591 0.0520423
\(277\) −12.7012 −0.763144 −0.381572 0.924339i \(-0.624617\pi\)
−0.381572 + 0.924339i \(0.624617\pi\)
\(278\) 5.36732 0.321911
\(279\) 41.6078 2.49099
\(280\) −1.47847 −0.0883554
\(281\) 15.4255 0.920206 0.460103 0.887866i \(-0.347812\pi\)
0.460103 + 0.887866i \(0.347812\pi\)
\(282\) 20.5395 1.22311
\(283\) −21.1494 −1.25720 −0.628600 0.777729i \(-0.716372\pi\)
−0.628600 + 0.777729i \(0.716372\pi\)
\(284\) 10.3122 0.611915
\(285\) 25.8481 1.53111
\(286\) 3.99843 0.236432
\(287\) 3.28450 0.193878
\(288\) 8.16382 0.481058
\(289\) −10.9267 −0.642747
\(290\) 1.14719 0.0673654
\(291\) −14.5323 −0.851897
\(292\) 10.5627 0.618137
\(293\) −0.915584 −0.0534890 −0.0267445 0.999642i \(-0.508514\pi\)
−0.0267445 + 0.999642i \(0.508514\pi\)
\(294\) 18.4789 1.07771
\(295\) −2.89468 −0.168535
\(296\) 0.621932 0.0361490
\(297\) 25.5711 1.48378
\(298\) −18.6843 −1.08235
\(299\) 0.698109 0.0403727
\(300\) 11.7358 0.677568
\(301\) −0.480859 −0.0277163
\(302\) 16.3982 0.943611
\(303\) −16.3498 −0.939272
\(304\) 6.34284 0.363787
\(305\) 0.933842 0.0534717
\(306\) 20.1190 1.15013
\(307\) −6.21151 −0.354510 −0.177255 0.984165i \(-0.556722\pi\)
−0.177255 + 0.984165i \(0.556722\pi\)
\(308\) −1.79657 −0.102369
\(309\) 56.0047 3.18599
\(310\) −6.21613 −0.353053
\(311\) 0.368999 0.0209240 0.0104620 0.999945i \(-0.496670\pi\)
0.0104620 + 0.999945i \(0.496670\pi\)
\(312\) 9.01416 0.510326
\(313\) 2.93116 0.165679 0.0828394 0.996563i \(-0.473601\pi\)
0.0828394 + 0.996563i \(0.473601\pi\)
\(314\) 11.5783 0.653399
\(315\) −12.0700 −0.680065
\(316\) −8.44573 −0.475110
\(317\) −1.58766 −0.0891718 −0.0445859 0.999006i \(-0.514197\pi\)
−0.0445859 + 0.999006i \(0.514197\pi\)
\(318\) 34.2492 1.92060
\(319\) 1.39402 0.0780499
\(320\) −1.21966 −0.0681811
\(321\) −41.3223 −2.30638
\(322\) −0.313673 −0.0174803
\(323\) 15.6313 0.869751
\(324\) 33.1566 1.84203
\(325\) 9.47602 0.525635
\(326\) 2.77315 0.153590
\(327\) 50.9427 2.81714
\(328\) 2.70955 0.149610
\(329\) −7.45173 −0.410827
\(330\) −6.03972 −0.332476
\(331\) 11.4159 0.627474 0.313737 0.949510i \(-0.398419\pi\)
0.313737 + 0.949510i \(0.398419\pi\)
\(332\) 10.3832 0.569851
\(333\) 5.07734 0.278236
\(334\) 13.3818 0.732217
\(335\) 7.82962 0.427778
\(336\) −4.05023 −0.220958
\(337\) −16.0047 −0.871834 −0.435917 0.899987i \(-0.643576\pi\)
−0.435917 + 0.899987i \(0.643576\pi\)
\(338\) −5.72158 −0.311213
\(339\) −14.6779 −0.797192
\(340\) −3.00574 −0.163009
\(341\) −7.55357 −0.409049
\(342\) 51.7818 2.80004
\(343\) −15.1895 −0.820157
\(344\) −0.396684 −0.0213878
\(345\) −1.05451 −0.0567728
\(346\) −11.2336 −0.603920
\(347\) 14.1373 0.758927 0.379464 0.925207i \(-0.376109\pi\)
0.379464 + 0.925207i \(0.376109\pi\)
\(348\) 3.14270 0.168467
\(349\) −16.1681 −0.865456 −0.432728 0.901524i \(-0.642449\pi\)
−0.432728 + 0.901524i \(0.642449\pi\)
\(350\) −4.25775 −0.227586
\(351\) 46.5475 2.48452
\(352\) −1.48208 −0.0789950
\(353\) −3.51525 −0.187098 −0.0935488 0.995615i \(-0.529821\pi\)
−0.0935488 + 0.995615i \(0.529821\pi\)
\(354\) −7.92990 −0.421470
\(355\) −12.5774 −0.667536
\(356\) 17.4152 0.923005
\(357\) −9.98141 −0.528272
\(358\) 4.85748 0.256726
\(359\) −21.8168 −1.15145 −0.575723 0.817645i \(-0.695279\pi\)
−0.575723 + 0.817645i \(0.695279\pi\)
\(360\) −9.95710 −0.524785
\(361\) 21.2316 1.11745
\(362\) 11.3297 0.595474
\(363\) 29.4143 1.54385
\(364\) −3.27033 −0.171412
\(365\) −12.8829 −0.674324
\(366\) 2.55824 0.133721
\(367\) 30.4989 1.59203 0.796015 0.605277i \(-0.206938\pi\)
0.796015 + 0.605277i \(0.206938\pi\)
\(368\) −0.258764 −0.0134890
\(369\) 22.1203 1.15153
\(370\) −0.758546 −0.0394349
\(371\) −12.4256 −0.645104
\(372\) −17.0289 −0.882909
\(373\) −11.8630 −0.614242 −0.307121 0.951670i \(-0.599366\pi\)
−0.307121 + 0.951670i \(0.599366\pi\)
\(374\) −3.65244 −0.188863
\(375\) −34.6896 −1.79136
\(376\) −6.14729 −0.317022
\(377\) 2.53755 0.130691
\(378\) −20.9147 −1.07573
\(379\) 33.6585 1.72892 0.864460 0.502702i \(-0.167661\pi\)
0.864460 + 0.502702i \(0.167661\pi\)
\(380\) −7.73611 −0.396854
\(381\) −32.5028 −1.66517
\(382\) 18.9452 0.969319
\(383\) 0.407761 0.0208356 0.0104178 0.999946i \(-0.496684\pi\)
0.0104178 + 0.999946i \(0.496684\pi\)
\(384\) −3.34123 −0.170506
\(385\) 2.19121 0.111674
\(386\) −8.34283 −0.424639
\(387\) −3.23846 −0.164620
\(388\) 4.34938 0.220806
\(389\) −35.9046 −1.82043 −0.910217 0.414131i \(-0.864085\pi\)
−0.910217 + 0.414131i \(0.864085\pi\)
\(390\) −10.9942 −0.556714
\(391\) −0.637700 −0.0322499
\(392\) −5.53058 −0.279336
\(393\) −41.3559 −2.08613
\(394\) 11.5578 0.582272
\(395\) 10.3009 0.518296
\(396\) −12.0994 −0.608019
\(397\) −6.57815 −0.330148 −0.165074 0.986281i \(-0.552786\pi\)
−0.165074 + 0.986281i \(0.552786\pi\)
\(398\) 18.1935 0.911957
\(399\) −25.6900 −1.28611
\(400\) −3.51243 −0.175621
\(401\) 5.15226 0.257292 0.128646 0.991691i \(-0.458937\pi\)
0.128646 + 0.991691i \(0.458937\pi\)
\(402\) 21.4490 1.06978
\(403\) −13.7499 −0.684932
\(404\) 4.89335 0.243453
\(405\) −40.4397 −2.00947
\(406\) −1.14017 −0.0565857
\(407\) −0.921751 −0.0456895
\(408\) −8.23415 −0.407651
\(409\) 25.0138 1.23685 0.618425 0.785843i \(-0.287771\pi\)
0.618425 + 0.785843i \(0.287771\pi\)
\(410\) −3.30473 −0.163209
\(411\) 2.55252 0.125906
\(412\) −16.7617 −0.825789
\(413\) 2.87696 0.141566
\(414\) −2.11251 −0.103824
\(415\) −12.6640 −0.621649
\(416\) −2.69785 −0.132273
\(417\) −17.9335 −0.878206
\(418\) −9.40058 −0.459798
\(419\) −2.10910 −0.103036 −0.0515181 0.998672i \(-0.516406\pi\)
−0.0515181 + 0.998672i \(0.516406\pi\)
\(420\) 4.93991 0.241043
\(421\) 28.4560 1.38686 0.693431 0.720523i \(-0.256098\pi\)
0.693431 + 0.720523i \(0.256098\pi\)
\(422\) 16.2521 0.791139
\(423\) −50.1854 −2.44010
\(424\) −10.2505 −0.497807
\(425\) −8.65605 −0.419880
\(426\) −34.4553 −1.66937
\(427\) −0.928127 −0.0449152
\(428\) 12.3674 0.597800
\(429\) −13.3597 −0.645011
\(430\) 0.483820 0.0233319
\(431\) −19.7425 −0.950963 −0.475482 0.879726i \(-0.657726\pi\)
−0.475482 + 0.879726i \(0.657726\pi\)
\(432\) −17.2535 −0.830111
\(433\) 3.51768 0.169049 0.0845244 0.996421i \(-0.473063\pi\)
0.0845244 + 0.996421i \(0.473063\pi\)
\(434\) 6.17809 0.296558
\(435\) −3.83303 −0.183780
\(436\) −15.2467 −0.730183
\(437\) −1.64130 −0.0785141
\(438\) −35.2925 −1.68634
\(439\) −10.3595 −0.494431 −0.247215 0.968961i \(-0.579516\pi\)
−0.247215 + 0.968961i \(0.579516\pi\)
\(440\) 1.80763 0.0861755
\(441\) −45.1507 −2.15003
\(442\) −6.64861 −0.316242
\(443\) 21.0921 1.00212 0.501058 0.865413i \(-0.332944\pi\)
0.501058 + 0.865413i \(0.332944\pi\)
\(444\) −2.07802 −0.0986183
\(445\) −21.2407 −1.00690
\(446\) 25.1112 1.18905
\(447\) 62.4286 2.95277
\(448\) 1.21220 0.0572709
\(449\) 13.1074 0.618575 0.309288 0.950969i \(-0.399909\pi\)
0.309288 + 0.950969i \(0.399909\pi\)
\(450\) −28.6748 −1.35174
\(451\) −4.01576 −0.189095
\(452\) 4.39295 0.206627
\(453\) −54.7902 −2.57427
\(454\) −7.01735 −0.329341
\(455\) 3.98870 0.186993
\(456\) −21.1929 −0.992448
\(457\) 22.4781 1.05148 0.525742 0.850644i \(-0.323788\pi\)
0.525742 + 0.850644i \(0.323788\pi\)
\(458\) 1.11907 0.0522906
\(459\) −42.5197 −1.98465
\(460\) 0.315605 0.0147151
\(461\) 4.57015 0.212853 0.106427 0.994321i \(-0.466059\pi\)
0.106427 + 0.994321i \(0.466059\pi\)
\(462\) 6.00276 0.279273
\(463\) −22.5910 −1.04989 −0.524945 0.851136i \(-0.675914\pi\)
−0.524945 + 0.851136i \(0.675914\pi\)
\(464\) −0.940582 −0.0436654
\(465\) 20.7695 0.963164
\(466\) 12.2990 0.569742
\(467\) 4.44727 0.205795 0.102898 0.994692i \(-0.467189\pi\)
0.102898 + 0.994692i \(0.467189\pi\)
\(468\) −22.0248 −1.01810
\(469\) −7.78170 −0.359326
\(470\) 7.49761 0.345839
\(471\) −38.6856 −1.78254
\(472\) 2.37335 0.109242
\(473\) 0.587917 0.0270324
\(474\) 28.2191 1.29615
\(475\) −22.2788 −1.02222
\(476\) 2.98735 0.136925
\(477\) −83.6830 −3.83158
\(478\) 25.8095 1.18050
\(479\) 13.7272 0.627211 0.313606 0.949553i \(-0.398463\pi\)
0.313606 + 0.949553i \(0.398463\pi\)
\(480\) 4.07517 0.186005
\(481\) −1.67788 −0.0765048
\(482\) 14.9085 0.679064
\(483\) 1.04805 0.0476881
\(484\) −8.80345 −0.400157
\(485\) −5.30477 −0.240877
\(486\) −59.0231 −2.67734
\(487\) −33.0006 −1.49540 −0.747700 0.664037i \(-0.768842\pi\)
−0.747700 + 0.664037i \(0.768842\pi\)
\(488\) −0.765657 −0.0346597
\(489\) −9.26572 −0.419010
\(490\) 6.74543 0.304728
\(491\) −9.59044 −0.432810 −0.216405 0.976304i \(-0.569433\pi\)
−0.216405 + 0.976304i \(0.569433\pi\)
\(492\) −9.05322 −0.408151
\(493\) −2.31798 −0.104396
\(494\) −17.1121 −0.769908
\(495\) 14.7572 0.663287
\(496\) 5.09661 0.228844
\(497\) 12.5004 0.560719
\(498\) −34.6926 −1.55461
\(499\) −11.2467 −0.503473 −0.251736 0.967796i \(-0.581002\pi\)
−0.251736 + 0.967796i \(0.581002\pi\)
\(500\) 10.3823 0.464309
\(501\) −44.7115 −1.99756
\(502\) 19.2015 0.857004
\(503\) −14.1676 −0.631701 −0.315851 0.948809i \(-0.602290\pi\)
−0.315851 + 0.948809i \(0.602290\pi\)
\(504\) 9.89616 0.440810
\(505\) −5.96823 −0.265583
\(506\) 0.383509 0.0170490
\(507\) 19.1171 0.849021
\(508\) 9.72778 0.431600
\(509\) −28.3512 −1.25664 −0.628322 0.777954i \(-0.716258\pi\)
−0.628322 + 0.777954i \(0.716258\pi\)
\(510\) 10.0429 0.444706
\(511\) 12.8041 0.566420
\(512\) 1.00000 0.0441942
\(513\) −109.436 −4.83173
\(514\) 4.60640 0.203180
\(515\) 20.4436 0.900851
\(516\) 1.32541 0.0583480
\(517\) 9.11076 0.400691
\(518\) 0.753903 0.0331246
\(519\) 37.5340 1.64756
\(520\) 3.29047 0.144297
\(521\) 43.7602 1.91717 0.958584 0.284810i \(-0.0919306\pi\)
0.958584 + 0.284810i \(0.0919306\pi\)
\(522\) −7.67875 −0.336090
\(523\) 30.9261 1.35231 0.676153 0.736761i \(-0.263646\pi\)
0.676153 + 0.736761i \(0.263646\pi\)
\(524\) 12.3774 0.540711
\(525\) 14.2261 0.620880
\(526\) 9.92093 0.432573
\(527\) 12.5601 0.547127
\(528\) 4.95196 0.215507
\(529\) −22.9330 −0.997089
\(530\) 12.5021 0.543056
\(531\) 19.3756 0.840829
\(532\) 7.68877 0.333350
\(533\) −7.30996 −0.316630
\(534\) −58.1883 −2.51805
\(535\) −15.0840 −0.652138
\(536\) −6.41950 −0.277280
\(537\) −16.2300 −0.700374
\(538\) −1.01115 −0.0435938
\(539\) 8.19675 0.353059
\(540\) 21.0435 0.905566
\(541\) −13.4798 −0.579544 −0.289772 0.957096i \(-0.593579\pi\)
−0.289772 + 0.957096i \(0.593579\pi\)
\(542\) −4.03444 −0.173294
\(543\) −37.8550 −1.62451
\(544\) 2.46441 0.105661
\(545\) 18.5958 0.796555
\(546\) 10.9269 0.467629
\(547\) −1.43467 −0.0613422 −0.0306711 0.999530i \(-0.509764\pi\)
−0.0306711 + 0.999530i \(0.509764\pi\)
\(548\) −0.763945 −0.0326341
\(549\) −6.25069 −0.266773
\(550\) 5.20569 0.221971
\(551\) −5.96596 −0.254159
\(552\) 0.864591 0.0367995
\(553\) −10.2379 −0.435359
\(554\) −12.7012 −0.539624
\(555\) 2.53448 0.107583
\(556\) 5.36732 0.227625
\(557\) −33.2740 −1.40987 −0.704933 0.709274i \(-0.749023\pi\)
−0.704933 + 0.709274i \(0.749023\pi\)
\(558\) 41.6078 1.76140
\(559\) 1.07020 0.0452645
\(560\) −1.47847 −0.0624767
\(561\) 12.2037 0.515239
\(562\) 15.4255 0.650684
\(563\) −25.9575 −1.09398 −0.546990 0.837139i \(-0.684226\pi\)
−0.546990 + 0.837139i \(0.684226\pi\)
\(564\) 20.5395 0.864870
\(565\) −5.35791 −0.225409
\(566\) −21.1494 −0.888975
\(567\) 40.1923 1.68792
\(568\) 10.3122 0.432689
\(569\) −21.9936 −0.922019 −0.461009 0.887395i \(-0.652513\pi\)
−0.461009 + 0.887395i \(0.652513\pi\)
\(570\) 25.8481 1.08266
\(571\) 28.0715 1.17476 0.587378 0.809313i \(-0.300160\pi\)
0.587378 + 0.809313i \(0.300160\pi\)
\(572\) 3.99843 0.167183
\(573\) −63.3002 −2.64440
\(574\) 3.28450 0.137093
\(575\) 0.908891 0.0379034
\(576\) 8.16382 0.340159
\(577\) −0.973000 −0.0405065 −0.0202533 0.999795i \(-0.506447\pi\)
−0.0202533 + 0.999795i \(0.506447\pi\)
\(578\) −10.9267 −0.454491
\(579\) 27.8753 1.15846
\(580\) 1.14719 0.0476345
\(581\) 12.5865 0.522174
\(582\) −14.5323 −0.602382
\(583\) 15.1920 0.629188
\(584\) 10.5627 0.437089
\(585\) 26.8628 1.11064
\(586\) −0.915584 −0.0378224
\(587\) −5.07927 −0.209644 −0.104822 0.994491i \(-0.533427\pi\)
−0.104822 + 0.994491i \(0.533427\pi\)
\(588\) 18.4789 0.762059
\(589\) 32.3270 1.33201
\(590\) −2.89468 −0.119172
\(591\) −38.6172 −1.58850
\(592\) 0.621932 0.0255612
\(593\) −48.1262 −1.97631 −0.988154 0.153466i \(-0.950956\pi\)
−0.988154 + 0.153466i \(0.950956\pi\)
\(594\) 25.5711 1.04919
\(595\) −3.64355 −0.149371
\(596\) −18.6843 −0.765339
\(597\) −60.7887 −2.48791
\(598\) 0.698109 0.0285478
\(599\) −1.07872 −0.0440753 −0.0220376 0.999757i \(-0.507015\pi\)
−0.0220376 + 0.999757i \(0.507015\pi\)
\(600\) 11.7358 0.479113
\(601\) −27.7795 −1.13315 −0.566575 0.824010i \(-0.691732\pi\)
−0.566575 + 0.824010i \(0.691732\pi\)
\(602\) −0.480859 −0.0195984
\(603\) −52.4077 −2.13421
\(604\) 16.3982 0.667234
\(605\) 10.7372 0.436530
\(606\) −16.3498 −0.664165
\(607\) −46.5379 −1.88891 −0.944457 0.328635i \(-0.893411\pi\)
−0.944457 + 0.328635i \(0.893411\pi\)
\(608\) 6.34284 0.257236
\(609\) 3.80957 0.154372
\(610\) 0.933842 0.0378102
\(611\) 16.5845 0.670937
\(612\) 20.1190 0.813262
\(613\) 13.8563 0.559649 0.279825 0.960051i \(-0.409724\pi\)
0.279825 + 0.960051i \(0.409724\pi\)
\(614\) −6.21151 −0.250676
\(615\) 11.0419 0.445251
\(616\) −1.79657 −0.0723859
\(617\) 26.9736 1.08592 0.542958 0.839760i \(-0.317304\pi\)
0.542958 + 0.839760i \(0.317304\pi\)
\(618\) 56.0047 2.25284
\(619\) −38.6323 −1.55276 −0.776381 0.630264i \(-0.782947\pi\)
−0.776381 + 0.630264i \(0.782947\pi\)
\(620\) −6.21613 −0.249646
\(621\) 4.46460 0.179158
\(622\) 0.368999 0.0147955
\(623\) 21.1107 0.845782
\(624\) 9.01416 0.360855
\(625\) 4.89928 0.195971
\(626\) 2.93116 0.117153
\(627\) 31.4095 1.25438
\(628\) 11.5783 0.462023
\(629\) 1.53269 0.0611124
\(630\) −12.0700 −0.480879
\(631\) −7.43524 −0.295992 −0.147996 0.988988i \(-0.547282\pi\)
−0.147996 + 0.988988i \(0.547282\pi\)
\(632\) −8.44573 −0.335953
\(633\) −54.3020 −2.15831
\(634\) −1.58766 −0.0630540
\(635\) −11.8646 −0.470832
\(636\) 34.2492 1.35807
\(637\) 14.9207 0.591180
\(638\) 1.39402 0.0551896
\(639\) 84.1867 3.33038
\(640\) −1.21966 −0.0482113
\(641\) 2.07523 0.0819667 0.0409834 0.999160i \(-0.486951\pi\)
0.0409834 + 0.999160i \(0.486951\pi\)
\(642\) −41.3223 −1.63086
\(643\) −16.3846 −0.646147 −0.323073 0.946374i \(-0.604716\pi\)
−0.323073 + 0.946374i \(0.604716\pi\)
\(644\) −0.313673 −0.0123605
\(645\) −1.61655 −0.0636518
\(646\) 15.6313 0.615007
\(647\) −16.2916 −0.640487 −0.320244 0.947335i \(-0.603765\pi\)
−0.320244 + 0.947335i \(0.603765\pi\)
\(648\) 33.1566 1.30251
\(649\) −3.51749 −0.138073
\(650\) 9.47602 0.371680
\(651\) −20.6424 −0.809041
\(652\) 2.77315 0.108605
\(653\) 29.6877 1.16177 0.580885 0.813986i \(-0.302707\pi\)
0.580885 + 0.813986i \(0.302707\pi\)
\(654\) 50.9427 1.99202
\(655\) −15.0963 −0.589860
\(656\) 2.70955 0.105790
\(657\) 86.2323 3.36424
\(658\) −7.45173 −0.290498
\(659\) 34.2012 1.33229 0.666144 0.745823i \(-0.267944\pi\)
0.666144 + 0.745823i \(0.267944\pi\)
\(660\) −6.03972 −0.235096
\(661\) 5.20043 0.202273 0.101137 0.994873i \(-0.467752\pi\)
0.101137 + 0.994873i \(0.467752\pi\)
\(662\) 11.4159 0.443691
\(663\) 22.2145 0.862741
\(664\) 10.3832 0.402946
\(665\) −9.37769 −0.363651
\(666\) 5.07734 0.196743
\(667\) 0.243389 0.00942406
\(668\) 13.3818 0.517756
\(669\) −83.9022 −3.24384
\(670\) 7.82962 0.302485
\(671\) 1.13476 0.0438071
\(672\) −4.05023 −0.156241
\(673\) 45.3268 1.74722 0.873609 0.486628i \(-0.161773\pi\)
0.873609 + 0.486628i \(0.161773\pi\)
\(674\) −16.0047 −0.616480
\(675\) 60.6018 2.33256
\(676\) −5.72158 −0.220061
\(677\) 39.8869 1.53298 0.766489 0.642257i \(-0.222002\pi\)
0.766489 + 0.642257i \(0.222002\pi\)
\(678\) −14.6779 −0.563700
\(679\) 5.27230 0.202332
\(680\) −3.00574 −0.115265
\(681\) 23.4466 0.898476
\(682\) −7.55357 −0.289241
\(683\) 23.1146 0.884455 0.442227 0.896903i \(-0.354188\pi\)
0.442227 + 0.896903i \(0.354188\pi\)
\(684\) 51.7818 1.97993
\(685\) 0.931754 0.0356005
\(686\) −15.1895 −0.579939
\(687\) −3.73906 −0.142654
\(688\) −0.396684 −0.0151234
\(689\) 27.6543 1.05354
\(690\) −1.05451 −0.0401444
\(691\) −26.1627 −0.995275 −0.497638 0.867385i \(-0.665799\pi\)
−0.497638 + 0.867385i \(0.665799\pi\)
\(692\) −11.2336 −0.427036
\(693\) −14.6669 −0.557149
\(694\) 14.1373 0.536643
\(695\) −6.54631 −0.248316
\(696\) 3.14270 0.119124
\(697\) 6.67742 0.252925
\(698\) −16.1681 −0.611970
\(699\) −41.0939 −1.55431
\(700\) −4.25775 −0.160928
\(701\) −9.08855 −0.343270 −0.171635 0.985161i \(-0.554905\pi\)
−0.171635 + 0.985161i \(0.554905\pi\)
\(702\) 46.5475 1.75682
\(703\) 3.94481 0.148781
\(704\) −1.48208 −0.0558579
\(705\) −25.0512 −0.943484
\(706\) −3.51525 −0.132298
\(707\) 5.93170 0.223085
\(708\) −7.92990 −0.298024
\(709\) −23.0240 −0.864685 −0.432343 0.901709i \(-0.642313\pi\)
−0.432343 + 0.901709i \(0.642313\pi\)
\(710\) −12.5774 −0.472020
\(711\) −68.9495 −2.58581
\(712\) 17.4152 0.652663
\(713\) −1.31882 −0.0493902
\(714\) −9.98141 −0.373545
\(715\) −4.87673 −0.182379
\(716\) 4.85748 0.181533
\(717\) −86.2355 −3.22052
\(718\) −21.8168 −0.814195
\(719\) 19.4536 0.725497 0.362749 0.931887i \(-0.381838\pi\)
0.362749 + 0.931887i \(0.381838\pi\)
\(720\) −9.95710 −0.371079
\(721\) −20.3185 −0.756699
\(722\) 21.2316 0.790159
\(723\) −49.8128 −1.85256
\(724\) 11.3297 0.421064
\(725\) 3.30373 0.122697
\(726\) 29.4143 1.09167
\(727\) 24.9028 0.923595 0.461797 0.886985i \(-0.347205\pi\)
0.461797 + 0.886985i \(0.347205\pi\)
\(728\) −3.27033 −0.121207
\(729\) 97.7402 3.62001
\(730\) −12.8829 −0.476819
\(731\) −0.977591 −0.0361575
\(732\) 2.55824 0.0945552
\(733\) 31.1851 1.15185 0.575925 0.817503i \(-0.304642\pi\)
0.575925 + 0.817503i \(0.304642\pi\)
\(734\) 30.4989 1.12574
\(735\) −22.5380 −0.831328
\(736\) −0.258764 −0.00953818
\(737\) 9.51420 0.350460
\(738\) 22.1203 0.814258
\(739\) −44.6533 −1.64260 −0.821298 0.570499i \(-0.806750\pi\)
−0.821298 + 0.570499i \(0.806750\pi\)
\(740\) −0.758546 −0.0278847
\(741\) 57.1753 2.10039
\(742\) −12.4256 −0.456157
\(743\) 37.5848 1.37885 0.689426 0.724356i \(-0.257863\pi\)
0.689426 + 0.724356i \(0.257863\pi\)
\(744\) −17.0289 −0.624311
\(745\) 22.7885 0.834907
\(746\) −11.8630 −0.434335
\(747\) 84.7665 3.10144
\(748\) −3.65244 −0.133547
\(749\) 14.9917 0.547785
\(750\) −34.6896 −1.26668
\(751\) −19.1470 −0.698685 −0.349343 0.936995i \(-0.613595\pi\)
−0.349343 + 0.936995i \(0.613595\pi\)
\(752\) −6.14729 −0.224169
\(753\) −64.1566 −2.33799
\(754\) 2.53755 0.0924123
\(755\) −20.0003 −0.727884
\(756\) −20.9147 −0.760659
\(757\) −26.0241 −0.945863 −0.472932 0.881099i \(-0.656804\pi\)
−0.472932 + 0.881099i \(0.656804\pi\)
\(758\) 33.6585 1.22253
\(759\) −1.28139 −0.0465116
\(760\) −7.73611 −0.280618
\(761\) −7.89024 −0.286021 −0.143010 0.989721i \(-0.545678\pi\)
−0.143010 + 0.989721i \(0.545678\pi\)
\(762\) −32.5028 −1.17745
\(763\) −18.4820 −0.669092
\(764\) 18.9452 0.685412
\(765\) −24.5383 −0.887185
\(766\) 0.407761 0.0147330
\(767\) −6.40295 −0.231197
\(768\) −3.34123 −0.120566
\(769\) −35.8978 −1.29451 −0.647254 0.762274i \(-0.724083\pi\)
−0.647254 + 0.762274i \(0.724083\pi\)
\(770\) 2.19121 0.0789656
\(771\) −15.3911 −0.554296
\(772\) −8.34283 −0.300265
\(773\) 24.1793 0.869668 0.434834 0.900511i \(-0.356807\pi\)
0.434834 + 0.900511i \(0.356807\pi\)
\(774\) −3.23846 −0.116404
\(775\) −17.9015 −0.643039
\(776\) 4.34938 0.156134
\(777\) −2.51897 −0.0903674
\(778\) −35.9046 −1.28724
\(779\) 17.1862 0.615760
\(780\) −10.9942 −0.393656
\(781\) −15.2834 −0.546884
\(782\) −0.637700 −0.0228041
\(783\) 16.2284 0.579954
\(784\) −5.53058 −0.197521
\(785\) −14.1216 −0.504020
\(786\) −41.3559 −1.47511
\(787\) 22.1478 0.789482 0.394741 0.918792i \(-0.370834\pi\)
0.394741 + 0.918792i \(0.370834\pi\)
\(788\) 11.5578 0.411728
\(789\) −33.1481 −1.18010
\(790\) 10.3009 0.366491
\(791\) 5.32512 0.189340
\(792\) −12.0994 −0.429934
\(793\) 2.06563 0.0733528
\(794\) −6.57815 −0.233450
\(795\) −41.7724 −1.48151
\(796\) 18.1935 0.644851
\(797\) −37.7070 −1.33565 −0.667824 0.744319i \(-0.732774\pi\)
−0.667824 + 0.744319i \(0.732774\pi\)
\(798\) −25.6900 −0.909415
\(799\) −15.1494 −0.535948
\(800\) −3.51243 −0.124183
\(801\) 142.175 5.02350
\(802\) 5.15226 0.181933
\(803\) −15.6548 −0.552445
\(804\) 21.4490 0.756449
\(805\) 0.382575 0.0134840
\(806\) −13.7499 −0.484320
\(807\) 3.37849 0.118929
\(808\) 4.89335 0.172147
\(809\) 1.60179 0.0563161 0.0281580 0.999603i \(-0.491036\pi\)
0.0281580 + 0.999603i \(0.491036\pi\)
\(810\) −40.4397 −1.42091
\(811\) 7.08262 0.248704 0.124352 0.992238i \(-0.460315\pi\)
0.124352 + 0.992238i \(0.460315\pi\)
\(812\) −1.14017 −0.0400122
\(813\) 13.4800 0.472764
\(814\) −0.921751 −0.0323074
\(815\) −3.38230 −0.118477
\(816\) −8.23415 −0.288253
\(817\) −2.51610 −0.0880273
\(818\) 25.0138 0.874586
\(819\) −26.6984 −0.932918
\(820\) −3.30473 −0.115406
\(821\) −20.4638 −0.714191 −0.357095 0.934068i \(-0.616233\pi\)
−0.357095 + 0.934068i \(0.616233\pi\)
\(822\) 2.55252 0.0890292
\(823\) 13.8828 0.483924 0.241962 0.970286i \(-0.422209\pi\)
0.241962 + 0.970286i \(0.422209\pi\)
\(824\) −16.7617 −0.583921
\(825\) −17.3934 −0.605561
\(826\) 2.87696 0.100102
\(827\) 49.3448 1.71589 0.857943 0.513745i \(-0.171742\pi\)
0.857943 + 0.513745i \(0.171742\pi\)
\(828\) −2.11251 −0.0734147
\(829\) 29.8677 1.03735 0.518675 0.854972i \(-0.326426\pi\)
0.518675 + 0.854972i \(0.326426\pi\)
\(830\) −12.6640 −0.439573
\(831\) 42.4378 1.47215
\(832\) −2.69785 −0.0935313
\(833\) −13.6296 −0.472237
\(834\) −17.9335 −0.620985
\(835\) −16.3212 −0.564818
\(836\) −9.40058 −0.325126
\(837\) −87.9344 −3.03946
\(838\) −2.10910 −0.0728575
\(839\) −36.6082 −1.26386 −0.631928 0.775027i \(-0.717736\pi\)
−0.631928 + 0.775027i \(0.717736\pi\)
\(840\) 4.93991 0.170443
\(841\) −28.1153 −0.969493
\(842\) 28.4560 0.980660
\(843\) −51.5400 −1.77513
\(844\) 16.2521 0.559420
\(845\) 6.97839 0.240064
\(846\) −50.1854 −1.72541
\(847\) −10.6715 −0.366677
\(848\) −10.2505 −0.352002
\(849\) 70.6650 2.42522
\(850\) −8.65605 −0.296900
\(851\) −0.160934 −0.00551674
\(852\) −34.4553 −1.18042
\(853\) 32.6349 1.11740 0.558699 0.829371i \(-0.311301\pi\)
0.558699 + 0.829371i \(0.311301\pi\)
\(854\) −0.928127 −0.0317599
\(855\) −63.1563 −2.15990
\(856\) 12.3674 0.422708
\(857\) 28.9487 0.988869 0.494435 0.869215i \(-0.335375\pi\)
0.494435 + 0.869215i \(0.335375\pi\)
\(858\) −13.3597 −0.456092
\(859\) 33.4234 1.14039 0.570195 0.821509i \(-0.306868\pi\)
0.570195 + 0.821509i \(0.306868\pi\)
\(860\) 0.483820 0.0164981
\(861\) −10.9743 −0.374003
\(862\) −19.7425 −0.672432
\(863\) 2.24065 0.0762728 0.0381364 0.999273i \(-0.487858\pi\)
0.0381364 + 0.999273i \(0.487858\pi\)
\(864\) −17.2535 −0.586977
\(865\) 13.7011 0.465853
\(866\) 3.51768 0.119536
\(867\) 36.5086 1.23990
\(868\) 6.17809 0.209698
\(869\) 12.5172 0.424618
\(870\) −3.83303 −0.129952
\(871\) 17.3189 0.586828
\(872\) −15.2467 −0.516317
\(873\) 35.5076 1.20175
\(874\) −1.64130 −0.0555178
\(875\) 12.5854 0.425463
\(876\) −35.2925 −1.19242
\(877\) 29.8748 1.00880 0.504400 0.863470i \(-0.331714\pi\)
0.504400 + 0.863470i \(0.331714\pi\)
\(878\) −10.3595 −0.349615
\(879\) 3.05918 0.103184
\(880\) 1.80763 0.0609353
\(881\) 20.2016 0.680609 0.340305 0.940315i \(-0.389470\pi\)
0.340305 + 0.940315i \(0.389470\pi\)
\(882\) −45.1507 −1.52030
\(883\) −46.3372 −1.55937 −0.779685 0.626172i \(-0.784621\pi\)
−0.779685 + 0.626172i \(0.784621\pi\)
\(884\) −6.64861 −0.223617
\(885\) 9.67179 0.325114
\(886\) 21.0921 0.708604
\(887\) 53.6955 1.80292 0.901459 0.432864i \(-0.142497\pi\)
0.901459 + 0.432864i \(0.142497\pi\)
\(888\) −2.07802 −0.0697337
\(889\) 11.7920 0.395490
\(890\) −21.2407 −0.711989
\(891\) −49.1406 −1.64627
\(892\) 25.1112 0.840784
\(893\) −38.9913 −1.30479
\(894\) 62.4286 2.08792
\(895\) −5.92448 −0.198033
\(896\) 1.21220 0.0404967
\(897\) −2.33254 −0.0778813
\(898\) 13.1074 0.437399
\(899\) −4.79378 −0.159881
\(900\) −28.6748 −0.955828
\(901\) −25.2613 −0.841576
\(902\) −4.01576 −0.133710
\(903\) 1.60666 0.0534663
\(904\) 4.39295 0.146107
\(905\) −13.8183 −0.459337
\(906\) −54.7902 −1.82028
\(907\) −9.82273 −0.326158 −0.163079 0.986613i \(-0.552143\pi\)
−0.163079 + 0.986613i \(0.552143\pi\)
\(908\) −7.01735 −0.232879
\(909\) 39.9484 1.32501
\(910\) 3.98870 0.132224
\(911\) 32.3563 1.07201 0.536007 0.844214i \(-0.319932\pi\)
0.536007 + 0.844214i \(0.319932\pi\)
\(912\) −21.1929 −0.701767
\(913\) −15.3887 −0.509291
\(914\) 22.4781 0.743511
\(915\) −3.12018 −0.103150
\(916\) 1.11907 0.0369750
\(917\) 15.0039 0.495472
\(918\) −42.5197 −1.40336
\(919\) 19.4731 0.642358 0.321179 0.947019i \(-0.395921\pi\)
0.321179 + 0.947019i \(0.395921\pi\)
\(920\) 0.315605 0.0104052
\(921\) 20.7541 0.683871
\(922\) 4.57015 0.150510
\(923\) −27.8207 −0.915731
\(924\) 6.00276 0.197476
\(925\) −2.18449 −0.0718256
\(926\) −22.5910 −0.742385
\(927\) −136.839 −4.49440
\(928\) −0.940582 −0.0308761
\(929\) 34.8186 1.14236 0.571181 0.820824i \(-0.306485\pi\)
0.571181 + 0.820824i \(0.306485\pi\)
\(930\) 20.7695 0.681060
\(931\) −35.0796 −1.14969
\(932\) 12.2990 0.402868
\(933\) −1.23291 −0.0403637
\(934\) 4.44727 0.145519
\(935\) 4.45474 0.145686
\(936\) −22.0248 −0.719903
\(937\) 31.6423 1.03371 0.516854 0.856073i \(-0.327103\pi\)
0.516854 + 0.856073i \(0.327103\pi\)
\(938\) −7.78170 −0.254082
\(939\) −9.79367 −0.319604
\(940\) 7.49761 0.244545
\(941\) −21.2057 −0.691287 −0.345643 0.938366i \(-0.612339\pi\)
−0.345643 + 0.938366i \(0.612339\pi\)
\(942\) −38.6856 −1.26045
\(943\) −0.701134 −0.0228321
\(944\) 2.37335 0.0772459
\(945\) 25.5088 0.829802
\(946\) 0.587917 0.0191148
\(947\) 7.74830 0.251786 0.125893 0.992044i \(-0.459820\pi\)
0.125893 + 0.992044i \(0.459820\pi\)
\(948\) 28.2191 0.916515
\(949\) −28.4967 −0.925042
\(950\) −22.2788 −0.722819
\(951\) 5.30474 0.172018
\(952\) 2.98735 0.0968204
\(953\) 18.8056 0.609174 0.304587 0.952485i \(-0.401482\pi\)
0.304587 + 0.952485i \(0.401482\pi\)
\(954\) −83.6830 −2.70934
\(955\) −23.1067 −0.747715
\(956\) 25.8095 0.834739
\(957\) −4.65773 −0.150563
\(958\) 13.7272 0.443505
\(959\) −0.926052 −0.0299038
\(960\) 4.07517 0.131526
\(961\) −5.02460 −0.162084
\(962\) −1.67788 −0.0540971
\(963\) 100.965 3.25355
\(964\) 14.9085 0.480171
\(965\) 10.1754 0.327559
\(966\) 1.04805 0.0337206
\(967\) 2.39308 0.0769561 0.0384781 0.999259i \(-0.487749\pi\)
0.0384781 + 0.999259i \(0.487749\pi\)
\(968\) −8.80345 −0.282953
\(969\) −52.2279 −1.67780
\(970\) −5.30477 −0.170326
\(971\) 41.4345 1.32970 0.664849 0.746978i \(-0.268496\pi\)
0.664849 + 0.746978i \(0.268496\pi\)
\(972\) −59.0231 −1.89317
\(973\) 6.50625 0.208581
\(974\) −33.0006 −1.05741
\(975\) −31.6616 −1.01398
\(976\) −0.765657 −0.0245081
\(977\) 15.3409 0.490799 0.245399 0.969422i \(-0.421081\pi\)
0.245399 + 0.969422i \(0.421081\pi\)
\(978\) −9.26572 −0.296285
\(979\) −25.8107 −0.824915
\(980\) 6.74543 0.215475
\(981\) −124.471 −3.97406
\(982\) −9.59044 −0.306043
\(983\) −42.7699 −1.36415 −0.682074 0.731283i \(-0.738922\pi\)
−0.682074 + 0.731283i \(0.738922\pi\)
\(984\) −9.05322 −0.288606
\(985\) −14.0966 −0.449153
\(986\) −2.31798 −0.0738194
\(987\) 24.8979 0.792510
\(988\) −17.1121 −0.544407
\(989\) 0.102648 0.00326401
\(990\) 14.7572 0.469014
\(991\) 34.3522 1.09123 0.545617 0.838034i \(-0.316295\pi\)
0.545617 + 0.838034i \(0.316295\pi\)
\(992\) 5.09661 0.161817
\(993\) −38.1431 −1.21043
\(994\) 12.5004 0.396488
\(995\) −22.1899 −0.703467
\(996\) −34.6926 −1.09928
\(997\) 28.1056 0.890112 0.445056 0.895503i \(-0.353184\pi\)
0.445056 + 0.895503i \(0.353184\pi\)
\(998\) −11.2467 −0.356009
\(999\) −10.7305 −0.339498
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 4006.2.a.i.1.1 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4006.2.a.i.1.1 46 1.1 even 1 trivial