Properties

Label 4033.2.a.f.1.14
Level $4033$
Weight $2$
Character 4033.1
Self dual yes
Analytic conductor $32.204$
Analytic rank $0$
Dimension $85$
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] = [4033,2,Mod(1,4033)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4033, 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("4033.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 4033 = 37 \cdot 109 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 4033.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: \(32.2036671352\)
Analytic rank: \(0\)
Dimension: \(85\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 4033.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.99373 q^{2} -2.36120 q^{3} +1.97494 q^{4} -0.776635 q^{5} +4.70759 q^{6} -0.440394 q^{7} +0.0499623 q^{8} +2.57527 q^{9} +O(q^{10})\) \(q-1.99373 q^{2} -2.36120 q^{3} +1.97494 q^{4} -0.776635 q^{5} +4.70759 q^{6} -0.440394 q^{7} +0.0499623 q^{8} +2.57527 q^{9} +1.54840 q^{10} -2.15629 q^{11} -4.66323 q^{12} +0.754850 q^{13} +0.878024 q^{14} +1.83379 q^{15} -4.04949 q^{16} -6.90916 q^{17} -5.13438 q^{18} +4.91582 q^{19} -1.53381 q^{20} +1.03986 q^{21} +4.29904 q^{22} +1.37766 q^{23} -0.117971 q^{24} -4.39684 q^{25} -1.50496 q^{26} +1.00287 q^{27} -0.869751 q^{28} -1.02580 q^{29} -3.65608 q^{30} -9.65359 q^{31} +7.97365 q^{32} +5.09143 q^{33} +13.7750 q^{34} +0.342025 q^{35} +5.08601 q^{36} +1.00000 q^{37} -9.80080 q^{38} -1.78235 q^{39} -0.0388025 q^{40} +10.7474 q^{41} -2.07319 q^{42} -2.65371 q^{43} -4.25854 q^{44} -2.00005 q^{45} -2.74668 q^{46} +2.72977 q^{47} +9.56167 q^{48} -6.80605 q^{49} +8.76609 q^{50} +16.3139 q^{51} +1.49078 q^{52} +12.7984 q^{53} -1.99944 q^{54} +1.67465 q^{55} -0.0220031 q^{56} -11.6072 q^{57} +2.04515 q^{58} -10.5962 q^{59} +3.62163 q^{60} +0.725629 q^{61} +19.2466 q^{62} -1.13413 q^{63} -7.79828 q^{64} -0.586243 q^{65} -10.1509 q^{66} -6.18534 q^{67} -13.6452 q^{68} -3.25294 q^{69} -0.681904 q^{70} -3.51520 q^{71} +0.128667 q^{72} -16.2009 q^{73} -1.99373 q^{74} +10.3818 q^{75} +9.70846 q^{76} +0.949615 q^{77} +3.55352 q^{78} -1.40676 q^{79} +3.14498 q^{80} -10.0938 q^{81} -21.4274 q^{82} +13.0553 q^{83} +2.05366 q^{84} +5.36590 q^{85} +5.29078 q^{86} +2.42211 q^{87} -0.107733 q^{88} -7.37894 q^{89} +3.98754 q^{90} -0.332431 q^{91} +2.72080 q^{92} +22.7941 q^{93} -5.44241 q^{94} -3.81780 q^{95} -18.8274 q^{96} -3.31898 q^{97} +13.5694 q^{98} -5.55303 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 85 q + 11 q^{2} + 21 q^{3} + 93 q^{4} + 12 q^{5} + 4 q^{6} + 17 q^{7} + 30 q^{8} + 98 q^{9} + 9 q^{10} + 37 q^{11} + 44 q^{12} + 14 q^{13} + 26 q^{14} + 27 q^{15} + 85 q^{16} + 34 q^{17} + 3 q^{18} + 15 q^{19} + 15 q^{20} + 17 q^{21} + q^{22} + 72 q^{23} + 15 q^{24} + 85 q^{25} + 33 q^{26} + 69 q^{27} + 7 q^{28} + 19 q^{29} - 9 q^{30} + 23 q^{31} + 51 q^{32} + 32 q^{33} + 49 q^{34} + 40 q^{35} + 121 q^{36} + 85 q^{37} + 84 q^{38} + 39 q^{39} + 22 q^{40} + 55 q^{41} - 28 q^{42} + 78 q^{44} + 28 q^{45} + 17 q^{46} + 184 q^{47} + 97 q^{48} + 88 q^{49} + 26 q^{50} + 27 q^{51} + 73 q^{52} + 64 q^{53} + 31 q^{54} + 39 q^{55} + 68 q^{56} - 33 q^{57} + 28 q^{58} + 60 q^{59} - 22 q^{60} + 7 q^{61} + 70 q^{62} + 28 q^{63} + 102 q^{64} + 17 q^{65} - 15 q^{66} + 82 q^{67} + 92 q^{68} + 22 q^{69} - 41 q^{70} + 113 q^{71} - 19 q^{73} + 11 q^{74} + 45 q^{75} + 34 q^{76} + 64 q^{77} + 29 q^{78} + 23 q^{79} + 54 q^{80} + 149 q^{81} + 4 q^{82} + 100 q^{83} - 49 q^{84} - 5 q^{85} - 24 q^{86} + 65 q^{87} + 14 q^{88} + 84 q^{89} - 21 q^{90} + 32 q^{91} + 95 q^{92} + 19 q^{93} - 47 q^{94} + 102 q^{95} + 29 q^{96} + 7 q^{97} + 26 q^{98} + 107 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99373 −1.40978 −0.704888 0.709318i \(-0.749003\pi\)
−0.704888 + 0.709318i \(0.749003\pi\)
\(3\) −2.36120 −1.36324 −0.681620 0.731706i \(-0.738724\pi\)
−0.681620 + 0.731706i \(0.738724\pi\)
\(4\) 1.97494 0.987470
\(5\) −0.776635 −0.347322 −0.173661 0.984806i \(-0.555560\pi\)
−0.173661 + 0.984806i \(0.555560\pi\)
\(6\) 4.70759 1.92186
\(7\) −0.440394 −0.166453 −0.0832266 0.996531i \(-0.526523\pi\)
−0.0832266 + 0.996531i \(0.526523\pi\)
\(8\) 0.0499623 0.0176644
\(9\) 2.57527 0.858424
\(10\) 1.54840 0.489646
\(11\) −2.15629 −0.650145 −0.325073 0.945689i \(-0.605389\pi\)
−0.325073 + 0.945689i \(0.605389\pi\)
\(12\) −4.66323 −1.34616
\(13\) 0.754850 0.209358 0.104679 0.994506i \(-0.466619\pi\)
0.104679 + 0.994506i \(0.466619\pi\)
\(14\) 0.878024 0.234662
\(15\) 1.83379 0.473483
\(16\) −4.04949 −1.01237
\(17\) −6.90916 −1.67572 −0.837859 0.545887i \(-0.816193\pi\)
−0.837859 + 0.545887i \(0.816193\pi\)
\(18\) −5.13438 −1.21019
\(19\) 4.91582 1.12777 0.563884 0.825854i \(-0.309307\pi\)
0.563884 + 0.825854i \(0.309307\pi\)
\(20\) −1.53381 −0.342970
\(21\) 1.03986 0.226916
\(22\) 4.29904 0.916559
\(23\) 1.37766 0.287262 0.143631 0.989631i \(-0.454122\pi\)
0.143631 + 0.989631i \(0.454122\pi\)
\(24\) −0.117971 −0.0240808
\(25\) −4.39684 −0.879368
\(26\) −1.50496 −0.295148
\(27\) 1.00287 0.193002
\(28\) −0.869751 −0.164368
\(29\) −1.02580 −0.190485 −0.0952427 0.995454i \(-0.530363\pi\)
−0.0952427 + 0.995454i \(0.530363\pi\)
\(30\) −3.65608 −0.667505
\(31\) −9.65359 −1.73384 −0.866918 0.498452i \(-0.833902\pi\)
−0.866918 + 0.498452i \(0.833902\pi\)
\(32\) 7.97365 1.40956
\(33\) 5.09143 0.886304
\(34\) 13.7750 2.36239
\(35\) 0.342025 0.0578128
\(36\) 5.08601 0.847668
\(37\) 1.00000 0.164399
\(38\) −9.80080 −1.58990
\(39\) −1.78235 −0.285405
\(40\) −0.0388025 −0.00613521
\(41\) 10.7474 1.67846 0.839232 0.543773i \(-0.183005\pi\)
0.839232 + 0.543773i \(0.183005\pi\)
\(42\) −2.07319 −0.319900
\(43\) −2.65371 −0.404688 −0.202344 0.979315i \(-0.564856\pi\)
−0.202344 + 0.979315i \(0.564856\pi\)
\(44\) −4.25854 −0.641999
\(45\) −2.00005 −0.298149
\(46\) −2.74668 −0.404976
\(47\) 2.72977 0.398178 0.199089 0.979981i \(-0.436202\pi\)
0.199089 + 0.979981i \(0.436202\pi\)
\(48\) 9.56167 1.38011
\(49\) −6.80605 −0.972293
\(50\) 8.76609 1.23971
\(51\) 16.3139 2.28441
\(52\) 1.49078 0.206734
\(53\) 12.7984 1.75800 0.879001 0.476820i \(-0.158211\pi\)
0.879001 + 0.476820i \(0.158211\pi\)
\(54\) −1.99944 −0.272090
\(55\) 1.67465 0.225809
\(56\) −0.0220031 −0.00294029
\(57\) −11.6072 −1.53742
\(58\) 2.04515 0.268542
\(59\) −10.5962 −1.37951 −0.689754 0.724044i \(-0.742281\pi\)
−0.689754 + 0.724044i \(0.742281\pi\)
\(60\) 3.62163 0.467550
\(61\) 0.725629 0.0929072 0.0464536 0.998920i \(-0.485208\pi\)
0.0464536 + 0.998920i \(0.485208\pi\)
\(62\) 19.2466 2.44432
\(63\) −1.13413 −0.142887
\(64\) −7.79828 −0.974785
\(65\) −0.586243 −0.0727145
\(66\) −10.1509 −1.24949
\(67\) −6.18534 −0.755659 −0.377830 0.925875i \(-0.623329\pi\)
−0.377830 + 0.925875i \(0.623329\pi\)
\(68\) −13.6452 −1.65472
\(69\) −3.25294 −0.391607
\(70\) −0.681904 −0.0815031
\(71\) −3.51520 −0.417178 −0.208589 0.978003i \(-0.566887\pi\)
−0.208589 + 0.978003i \(0.566887\pi\)
\(72\) 0.128667 0.0151635
\(73\) −16.2009 −1.89617 −0.948085 0.318018i \(-0.896983\pi\)
−0.948085 + 0.318018i \(0.896983\pi\)
\(74\) −1.99373 −0.231766
\(75\) 10.3818 1.19879
\(76\) 9.70846 1.11364
\(77\) 0.949615 0.108219
\(78\) 3.55352 0.402357
\(79\) −1.40676 −0.158273 −0.0791363 0.996864i \(-0.525216\pi\)
−0.0791363 + 0.996864i \(0.525216\pi\)
\(80\) 3.14498 0.351619
\(81\) −10.0938 −1.12153
\(82\) −21.4274 −2.36626
\(83\) 13.0553 1.43300 0.716502 0.697585i \(-0.245742\pi\)
0.716502 + 0.697585i \(0.245742\pi\)
\(84\) 2.05366 0.224072
\(85\) 5.36590 0.582013
\(86\) 5.29078 0.570519
\(87\) 2.42211 0.259677
\(88\) −0.107733 −0.0114844
\(89\) −7.37894 −0.782166 −0.391083 0.920355i \(-0.627899\pi\)
−0.391083 + 0.920355i \(0.627899\pi\)
\(90\) 3.98754 0.420324
\(91\) −0.332431 −0.0348482
\(92\) 2.72080 0.283663
\(93\) 22.7941 2.36363
\(94\) −5.44241 −0.561342
\(95\) −3.81780 −0.391698
\(96\) −18.8274 −1.92156
\(97\) −3.31898 −0.336991 −0.168496 0.985702i \(-0.553891\pi\)
−0.168496 + 0.985702i \(0.553891\pi\)
\(98\) 13.5694 1.37072
\(99\) −5.55303 −0.558100
\(100\) −8.68349 −0.868349
\(101\) −0.0925698 −0.00921104 −0.00460552 0.999989i \(-0.501466\pi\)
−0.00460552 + 0.999989i \(0.501466\pi\)
\(102\) −32.5255 −3.22050
\(103\) 2.72054 0.268063 0.134031 0.990977i \(-0.457208\pi\)
0.134031 + 0.990977i \(0.457208\pi\)
\(104\) 0.0377141 0.00369817
\(105\) −0.807590 −0.0788127
\(106\) −25.5166 −2.47839
\(107\) −8.24268 −0.796850 −0.398425 0.917201i \(-0.630443\pi\)
−0.398425 + 0.917201i \(0.630443\pi\)
\(108\) 1.98061 0.190584
\(109\) −1.00000 −0.0957826
\(110\) −3.33879 −0.318341
\(111\) −2.36120 −0.224115
\(112\) 1.78337 0.168513
\(113\) −5.96935 −0.561549 −0.280774 0.959774i \(-0.590591\pi\)
−0.280774 + 0.959774i \(0.590591\pi\)
\(114\) 23.1417 2.16742
\(115\) −1.06994 −0.0997724
\(116\) −2.02588 −0.188099
\(117\) 1.94394 0.179718
\(118\) 21.1259 1.94480
\(119\) 3.04275 0.278929
\(120\) 0.0916205 0.00836377
\(121\) −6.35042 −0.577311
\(122\) −1.44670 −0.130978
\(123\) −25.3768 −2.28815
\(124\) −19.0653 −1.71211
\(125\) 7.29791 0.652745
\(126\) 2.26115 0.201439
\(127\) −15.6542 −1.38908 −0.694541 0.719453i \(-0.744393\pi\)
−0.694541 + 0.719453i \(0.744393\pi\)
\(128\) −0.399667 −0.0353259
\(129\) 6.26595 0.551686
\(130\) 1.16881 0.102511
\(131\) −6.45718 −0.564166 −0.282083 0.959390i \(-0.591025\pi\)
−0.282083 + 0.959390i \(0.591025\pi\)
\(132\) 10.0553 0.875199
\(133\) −2.16490 −0.187720
\(134\) 12.3319 1.06531
\(135\) −0.778863 −0.0670338
\(136\) −0.345198 −0.0296005
\(137\) 12.1342 1.03670 0.518349 0.855169i \(-0.326547\pi\)
0.518349 + 0.855169i \(0.326547\pi\)
\(138\) 6.48546 0.552079
\(139\) 7.42721 0.629967 0.314984 0.949097i \(-0.398001\pi\)
0.314984 + 0.949097i \(0.398001\pi\)
\(140\) 0.675479 0.0570884
\(141\) −6.44554 −0.542812
\(142\) 7.00834 0.588127
\(143\) −1.62767 −0.136113
\(144\) −10.4285 −0.869045
\(145\) 0.796669 0.0661597
\(146\) 32.3001 2.67318
\(147\) 16.0705 1.32547
\(148\) 1.97494 0.162339
\(149\) −3.40709 −0.279120 −0.139560 0.990214i \(-0.544569\pi\)
−0.139560 + 0.990214i \(0.544569\pi\)
\(150\) −20.6985 −1.69003
\(151\) −5.51750 −0.449008 −0.224504 0.974473i \(-0.572076\pi\)
−0.224504 + 0.974473i \(0.572076\pi\)
\(152\) 0.245606 0.0199213
\(153\) −17.7930 −1.43848
\(154\) −1.89327 −0.152564
\(155\) 7.49731 0.602199
\(156\) −3.52004 −0.281829
\(157\) 0.423026 0.0337612 0.0168806 0.999858i \(-0.494626\pi\)
0.0168806 + 0.999858i \(0.494626\pi\)
\(158\) 2.80469 0.223129
\(159\) −30.2197 −2.39658
\(160\) −6.19261 −0.489569
\(161\) −0.606713 −0.0478157
\(162\) 20.1242 1.58111
\(163\) 6.31014 0.494248 0.247124 0.968984i \(-0.420514\pi\)
0.247124 + 0.968984i \(0.420514\pi\)
\(164\) 21.2255 1.65743
\(165\) −3.95418 −0.307833
\(166\) −26.0287 −2.02022
\(167\) −7.87108 −0.609082 −0.304541 0.952499i \(-0.598503\pi\)
−0.304541 + 0.952499i \(0.598503\pi\)
\(168\) 0.0519538 0.00400832
\(169\) −12.4302 −0.956169
\(170\) −10.6981 −0.820508
\(171\) 12.6596 0.968103
\(172\) −5.24093 −0.399617
\(173\) −17.9454 −1.36437 −0.682183 0.731181i \(-0.738969\pi\)
−0.682183 + 0.731181i \(0.738969\pi\)
\(174\) −4.82902 −0.366087
\(175\) 1.93634 0.146374
\(176\) 8.73187 0.658189
\(177\) 25.0198 1.88060
\(178\) 14.7116 1.10268
\(179\) −26.5291 −1.98288 −0.991440 0.130565i \(-0.958321\pi\)
−0.991440 + 0.130565i \(0.958321\pi\)
\(180\) −3.94997 −0.294413
\(181\) −17.8134 −1.32406 −0.662029 0.749478i \(-0.730304\pi\)
−0.662029 + 0.749478i \(0.730304\pi\)
\(182\) 0.662776 0.0491282
\(183\) −1.71336 −0.126655
\(184\) 0.0688312 0.00507430
\(185\) −0.776635 −0.0570993
\(186\) −45.4451 −3.33220
\(187\) 14.8981 1.08946
\(188\) 5.39114 0.393189
\(189\) −0.441657 −0.0321258
\(190\) 7.61164 0.552207
\(191\) −16.3367 −1.18208 −0.591042 0.806640i \(-0.701283\pi\)
−0.591042 + 0.806640i \(0.701283\pi\)
\(192\) 18.4133 1.32887
\(193\) 4.74151 0.341301 0.170651 0.985332i \(-0.445413\pi\)
0.170651 + 0.985332i \(0.445413\pi\)
\(194\) 6.61713 0.475082
\(195\) 1.38424 0.0991273
\(196\) −13.4415 −0.960111
\(197\) 11.0774 0.789231 0.394616 0.918846i \(-0.370878\pi\)
0.394616 + 0.918846i \(0.370878\pi\)
\(198\) 11.0712 0.786797
\(199\) −23.0269 −1.63233 −0.816167 0.577817i \(-0.803905\pi\)
−0.816167 + 0.577817i \(0.803905\pi\)
\(200\) −0.219676 −0.0155335
\(201\) 14.6048 1.03015
\(202\) 0.184559 0.0129855
\(203\) 0.451754 0.0317069
\(204\) 32.2190 2.25578
\(205\) −8.34682 −0.582967
\(206\) −5.42401 −0.377909
\(207\) 3.54785 0.246593
\(208\) −3.05676 −0.211948
\(209\) −10.5999 −0.733212
\(210\) 1.61011 0.111108
\(211\) 28.2282 1.94331 0.971656 0.236398i \(-0.0759669\pi\)
0.971656 + 0.236398i \(0.0759669\pi\)
\(212\) 25.2762 1.73597
\(213\) 8.30010 0.568713
\(214\) 16.4336 1.12338
\(215\) 2.06097 0.140557
\(216\) 0.0501057 0.00340926
\(217\) 4.25138 0.288602
\(218\) 1.99373 0.135032
\(219\) 38.2535 2.58493
\(220\) 3.30733 0.222980
\(221\) −5.21538 −0.350824
\(222\) 4.70759 0.315953
\(223\) 21.9472 1.46969 0.734846 0.678234i \(-0.237254\pi\)
0.734846 + 0.678234i \(0.237254\pi\)
\(224\) −3.51155 −0.234625
\(225\) −11.3231 −0.754870
\(226\) 11.9012 0.791658
\(227\) 8.10310 0.537822 0.268911 0.963165i \(-0.413336\pi\)
0.268911 + 0.963165i \(0.413336\pi\)
\(228\) −22.9236 −1.51815
\(229\) −17.0447 −1.12634 −0.563171 0.826340i \(-0.690419\pi\)
−0.563171 + 0.826340i \(0.690419\pi\)
\(230\) 2.13317 0.140657
\(231\) −2.24223 −0.147528
\(232\) −0.0512512 −0.00336480
\(233\) 23.3146 1.52739 0.763696 0.645576i \(-0.223383\pi\)
0.763696 + 0.645576i \(0.223383\pi\)
\(234\) −3.87569 −0.253362
\(235\) −2.12004 −0.138296
\(236\) −20.9269 −1.36222
\(237\) 3.32164 0.215764
\(238\) −6.06641 −0.393227
\(239\) 11.9388 0.772259 0.386129 0.922445i \(-0.373812\pi\)
0.386129 + 0.922445i \(0.373812\pi\)
\(240\) −7.42592 −0.479341
\(241\) 9.37800 0.604090 0.302045 0.953294i \(-0.402331\pi\)
0.302045 + 0.953294i \(0.402331\pi\)
\(242\) 12.6610 0.813880
\(243\) 20.8249 1.33592
\(244\) 1.43307 0.0917431
\(245\) 5.28582 0.337699
\(246\) 50.5944 3.22578
\(247\) 3.71071 0.236107
\(248\) −0.482316 −0.0306271
\(249\) −30.8262 −1.95353
\(250\) −14.5500 −0.920225
\(251\) 16.8239 1.06191 0.530957 0.847399i \(-0.321833\pi\)
0.530957 + 0.847399i \(0.321833\pi\)
\(252\) −2.23985 −0.141097
\(253\) −2.97063 −0.186762
\(254\) 31.2101 1.95830
\(255\) −12.6700 −0.793424
\(256\) 16.3934 1.02459
\(257\) 4.10579 0.256112 0.128056 0.991767i \(-0.459126\pi\)
0.128056 + 0.991767i \(0.459126\pi\)
\(258\) −12.4926 −0.777755
\(259\) −0.440394 −0.0273647
\(260\) −1.15779 −0.0718033
\(261\) −2.64170 −0.163517
\(262\) 12.8738 0.795348
\(263\) 18.6388 1.14932 0.574658 0.818393i \(-0.305135\pi\)
0.574658 + 0.818393i \(0.305135\pi\)
\(264\) 0.254380 0.0156560
\(265\) −9.93972 −0.610592
\(266\) 4.31621 0.264644
\(267\) 17.4232 1.06628
\(268\) −12.2157 −0.746191
\(269\) −14.0626 −0.857409 −0.428704 0.903445i \(-0.641030\pi\)
−0.428704 + 0.903445i \(0.641030\pi\)
\(270\) 1.55284 0.0945027
\(271\) 20.0510 1.21801 0.609004 0.793167i \(-0.291569\pi\)
0.609004 + 0.793167i \(0.291569\pi\)
\(272\) 27.9786 1.69645
\(273\) 0.784937 0.0475065
\(274\) −24.1923 −1.46151
\(275\) 9.48085 0.571717
\(276\) −6.42435 −0.386701
\(277\) −25.2267 −1.51572 −0.757862 0.652415i \(-0.773756\pi\)
−0.757862 + 0.652415i \(0.773756\pi\)
\(278\) −14.8078 −0.888113
\(279\) −24.8606 −1.48837
\(280\) 0.0170884 0.00102123
\(281\) 15.1429 0.903349 0.451674 0.892183i \(-0.350827\pi\)
0.451674 + 0.892183i \(0.350827\pi\)
\(282\) 12.8506 0.765244
\(283\) 10.0446 0.597088 0.298544 0.954396i \(-0.403499\pi\)
0.298544 + 0.954396i \(0.403499\pi\)
\(284\) −6.94231 −0.411950
\(285\) 9.01460 0.533979
\(286\) 3.24513 0.191889
\(287\) −4.73310 −0.279386
\(288\) 20.5343 1.21000
\(289\) 30.7365 1.80803
\(290\) −1.58834 −0.0932704
\(291\) 7.83677 0.459400
\(292\) −31.9958 −1.87241
\(293\) −9.43432 −0.551159 −0.275579 0.961278i \(-0.588870\pi\)
−0.275579 + 0.961278i \(0.588870\pi\)
\(294\) −32.0401 −1.86862
\(295\) 8.22938 0.479133
\(296\) 0.0499623 0.00290400
\(297\) −2.16247 −0.125479
\(298\) 6.79281 0.393497
\(299\) 1.03993 0.0601405
\(300\) 20.5035 1.18377
\(301\) 1.16868 0.0673615
\(302\) 11.0004 0.633001
\(303\) 0.218576 0.0125569
\(304\) −19.9066 −1.14172
\(305\) −0.563549 −0.0322687
\(306\) 35.4743 2.02793
\(307\) −26.1496 −1.49243 −0.746217 0.665702i \(-0.768132\pi\)
−0.746217 + 0.665702i \(0.768132\pi\)
\(308\) 1.87543 0.106863
\(309\) −6.42375 −0.365434
\(310\) −14.9476 −0.848965
\(311\) 10.0184 0.568091 0.284046 0.958811i \(-0.408323\pi\)
0.284046 + 0.958811i \(0.408323\pi\)
\(312\) −0.0890505 −0.00504149
\(313\) −6.92225 −0.391269 −0.195634 0.980677i \(-0.562677\pi\)
−0.195634 + 0.980677i \(0.562677\pi\)
\(314\) −0.843398 −0.0475957
\(315\) 0.880808 0.0496279
\(316\) −2.77826 −0.156289
\(317\) −13.7542 −0.772511 −0.386255 0.922392i \(-0.626232\pi\)
−0.386255 + 0.922392i \(0.626232\pi\)
\(318\) 60.2498 3.37864
\(319\) 2.21191 0.123843
\(320\) 6.05642 0.338564
\(321\) 19.4626 1.08630
\(322\) 1.20962 0.0674095
\(323\) −33.9642 −1.88982
\(324\) −19.9346 −1.10748
\(325\) −3.31895 −0.184102
\(326\) −12.5807 −0.696779
\(327\) 2.36120 0.130575
\(328\) 0.536966 0.0296490
\(329\) −1.20217 −0.0662780
\(330\) 7.88355 0.433975
\(331\) 32.3758 1.77954 0.889768 0.456414i \(-0.150866\pi\)
0.889768 + 0.456414i \(0.150866\pi\)
\(332\) 25.7834 1.41505
\(333\) 2.57527 0.141124
\(334\) 15.6928 0.858670
\(335\) 4.80375 0.262457
\(336\) −4.21090 −0.229723
\(337\) 3.48271 0.189715 0.0948576 0.995491i \(-0.469760\pi\)
0.0948576 + 0.995491i \(0.469760\pi\)
\(338\) 24.7824 1.34799
\(339\) 14.0948 0.765526
\(340\) 10.5973 0.574721
\(341\) 20.8159 1.12724
\(342\) −25.2397 −1.36481
\(343\) 6.08010 0.328295
\(344\) −0.132586 −0.00714855
\(345\) 2.52634 0.136014
\(346\) 35.7783 1.92345
\(347\) 22.6438 1.21559 0.607793 0.794096i \(-0.292055\pi\)
0.607793 + 0.794096i \(0.292055\pi\)
\(348\) 4.78352 0.256424
\(349\) 21.1651 1.13294 0.566471 0.824082i \(-0.308308\pi\)
0.566471 + 0.824082i \(0.308308\pi\)
\(350\) −3.86053 −0.206354
\(351\) 0.757015 0.0404065
\(352\) −17.1935 −0.916415
\(353\) 9.18330 0.488777 0.244389 0.969677i \(-0.421413\pi\)
0.244389 + 0.969677i \(0.421413\pi\)
\(354\) −49.8825 −2.65123
\(355\) 2.73003 0.144895
\(356\) −14.5730 −0.772366
\(357\) −7.18455 −0.380247
\(358\) 52.8918 2.79542
\(359\) −18.5426 −0.978641 −0.489320 0.872104i \(-0.662755\pi\)
−0.489320 + 0.872104i \(0.662755\pi\)
\(360\) −0.0999270 −0.00526661
\(361\) 5.16532 0.271859
\(362\) 35.5150 1.86663
\(363\) 14.9946 0.787014
\(364\) −0.656532 −0.0344116
\(365\) 12.5822 0.658581
\(366\) 3.41596 0.178555
\(367\) 6.60638 0.344850 0.172425 0.985023i \(-0.444840\pi\)
0.172425 + 0.985023i \(0.444840\pi\)
\(368\) −5.57883 −0.290816
\(369\) 27.6775 1.44083
\(370\) 1.54840 0.0804973
\(371\) −5.63636 −0.292625
\(372\) 45.0169 2.33402
\(373\) −21.1469 −1.09494 −0.547471 0.836824i \(-0.684409\pi\)
−0.547471 + 0.836824i \(0.684409\pi\)
\(374\) −29.7028 −1.53589
\(375\) −17.2318 −0.889848
\(376\) 0.136386 0.00703356
\(377\) −0.774322 −0.0398796
\(378\) 0.880543 0.0452902
\(379\) −36.6965 −1.88497 −0.942486 0.334247i \(-0.891518\pi\)
−0.942486 + 0.334247i \(0.891518\pi\)
\(380\) −7.53993 −0.386790
\(381\) 36.9626 1.89365
\(382\) 32.5710 1.66648
\(383\) 17.2626 0.882076 0.441038 0.897488i \(-0.354610\pi\)
0.441038 + 0.897488i \(0.354610\pi\)
\(384\) 0.943695 0.0481577
\(385\) −0.737505 −0.0375867
\(386\) −9.45327 −0.481159
\(387\) −6.83404 −0.347394
\(388\) −6.55478 −0.332769
\(389\) 24.7114 1.25292 0.626459 0.779455i \(-0.284504\pi\)
0.626459 + 0.779455i \(0.284504\pi\)
\(390\) −2.75979 −0.139747
\(391\) −9.51848 −0.481370
\(392\) −0.340046 −0.0171749
\(393\) 15.2467 0.769094
\(394\) −22.0853 −1.11264
\(395\) 1.09254 0.0549715
\(396\) −10.9669 −0.551107
\(397\) −8.98396 −0.450892 −0.225446 0.974256i \(-0.572384\pi\)
−0.225446 + 0.974256i \(0.572384\pi\)
\(398\) 45.9093 2.30123
\(399\) 5.11176 0.255908
\(400\) 17.8050 0.890248
\(401\) −30.9343 −1.54478 −0.772392 0.635147i \(-0.780940\pi\)
−0.772392 + 0.635147i \(0.780940\pi\)
\(402\) −29.1180 −1.45227
\(403\) −7.28701 −0.362992
\(404\) −0.182820 −0.00909563
\(405\) 7.83919 0.389532
\(406\) −0.900673 −0.0446997
\(407\) −2.15629 −0.106883
\(408\) 0.815082 0.0403526
\(409\) 7.61058 0.376319 0.188160 0.982138i \(-0.439748\pi\)
0.188160 + 0.982138i \(0.439748\pi\)
\(410\) 16.6413 0.821854
\(411\) −28.6514 −1.41327
\(412\) 5.37291 0.264704
\(413\) 4.66650 0.229624
\(414\) −7.07344 −0.347641
\(415\) −10.1392 −0.497714
\(416\) 6.01891 0.295101
\(417\) −17.5371 −0.858797
\(418\) 21.1333 1.03367
\(419\) 20.5172 1.00233 0.501165 0.865352i \(-0.332905\pi\)
0.501165 + 0.865352i \(0.332905\pi\)
\(420\) −1.59494 −0.0778252
\(421\) −24.1604 −1.17750 −0.588752 0.808313i \(-0.700381\pi\)
−0.588752 + 0.808313i \(0.700381\pi\)
\(422\) −56.2794 −2.73964
\(423\) 7.02990 0.341806
\(424\) 0.639440 0.0310540
\(425\) 30.3785 1.47357
\(426\) −16.5481 −0.801759
\(427\) −0.319562 −0.0154647
\(428\) −16.2788 −0.786866
\(429\) 3.84326 0.185555
\(430\) −4.10900 −0.198154
\(431\) 19.8449 0.955894 0.477947 0.878389i \(-0.341381\pi\)
0.477947 + 0.878389i \(0.341381\pi\)
\(432\) −4.06111 −0.195390
\(433\) 24.9681 1.19989 0.599945 0.800041i \(-0.295189\pi\)
0.599945 + 0.800041i \(0.295189\pi\)
\(434\) −8.47608 −0.406865
\(435\) −1.88110 −0.0901916
\(436\) −1.97494 −0.0945825
\(437\) 6.77234 0.323965
\(438\) −76.2670 −3.64418
\(439\) 20.1791 0.963097 0.481548 0.876419i \(-0.340075\pi\)
0.481548 + 0.876419i \(0.340075\pi\)
\(440\) 0.0836693 0.00398878
\(441\) −17.5274 −0.834640
\(442\) 10.3980 0.494584
\(443\) 17.1936 0.816893 0.408446 0.912782i \(-0.366071\pi\)
0.408446 + 0.912782i \(0.366071\pi\)
\(444\) −4.66323 −0.221307
\(445\) 5.73074 0.271663
\(446\) −43.7567 −2.07194
\(447\) 8.04484 0.380508
\(448\) 3.43431 0.162256
\(449\) −9.74972 −0.460118 −0.230059 0.973177i \(-0.573892\pi\)
−0.230059 + 0.973177i \(0.573892\pi\)
\(450\) 22.5751 1.06420
\(451\) −23.1745 −1.09125
\(452\) −11.7891 −0.554513
\(453\) 13.0279 0.612106
\(454\) −16.1554 −0.758208
\(455\) 0.258178 0.0121036
\(456\) −0.579925 −0.0271575
\(457\) 16.3041 0.762672 0.381336 0.924436i \(-0.375464\pi\)
0.381336 + 0.924436i \(0.375464\pi\)
\(458\) 33.9824 1.58789
\(459\) −6.92898 −0.323417
\(460\) −2.11307 −0.0985223
\(461\) −17.8277 −0.830319 −0.415160 0.909749i \(-0.636274\pi\)
−0.415160 + 0.909749i \(0.636274\pi\)
\(462\) 4.47040 0.207982
\(463\) 26.6964 1.24069 0.620344 0.784330i \(-0.286993\pi\)
0.620344 + 0.784330i \(0.286993\pi\)
\(464\) 4.15395 0.192842
\(465\) −17.7027 −0.820941
\(466\) −46.4829 −2.15328
\(467\) −20.3136 −0.940003 −0.470002 0.882666i \(-0.655747\pi\)
−0.470002 + 0.882666i \(0.655747\pi\)
\(468\) 3.83917 0.177466
\(469\) 2.72398 0.125782
\(470\) 4.22677 0.194966
\(471\) −0.998850 −0.0460246
\(472\) −0.529411 −0.0243681
\(473\) 5.72217 0.263106
\(474\) −6.62243 −0.304178
\(475\) −21.6141 −0.991722
\(476\) 6.00925 0.275434
\(477\) 32.9595 1.50911
\(478\) −23.8027 −1.08871
\(479\) 21.1669 0.967142 0.483571 0.875305i \(-0.339339\pi\)
0.483571 + 0.875305i \(0.339339\pi\)
\(480\) 14.6220 0.667400
\(481\) 0.754850 0.0344182
\(482\) −18.6972 −0.851632
\(483\) 1.43257 0.0651843
\(484\) −12.5417 −0.570078
\(485\) 2.57763 0.117044
\(486\) −41.5191 −1.88334
\(487\) 22.1990 1.00593 0.502967 0.864306i \(-0.332242\pi\)
0.502967 + 0.864306i \(0.332242\pi\)
\(488\) 0.0362541 0.00164115
\(489\) −14.8995 −0.673779
\(490\) −10.5385 −0.476080
\(491\) 12.0377 0.543252 0.271626 0.962403i \(-0.412439\pi\)
0.271626 + 0.962403i \(0.412439\pi\)
\(492\) −50.1177 −2.25948
\(493\) 7.08739 0.319200
\(494\) −7.39813 −0.332858
\(495\) 4.31267 0.193840
\(496\) 39.0921 1.75529
\(497\) 1.54807 0.0694405
\(498\) 61.4589 2.75404
\(499\) 8.63006 0.386334 0.193167 0.981166i \(-0.438124\pi\)
0.193167 + 0.981166i \(0.438124\pi\)
\(500\) 14.4129 0.644566
\(501\) 18.5852 0.830325
\(502\) −33.5422 −1.49706
\(503\) 11.8352 0.527704 0.263852 0.964563i \(-0.415007\pi\)
0.263852 + 0.964563i \(0.415007\pi\)
\(504\) −0.0566640 −0.00252401
\(505\) 0.0718930 0.00319919
\(506\) 5.92263 0.263293
\(507\) 29.3502 1.30349
\(508\) −30.9160 −1.37168
\(509\) 20.6534 0.915446 0.457723 0.889095i \(-0.348665\pi\)
0.457723 + 0.889095i \(0.348665\pi\)
\(510\) 25.2604 1.11855
\(511\) 7.13477 0.315623
\(512\) −31.8846 −1.40911
\(513\) 4.92992 0.217661
\(514\) −8.18582 −0.361061
\(515\) −2.11287 −0.0931041
\(516\) 12.3749 0.544774
\(517\) −5.88617 −0.258874
\(518\) 0.878024 0.0385782
\(519\) 42.3728 1.85996
\(520\) −0.0292901 −0.00128445
\(521\) −21.0988 −0.924355 −0.462178 0.886787i \(-0.652932\pi\)
−0.462178 + 0.886787i \(0.652932\pi\)
\(522\) 5.26683 0.230523
\(523\) 38.8319 1.69800 0.849000 0.528393i \(-0.177205\pi\)
0.849000 + 0.528393i \(0.177205\pi\)
\(524\) −12.7525 −0.557097
\(525\) −4.57209 −0.199542
\(526\) −37.1606 −1.62028
\(527\) 66.6982 2.90542
\(528\) −20.6177 −0.897270
\(529\) −21.1020 −0.917480
\(530\) 19.8171 0.860799
\(531\) −27.2881 −1.18420
\(532\) −4.27554 −0.185368
\(533\) 8.11269 0.351399
\(534\) −34.7370 −1.50322
\(535\) 6.40156 0.276763
\(536\) −0.309034 −0.0133482
\(537\) 62.6406 2.70314
\(538\) 28.0369 1.20876
\(539\) 14.6758 0.632132
\(540\) −1.53821 −0.0661939
\(541\) −16.5642 −0.712152 −0.356076 0.934457i \(-0.615886\pi\)
−0.356076 + 0.934457i \(0.615886\pi\)
\(542\) −39.9761 −1.71712
\(543\) 42.0610 1.80501
\(544\) −55.0912 −2.36202
\(545\) 0.776635 0.0332674
\(546\) −1.56495 −0.0669736
\(547\) −23.1140 −0.988285 −0.494142 0.869381i \(-0.664518\pi\)
−0.494142 + 0.869381i \(0.664518\pi\)
\(548\) 23.9644 1.02371
\(549\) 1.86869 0.0797538
\(550\) −18.9022 −0.805993
\(551\) −5.04263 −0.214823
\(552\) −0.162524 −0.00691749
\(553\) 0.619527 0.0263450
\(554\) 50.2950 2.13683
\(555\) 1.83379 0.0778401
\(556\) 14.6683 0.622074
\(557\) 8.07281 0.342056 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(558\) 49.5652 2.09826
\(559\) −2.00316 −0.0847244
\(560\) −1.38503 −0.0585281
\(561\) −35.1775 −1.48520
\(562\) −30.1907 −1.27352
\(563\) 7.07105 0.298009 0.149005 0.988836i \(-0.452393\pi\)
0.149005 + 0.988836i \(0.452393\pi\)
\(564\) −12.7296 −0.536011
\(565\) 4.63600 0.195038
\(566\) −20.0261 −0.841761
\(567\) 4.44524 0.186683
\(568\) −0.175628 −0.00736917
\(569\) −22.3535 −0.937109 −0.468555 0.883435i \(-0.655225\pi\)
−0.468555 + 0.883435i \(0.655225\pi\)
\(570\) −17.9726 −0.752790
\(571\) 10.9032 0.456285 0.228142 0.973628i \(-0.426735\pi\)
0.228142 + 0.973628i \(0.426735\pi\)
\(572\) −3.21456 −0.134407
\(573\) 38.5743 1.61147
\(574\) 9.43649 0.393872
\(575\) −6.05735 −0.252609
\(576\) −20.0827 −0.836779
\(577\) 17.6921 0.736532 0.368266 0.929720i \(-0.379952\pi\)
0.368266 + 0.929720i \(0.379952\pi\)
\(578\) −61.2801 −2.54892
\(579\) −11.1957 −0.465276
\(580\) 1.57337 0.0653308
\(581\) −5.74947 −0.238528
\(582\) −15.6244 −0.647651
\(583\) −27.5971 −1.14296
\(584\) −0.809434 −0.0334946
\(585\) −1.50973 −0.0624198
\(586\) 18.8094 0.777011
\(587\) 40.8074 1.68430 0.842151 0.539243i \(-0.181289\pi\)
0.842151 + 0.539243i \(0.181289\pi\)
\(588\) 31.7382 1.30886
\(589\) −47.4553 −1.95536
\(590\) −16.4071 −0.675471
\(591\) −26.1559 −1.07591
\(592\) −4.04949 −0.166433
\(593\) −32.7953 −1.34674 −0.673371 0.739305i \(-0.735154\pi\)
−0.673371 + 0.739305i \(0.735154\pi\)
\(594\) 4.31138 0.176898
\(595\) −2.36311 −0.0968779
\(596\) −6.72881 −0.275623
\(597\) 54.3711 2.22526
\(598\) −2.07333 −0.0847847
\(599\) 43.8619 1.79215 0.896075 0.443902i \(-0.146406\pi\)
0.896075 + 0.443902i \(0.146406\pi\)
\(600\) 0.518700 0.0211758
\(601\) −7.04820 −0.287502 −0.143751 0.989614i \(-0.545916\pi\)
−0.143751 + 0.989614i \(0.545916\pi\)
\(602\) −2.33002 −0.0949647
\(603\) −15.9289 −0.648676
\(604\) −10.8967 −0.443382
\(605\) 4.93196 0.200513
\(606\) −0.435780 −0.0177024
\(607\) 6.75581 0.274210 0.137105 0.990557i \(-0.456220\pi\)
0.137105 + 0.990557i \(0.456220\pi\)
\(608\) 39.1971 1.58965
\(609\) −1.06668 −0.0432241
\(610\) 1.12356 0.0454916
\(611\) 2.06057 0.0833616
\(612\) −35.1400 −1.42045
\(613\) 44.1438 1.78295 0.891476 0.453068i \(-0.149671\pi\)
0.891476 + 0.453068i \(0.149671\pi\)
\(614\) 52.1351 2.10400
\(615\) 19.7085 0.794724
\(616\) 0.0474450 0.00191161
\(617\) 34.8816 1.40428 0.702140 0.712039i \(-0.252228\pi\)
0.702140 + 0.712039i \(0.252228\pi\)
\(618\) 12.8072 0.515181
\(619\) −13.0627 −0.525035 −0.262517 0.964927i \(-0.584553\pi\)
−0.262517 + 0.964927i \(0.584553\pi\)
\(620\) 14.8067 0.594653
\(621\) 1.38161 0.0554422
\(622\) −19.9739 −0.800882
\(623\) 3.24964 0.130194
\(624\) 7.21762 0.288936
\(625\) 16.3164 0.652655
\(626\) 13.8011 0.551601
\(627\) 25.0286 0.999545
\(628\) 0.835452 0.0333382
\(629\) −6.90916 −0.275486
\(630\) −1.75609 −0.0699643
\(631\) 1.60229 0.0637860 0.0318930 0.999491i \(-0.489846\pi\)
0.0318930 + 0.999491i \(0.489846\pi\)
\(632\) −0.0702849 −0.00279578
\(633\) −66.6526 −2.64920
\(634\) 27.4220 1.08907
\(635\) 12.1576 0.482459
\(636\) −59.6821 −2.36655
\(637\) −5.13755 −0.203557
\(638\) −4.40994 −0.174591
\(639\) −9.05260 −0.358115
\(640\) 0.310396 0.0122695
\(641\) 4.22897 0.167034 0.0835171 0.996506i \(-0.473385\pi\)
0.0835171 + 0.996506i \(0.473385\pi\)
\(642\) −38.8031 −1.53144
\(643\) −28.7384 −1.13333 −0.566666 0.823948i \(-0.691767\pi\)
−0.566666 + 0.823948i \(0.691767\pi\)
\(644\) −1.19822 −0.0472166
\(645\) −4.86636 −0.191613
\(646\) 67.7153 2.66422
\(647\) 8.66230 0.340550 0.170275 0.985397i \(-0.445534\pi\)
0.170275 + 0.985397i \(0.445534\pi\)
\(648\) −0.504309 −0.0198111
\(649\) 22.8485 0.896880
\(650\) 6.61708 0.259543
\(651\) −10.0384 −0.393434
\(652\) 12.4621 0.488055
\(653\) −5.37806 −0.210460 −0.105230 0.994448i \(-0.533558\pi\)
−0.105230 + 0.994448i \(0.533558\pi\)
\(654\) −4.70759 −0.184081
\(655\) 5.01487 0.195947
\(656\) −43.5216 −1.69923
\(657\) −41.7217 −1.62772
\(658\) 2.39681 0.0934372
\(659\) −4.04480 −0.157563 −0.0787815 0.996892i \(-0.525103\pi\)
−0.0787815 + 0.996892i \(0.525103\pi\)
\(660\) −7.80927 −0.303975
\(661\) −5.41315 −0.210547 −0.105274 0.994443i \(-0.533572\pi\)
−0.105274 + 0.994443i \(0.533572\pi\)
\(662\) −64.5485 −2.50875
\(663\) 12.3146 0.478258
\(664\) 0.652273 0.0253131
\(665\) 1.68134 0.0651994
\(666\) −5.13438 −0.198953
\(667\) −1.41320 −0.0547193
\(668\) −15.5449 −0.601451
\(669\) −51.8217 −2.00354
\(670\) −9.57736 −0.370006
\(671\) −1.56466 −0.0604032
\(672\) 8.29147 0.319850
\(673\) 11.1253 0.428847 0.214424 0.976741i \(-0.431213\pi\)
0.214424 + 0.976741i \(0.431213\pi\)
\(674\) −6.94356 −0.267456
\(675\) −4.40945 −0.169720
\(676\) −24.5489 −0.944189
\(677\) −0.999958 −0.0384315 −0.0192158 0.999815i \(-0.506117\pi\)
−0.0192158 + 0.999815i \(0.506117\pi\)
\(678\) −28.1012 −1.07922
\(679\) 1.46166 0.0560932
\(680\) 0.268093 0.0102809
\(681\) −19.1330 −0.733180
\(682\) −41.5012 −1.58916
\(683\) −20.4639 −0.783029 −0.391515 0.920172i \(-0.628049\pi\)
−0.391515 + 0.920172i \(0.628049\pi\)
\(684\) 25.0019 0.955972
\(685\) −9.42387 −0.360068
\(686\) −12.1220 −0.462822
\(687\) 40.2459 1.53548
\(688\) 10.7462 0.409695
\(689\) 9.66091 0.368051
\(690\) −5.03683 −0.191749
\(691\) 9.06320 0.344780 0.172390 0.985029i \(-0.444851\pi\)
0.172390 + 0.985029i \(0.444851\pi\)
\(692\) −35.4412 −1.34727
\(693\) 2.44552 0.0928976
\(694\) −45.1456 −1.71370
\(695\) −5.76823 −0.218801
\(696\) 0.121014 0.00458703
\(697\) −74.2556 −2.81263
\(698\) −42.1974 −1.59719
\(699\) −55.0505 −2.08220
\(700\) 3.82416 0.144540
\(701\) −6.20654 −0.234418 −0.117209 0.993107i \(-0.537395\pi\)
−0.117209 + 0.993107i \(0.537395\pi\)
\(702\) −1.50928 −0.0569641
\(703\) 4.91582 0.185404
\(704\) 16.8153 0.633752
\(705\) 5.00583 0.188531
\(706\) −18.3090 −0.689067
\(707\) 0.0407672 0.00153321
\(708\) 49.4125 1.85704
\(709\) −37.1234 −1.39420 −0.697099 0.716975i \(-0.745526\pi\)
−0.697099 + 0.716975i \(0.745526\pi\)
\(710\) −5.44292 −0.204269
\(711\) −3.62278 −0.135865
\(712\) −0.368669 −0.0138165
\(713\) −13.2994 −0.498065
\(714\) 14.3240 0.536063
\(715\) 1.26411 0.0472749
\(716\) −52.3934 −1.95803
\(717\) −28.1900 −1.05277
\(718\) 36.9688 1.37967
\(719\) −31.2727 −1.16628 −0.583138 0.812373i \(-0.698175\pi\)
−0.583138 + 0.812373i \(0.698175\pi\)
\(720\) 8.09917 0.301838
\(721\) −1.19811 −0.0446199
\(722\) −10.2982 −0.383261
\(723\) −22.1434 −0.823520
\(724\) −35.1803 −1.30747
\(725\) 4.51026 0.167507
\(726\) −29.8952 −1.10951
\(727\) −12.3318 −0.457363 −0.228681 0.973501i \(-0.573441\pi\)
−0.228681 + 0.973501i \(0.573441\pi\)
\(728\) −0.0166090 −0.000615572 0
\(729\) −18.8903 −0.699642
\(730\) −25.0854 −0.928452
\(731\) 18.3349 0.678142
\(732\) −3.38377 −0.125068
\(733\) 24.8155 0.916582 0.458291 0.888802i \(-0.348462\pi\)
0.458291 + 0.888802i \(0.348462\pi\)
\(734\) −13.1713 −0.486161
\(735\) −12.4809 −0.460364
\(736\) 10.9850 0.404912
\(737\) 13.3374 0.491288
\(738\) −55.1814 −2.03125
\(739\) −28.7903 −1.05907 −0.529534 0.848288i \(-0.677633\pi\)
−0.529534 + 0.848288i \(0.677633\pi\)
\(740\) −1.53381 −0.0563839
\(741\) −8.76173 −0.321870
\(742\) 11.2373 0.412536
\(743\) 30.3143 1.11213 0.556063 0.831140i \(-0.312311\pi\)
0.556063 + 0.831140i \(0.312311\pi\)
\(744\) 1.13884 0.0417521
\(745\) 2.64607 0.0969444
\(746\) 42.1610 1.54362
\(747\) 33.6209 1.23013
\(748\) 29.4229 1.07581
\(749\) 3.63003 0.132638
\(750\) 34.3556 1.25449
\(751\) −34.1201 −1.24506 −0.622531 0.782595i \(-0.713896\pi\)
−0.622531 + 0.782595i \(0.713896\pi\)
\(752\) −11.0542 −0.403105
\(753\) −39.7246 −1.44764
\(754\) 1.54378 0.0562213
\(755\) 4.28509 0.155950
\(756\) −0.872246 −0.0317233
\(757\) −20.7545 −0.754334 −0.377167 0.926145i \(-0.623102\pi\)
−0.377167 + 0.926145i \(0.623102\pi\)
\(758\) 73.1627 2.65739
\(759\) 7.01426 0.254602
\(760\) −0.190746 −0.00691909
\(761\) 38.9968 1.41363 0.706816 0.707398i \(-0.250131\pi\)
0.706816 + 0.707398i \(0.250131\pi\)
\(762\) −73.6934 −2.66963
\(763\) 0.440394 0.0159433
\(764\) −32.2641 −1.16727
\(765\) 13.8186 0.499614
\(766\) −34.4168 −1.24353
\(767\) −7.99854 −0.288811
\(768\) −38.7081 −1.39676
\(769\) 21.5805 0.778212 0.389106 0.921193i \(-0.372784\pi\)
0.389106 + 0.921193i \(0.372784\pi\)
\(770\) 1.47038 0.0529889
\(771\) −9.69460 −0.349142
\(772\) 9.36420 0.337025
\(773\) −47.9276 −1.72384 −0.861918 0.507047i \(-0.830737\pi\)
−0.861918 + 0.507047i \(0.830737\pi\)
\(774\) 13.6252 0.489747
\(775\) 42.4453 1.52468
\(776\) −0.165824 −0.00595273
\(777\) 1.03986 0.0373047
\(778\) −49.2677 −1.76633
\(779\) 52.8324 1.89292
\(780\) 2.73379 0.0978852
\(781\) 7.57978 0.271226
\(782\) 18.9772 0.678625
\(783\) −1.02874 −0.0367641
\(784\) 27.5611 0.984323
\(785\) −0.328537 −0.0117260
\(786\) −30.3977 −1.08425
\(787\) 30.9063 1.10169 0.550846 0.834607i \(-0.314305\pi\)
0.550846 + 0.834607i \(0.314305\pi\)
\(788\) 21.8772 0.779342
\(789\) −44.0099 −1.56679
\(790\) −2.17822 −0.0774975
\(791\) 2.62886 0.0934716
\(792\) −0.277442 −0.00985848
\(793\) 0.547741 0.0194508
\(794\) 17.9115 0.635657
\(795\) 23.4697 0.832384
\(796\) −45.4767 −1.61188
\(797\) −9.94990 −0.352444 −0.176222 0.984350i \(-0.556388\pi\)
−0.176222 + 0.984350i \(0.556388\pi\)
\(798\) −10.1914 −0.360773
\(799\) −18.8604 −0.667234
\(800\) −35.0588 −1.23952
\(801\) −19.0028 −0.671430
\(802\) 61.6744 2.17780
\(803\) 34.9338 1.23279
\(804\) 28.8437 1.01724
\(805\) 0.471195 0.0166074
\(806\) 14.5283 0.511737
\(807\) 33.2045 1.16885
\(808\) −0.00462501 −0.000162707 0
\(809\) 0.137829 0.00484582 0.00242291 0.999997i \(-0.499229\pi\)
0.00242291 + 0.999997i \(0.499229\pi\)
\(810\) −15.6292 −0.549154
\(811\) 38.8734 1.36503 0.682514 0.730872i \(-0.260887\pi\)
0.682514 + 0.730872i \(0.260887\pi\)
\(812\) 0.892187 0.0313096
\(813\) −47.3443 −1.66044
\(814\) 4.29904 0.150681
\(815\) −4.90067 −0.171663
\(816\) −66.0631 −2.31267
\(817\) −13.0452 −0.456393
\(818\) −15.1734 −0.530526
\(819\) −0.856101 −0.0299146
\(820\) −16.4845 −0.575663
\(821\) 17.2529 0.602130 0.301065 0.953604i \(-0.402658\pi\)
0.301065 + 0.953604i \(0.402658\pi\)
\(822\) 57.1230 1.99239
\(823\) −7.84996 −0.273632 −0.136816 0.990596i \(-0.543687\pi\)
−0.136816 + 0.990596i \(0.543687\pi\)
\(824\) 0.135925 0.00473516
\(825\) −22.3862 −0.779387
\(826\) −9.30372 −0.323718
\(827\) 29.7916 1.03595 0.517977 0.855394i \(-0.326685\pi\)
0.517977 + 0.855394i \(0.326685\pi\)
\(828\) 7.00680 0.243503
\(829\) −16.8482 −0.585162 −0.292581 0.956241i \(-0.594514\pi\)
−0.292581 + 0.956241i \(0.594514\pi\)
\(830\) 20.2148 0.701665
\(831\) 59.5652 2.06629
\(832\) −5.88653 −0.204079
\(833\) 47.0241 1.62929
\(834\) 34.9642 1.21071
\(835\) 6.11295 0.211547
\(836\) −20.9342 −0.724025
\(837\) −9.68128 −0.334634
\(838\) −40.9056 −1.41306
\(839\) 43.7370 1.50997 0.754985 0.655742i \(-0.227644\pi\)
0.754985 + 0.655742i \(0.227644\pi\)
\(840\) −0.0403491 −0.00139218
\(841\) −27.9477 −0.963715
\(842\) 48.1692 1.66002
\(843\) −35.7554 −1.23148
\(844\) 55.7491 1.91896
\(845\) 9.65373 0.332098
\(846\) −14.0157 −0.481870
\(847\) 2.79669 0.0960953
\(848\) −51.8272 −1.77975
\(849\) −23.7173 −0.813974
\(850\) −60.5663 −2.07741
\(851\) 1.37766 0.0472256
\(852\) 16.3922 0.561587
\(853\) 10.2227 0.350020 0.175010 0.984567i \(-0.444004\pi\)
0.175010 + 0.984567i \(0.444004\pi\)
\(854\) 0.637119 0.0218018
\(855\) −9.83187 −0.336243
\(856\) −0.411824 −0.0140758
\(857\) 45.0054 1.53736 0.768678 0.639636i \(-0.220915\pi\)
0.768678 + 0.639636i \(0.220915\pi\)
\(858\) −7.66241 −0.261590
\(859\) −0.634499 −0.0216488 −0.0108244 0.999941i \(-0.503446\pi\)
−0.0108244 + 0.999941i \(0.503446\pi\)
\(860\) 4.07029 0.138796
\(861\) 11.1758 0.380870
\(862\) −39.5652 −1.34760
\(863\) −33.5175 −1.14095 −0.570475 0.821315i \(-0.693241\pi\)
−0.570475 + 0.821315i \(0.693241\pi\)
\(864\) 7.99652 0.272047
\(865\) 13.9371 0.473874
\(866\) −49.7795 −1.69158
\(867\) −72.5751 −2.46478
\(868\) 8.39622 0.284986
\(869\) 3.03337 0.102900
\(870\) 3.75039 0.127150
\(871\) −4.66900 −0.158203
\(872\) −0.0499623 −0.00169194
\(873\) −8.54727 −0.289281
\(874\) −13.5022 −0.456718
\(875\) −3.21396 −0.108652
\(876\) 75.5485 2.55255
\(877\) 17.7856 0.600577 0.300289 0.953848i \(-0.402917\pi\)
0.300289 + 0.953848i \(0.402917\pi\)
\(878\) −40.2316 −1.35775
\(879\) 22.2763 0.751362
\(880\) −6.78147 −0.228603
\(881\) −50.0743 −1.68705 −0.843524 0.537092i \(-0.819523\pi\)
−0.843524 + 0.537092i \(0.819523\pi\)
\(882\) 34.9449 1.17666
\(883\) −50.1864 −1.68891 −0.844454 0.535628i \(-0.820075\pi\)
−0.844454 + 0.535628i \(0.820075\pi\)
\(884\) −10.3001 −0.346429
\(885\) −19.4312 −0.653173
\(886\) −34.2793 −1.15164
\(887\) 17.0592 0.572791 0.286396 0.958111i \(-0.407543\pi\)
0.286396 + 0.958111i \(0.407543\pi\)
\(888\) −0.117971 −0.00395885
\(889\) 6.89400 0.231217
\(890\) −11.4255 −0.382985
\(891\) 21.7651 0.729159
\(892\) 43.3444 1.45128
\(893\) 13.4191 0.449052
\(894\) −16.0392 −0.536431
\(895\) 20.6034 0.688697
\(896\) 0.176011 0.00588012
\(897\) −2.45548 −0.0819860
\(898\) 19.4383 0.648663
\(899\) 9.90261 0.330270
\(900\) −22.3624 −0.745412
\(901\) −88.4265 −2.94592
\(902\) 46.2036 1.53841
\(903\) −2.75949 −0.0918300
\(904\) −0.298243 −0.00991940
\(905\) 13.8345 0.459874
\(906\) −25.9741 −0.862933
\(907\) 5.68431 0.188744 0.0943722 0.995537i \(-0.469916\pi\)
0.0943722 + 0.995537i \(0.469916\pi\)
\(908\) 16.0031 0.531083
\(909\) −0.238392 −0.00790698
\(910\) −0.514735 −0.0170633
\(911\) 50.0548 1.65839 0.829194 0.558961i \(-0.188800\pi\)
0.829194 + 0.558961i \(0.188800\pi\)
\(912\) 47.0035 1.55644
\(913\) −28.1510 −0.931661
\(914\) −32.5058 −1.07520
\(915\) 1.33065 0.0439900
\(916\) −33.6622 −1.11223
\(917\) 2.84370 0.0939073
\(918\) 13.8145 0.455946
\(919\) 16.8978 0.557406 0.278703 0.960377i \(-0.410095\pi\)
0.278703 + 0.960377i \(0.410095\pi\)
\(920\) −0.0534567 −0.00176242
\(921\) 61.7444 2.03455
\(922\) 35.5436 1.17056
\(923\) −2.65345 −0.0873393
\(924\) −4.42828 −0.145680
\(925\) −4.39684 −0.144567
\(926\) −53.2253 −1.74909
\(927\) 7.00613 0.230112
\(928\) −8.17933 −0.268500
\(929\) −8.12188 −0.266470 −0.133235 0.991084i \(-0.542537\pi\)
−0.133235 + 0.991084i \(0.542537\pi\)
\(930\) 35.2942 1.15734
\(931\) −33.4574 −1.09652
\(932\) 46.0450 1.50825
\(933\) −23.6555 −0.774445
\(934\) 40.4998 1.32519
\(935\) −11.5704 −0.378393
\(936\) 0.0971240 0.00317460
\(937\) −38.9561 −1.27264 −0.636321 0.771424i \(-0.719545\pi\)
−0.636321 + 0.771424i \(0.719545\pi\)
\(938\) −5.43088 −0.177324
\(939\) 16.3448 0.533393
\(940\) −4.18694 −0.136563
\(941\) −29.7168 −0.968739 −0.484370 0.874863i \(-0.660951\pi\)
−0.484370 + 0.874863i \(0.660951\pi\)
\(942\) 1.99143 0.0648844
\(943\) 14.8063 0.482160
\(944\) 42.9092 1.39658
\(945\) 0.343006 0.0111580
\(946\) −11.4084 −0.370920
\(947\) −15.1829 −0.493379 −0.246689 0.969095i \(-0.579343\pi\)
−0.246689 + 0.969095i \(0.579343\pi\)
\(948\) 6.56003 0.213060
\(949\) −12.2292 −0.396978
\(950\) 43.0925 1.39811
\(951\) 32.4764 1.05312
\(952\) 0.152023 0.00492709
\(953\) 2.41286 0.0781601 0.0390801 0.999236i \(-0.487557\pi\)
0.0390801 + 0.999236i \(0.487557\pi\)
\(954\) −65.7122 −2.12751
\(955\) 12.6877 0.410564
\(956\) 23.5785 0.762582
\(957\) −5.22277 −0.168828
\(958\) −42.2011 −1.36345
\(959\) −5.34384 −0.172562
\(960\) −14.3004 −0.461544
\(961\) 62.1917 2.00618
\(962\) −1.50496 −0.0485220
\(963\) −21.2271 −0.684035
\(964\) 18.5210 0.596521
\(965\) −3.68242 −0.118541
\(966\) −2.85616 −0.0918953
\(967\) −45.6819 −1.46903 −0.734516 0.678592i \(-0.762591\pi\)
−0.734516 + 0.678592i \(0.762591\pi\)
\(968\) −0.317282 −0.0101978
\(969\) 80.1964 2.57628
\(970\) −5.13909 −0.165006
\(971\) −22.4763 −0.721297 −0.360649 0.932702i \(-0.617445\pi\)
−0.360649 + 0.932702i \(0.617445\pi\)
\(972\) 41.1279 1.31918
\(973\) −3.27090 −0.104860
\(974\) −44.2588 −1.41814
\(975\) 7.83671 0.250976
\(976\) −2.93843 −0.0940568
\(977\) −28.9202 −0.925240 −0.462620 0.886557i \(-0.653091\pi\)
−0.462620 + 0.886557i \(0.653091\pi\)
\(978\) 29.7055 0.949878
\(979\) 15.9111 0.508521
\(980\) 10.4392 0.333467
\(981\) −2.57527 −0.0822221
\(982\) −23.9998 −0.765864
\(983\) 55.8722 1.78205 0.891023 0.453959i \(-0.149989\pi\)
0.891023 + 0.453959i \(0.149989\pi\)
\(984\) −1.26789 −0.0404187
\(985\) −8.60309 −0.274117
\(986\) −14.1303 −0.450000
\(987\) 2.83858 0.0903529
\(988\) 7.32843 0.233148
\(989\) −3.65592 −0.116251
\(990\) −8.59829 −0.273272
\(991\) 39.8801 1.26683 0.633416 0.773812i \(-0.281652\pi\)
0.633416 + 0.773812i \(0.281652\pi\)
\(992\) −76.9743 −2.44394
\(993\) −76.4458 −2.42593
\(994\) −3.08643 −0.0978956
\(995\) 17.8835 0.566945
\(996\) −60.8799 −1.92905
\(997\) −4.82631 −0.152851 −0.0764254 0.997075i \(-0.524351\pi\)
−0.0764254 + 0.997075i \(0.524351\pi\)
\(998\) −17.2060 −0.544645
\(999\) 1.00287 0.0317294
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 4033.2.a.f.1.14 85
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.f.1.14 85 1.1 even 1 trivial