Properties

Label 4033.2.a.e.1.18
Level $4033$
Weight $2$
Character 4033.1
Self dual yes
Analytic conductor $32.204$
Analytic rank $0$
Dimension $82$
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: \(82\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
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)
 
\(f(q)\) \(=\) \(q-1.58741 q^{2} -1.76709 q^{3} +0.519871 q^{4} +4.42213 q^{5} +2.80509 q^{6} +5.11364 q^{7} +2.34957 q^{8} +0.122598 q^{9} +O(q^{10})\) \(q-1.58741 q^{2} -1.76709 q^{3} +0.519871 q^{4} +4.42213 q^{5} +2.80509 q^{6} +5.11364 q^{7} +2.34957 q^{8} +0.122598 q^{9} -7.01973 q^{10} +2.77837 q^{11} -0.918658 q^{12} +3.42651 q^{13} -8.11744 q^{14} -7.81429 q^{15} -4.76948 q^{16} -1.72760 q^{17} -0.194614 q^{18} -0.486137 q^{19} +2.29894 q^{20} -9.03625 q^{21} -4.41042 q^{22} -1.12174 q^{23} -4.15190 q^{24} +14.5552 q^{25} -5.43927 q^{26} +5.08462 q^{27} +2.65843 q^{28} -5.83305 q^{29} +12.4045 q^{30} -1.64580 q^{31} +2.87197 q^{32} -4.90963 q^{33} +2.74241 q^{34} +22.6132 q^{35} +0.0637354 q^{36} -1.00000 q^{37} +0.771699 q^{38} -6.05494 q^{39} +10.3901 q^{40} +11.7093 q^{41} +14.3442 q^{42} -10.9423 q^{43} +1.44440 q^{44} +0.542146 q^{45} +1.78066 q^{46} +8.57759 q^{47} +8.42808 q^{48} +19.1493 q^{49} -23.1051 q^{50} +3.05282 q^{51} +1.78134 q^{52} -6.03514 q^{53} -8.07138 q^{54} +12.2863 q^{55} +12.0149 q^{56} +0.859047 q^{57} +9.25944 q^{58} +10.6848 q^{59} -4.06242 q^{60} -6.45823 q^{61} +2.61256 q^{62} +0.626924 q^{63} +4.97996 q^{64} +15.1525 q^{65} +7.79360 q^{66} +9.21587 q^{67} -0.898128 q^{68} +1.98221 q^{69} -35.8964 q^{70} -5.14194 q^{71} +0.288054 q^{72} -6.51491 q^{73} +1.58741 q^{74} -25.7204 q^{75} -0.252729 q^{76} +14.2076 q^{77} +9.61167 q^{78} +9.01818 q^{79} -21.0912 q^{80} -9.35277 q^{81} -18.5875 q^{82} -4.19788 q^{83} -4.69768 q^{84} -7.63966 q^{85} +17.3699 q^{86} +10.3075 q^{87} +6.52799 q^{88} +13.6231 q^{89} -0.860609 q^{90} +17.5219 q^{91} -0.583159 q^{92} +2.90828 q^{93} -13.6162 q^{94} -2.14976 q^{95} -5.07502 q^{96} +4.16270 q^{97} -30.3978 q^{98} +0.340624 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 82 q + 10 q^{2} + 17 q^{3} + 88 q^{4} + 22 q^{5} + 4 q^{6} + 15 q^{7} + 33 q^{8} + 91 q^{9} + 13 q^{10} + 2 q^{11} + 36 q^{12} + 23 q^{13} + 24 q^{14} + 35 q^{15} + 104 q^{16} + 43 q^{17} + 42 q^{18} + 15 q^{19} + 59 q^{20} + 9 q^{21} + 6 q^{22} + 70 q^{23} + 15 q^{24} + 98 q^{25} + 10 q^{26} + 65 q^{27} + 37 q^{28} + 27 q^{29} + 17 q^{30} + 59 q^{31} + 46 q^{32} + 16 q^{33} - 16 q^{34} + 80 q^{35} + 88 q^{36} - 82 q^{37} + 82 q^{38} + 13 q^{39} + 14 q^{40} + 3 q^{41} + 62 q^{42} + 7 q^{43} - 11 q^{44} + 42 q^{45} - 11 q^{46} + 123 q^{47} + 45 q^{48} + 105 q^{49} + 27 q^{50} + 3 q^{51} - 30 q^{52} + 82 q^{53} - 27 q^{54} + 37 q^{55} + 66 q^{56} + 29 q^{57} - 34 q^{58} + 60 q^{59} + 94 q^{60} + 9 q^{61} - 2 q^{62} + 106 q^{63} + 93 q^{64} + 9 q^{65} + 63 q^{66} + 113 q^{68} + 48 q^{69} + 47 q^{70} + 59 q^{71} + 63 q^{72} + 21 q^{73} - 10 q^{74} + 77 q^{75} + 22 q^{76} + 30 q^{77} + 29 q^{78} + 55 q^{79} + 88 q^{80} + 42 q^{81} + 4 q^{82} + 92 q^{83} + 43 q^{84} - 7 q^{85} + 17 q^{86} + 147 q^{87} - 13 q^{88} + 100 q^{89} + 91 q^{90} + 28 q^{91} + 127 q^{92} + 3 q^{93} + 30 q^{94} + 48 q^{95} - 31 q^{96} + 53 q^{97} + 101 q^{98} - 20 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.58741 −1.12247 −0.561234 0.827657i \(-0.689673\pi\)
−0.561234 + 0.827657i \(0.689673\pi\)
\(3\) −1.76709 −1.02023 −0.510114 0.860107i \(-0.670397\pi\)
−0.510114 + 0.860107i \(0.670397\pi\)
\(4\) 0.519871 0.259935
\(5\) 4.42213 1.97764 0.988818 0.149126i \(-0.0476459\pi\)
0.988818 + 0.149126i \(0.0476459\pi\)
\(6\) 2.80509 1.14517
\(7\) 5.11364 1.93277 0.966387 0.257092i \(-0.0827643\pi\)
0.966387 + 0.257092i \(0.0827643\pi\)
\(8\) 2.34957 0.830699
\(9\) 0.122598 0.0408662
\(10\) −7.01973 −2.21983
\(11\) 2.77837 0.837711 0.418856 0.908053i \(-0.362431\pi\)
0.418856 + 0.908053i \(0.362431\pi\)
\(12\) −0.918658 −0.265194
\(13\) 3.42651 0.950342 0.475171 0.879893i \(-0.342386\pi\)
0.475171 + 0.879893i \(0.342386\pi\)
\(14\) −8.11744 −2.16948
\(15\) −7.81429 −2.01764
\(16\) −4.76948 −1.19237
\(17\) −1.72760 −0.419004 −0.209502 0.977808i \(-0.567184\pi\)
−0.209502 + 0.977808i \(0.567184\pi\)
\(18\) −0.194614 −0.0458710
\(19\) −0.486137 −0.111527 −0.0557637 0.998444i \(-0.517759\pi\)
−0.0557637 + 0.998444i \(0.517759\pi\)
\(20\) 2.29894 0.514058
\(21\) −9.03625 −1.97187
\(22\) −4.41042 −0.940304
\(23\) −1.12174 −0.233898 −0.116949 0.993138i \(-0.537311\pi\)
−0.116949 + 0.993138i \(0.537311\pi\)
\(24\) −4.15190 −0.847503
\(25\) 14.5552 2.91105
\(26\) −5.43927 −1.06673
\(27\) 5.08462 0.978536
\(28\) 2.65843 0.502397
\(29\) −5.83305 −1.08317 −0.541585 0.840646i \(-0.682176\pi\)
−0.541585 + 0.840646i \(0.682176\pi\)
\(30\) 12.4045 2.26474
\(31\) −1.64580 −0.295595 −0.147797 0.989018i \(-0.547218\pi\)
−0.147797 + 0.989018i \(0.547218\pi\)
\(32\) 2.87197 0.507698
\(33\) −4.90963 −0.854657
\(34\) 2.74241 0.470319
\(35\) 22.6132 3.82232
\(36\) 0.0637354 0.0106226
\(37\) −1.00000 −0.164399
\(38\) 0.771699 0.125186
\(39\) −6.05494 −0.969566
\(40\) 10.3901 1.64282
\(41\) 11.7093 1.82869 0.914345 0.404935i \(-0.132706\pi\)
0.914345 + 0.404935i \(0.132706\pi\)
\(42\) 14.3442 2.21336
\(43\) −10.9423 −1.66868 −0.834340 0.551250i \(-0.814151\pi\)
−0.834340 + 0.551250i \(0.814151\pi\)
\(44\) 1.44440 0.217751
\(45\) 0.542146 0.0808184
\(46\) 1.78066 0.262544
\(47\) 8.57759 1.25117 0.625585 0.780156i \(-0.284860\pi\)
0.625585 + 0.780156i \(0.284860\pi\)
\(48\) 8.42808 1.21649
\(49\) 19.1493 2.73561
\(50\) −23.1051 −3.26756
\(51\) 3.05282 0.427480
\(52\) 1.78134 0.247028
\(53\) −6.03514 −0.828990 −0.414495 0.910052i \(-0.636042\pi\)
−0.414495 + 0.910052i \(0.636042\pi\)
\(54\) −8.07138 −1.09838
\(55\) 12.2863 1.65669
\(56\) 12.0149 1.60555
\(57\) 0.859047 0.113784
\(58\) 9.25944 1.21582
\(59\) 10.6848 1.39105 0.695523 0.718504i \(-0.255173\pi\)
0.695523 + 0.718504i \(0.255173\pi\)
\(60\) −4.06242 −0.524457
\(61\) −6.45823 −0.826892 −0.413446 0.910529i \(-0.635675\pi\)
−0.413446 + 0.910529i \(0.635675\pi\)
\(62\) 2.61256 0.331796
\(63\) 0.626924 0.0789850
\(64\) 4.97996 0.622494
\(65\) 15.1525 1.87943
\(66\) 7.79360 0.959325
\(67\) 9.21587 1.12590 0.562949 0.826492i \(-0.309667\pi\)
0.562949 + 0.826492i \(0.309667\pi\)
\(68\) −0.898128 −0.108914
\(69\) 1.98221 0.238630
\(70\) −35.8964 −4.29044
\(71\) −5.14194 −0.610236 −0.305118 0.952314i \(-0.598696\pi\)
−0.305118 + 0.952314i \(0.598696\pi\)
\(72\) 0.288054 0.0339475
\(73\) −6.51491 −0.762513 −0.381256 0.924469i \(-0.624508\pi\)
−0.381256 + 0.924469i \(0.624508\pi\)
\(74\) 1.58741 0.184533
\(75\) −25.7204 −2.96993
\(76\) −0.252729 −0.0289899
\(77\) 14.2076 1.61911
\(78\) 9.61167 1.08831
\(79\) 9.01818 1.01462 0.507312 0.861762i \(-0.330639\pi\)
0.507312 + 0.861762i \(0.330639\pi\)
\(80\) −21.0912 −2.35807
\(81\) −9.35277 −1.03920
\(82\) −18.5875 −2.05265
\(83\) −4.19788 −0.460777 −0.230388 0.973099i \(-0.574000\pi\)
−0.230388 + 0.973099i \(0.574000\pi\)
\(84\) −4.69768 −0.512559
\(85\) −7.63966 −0.828638
\(86\) 17.3699 1.87304
\(87\) 10.3075 1.10508
\(88\) 6.52799 0.695886
\(89\) 13.6231 1.44405 0.722023 0.691869i \(-0.243213\pi\)
0.722023 + 0.691869i \(0.243213\pi\)
\(90\) −0.860609 −0.0907161
\(91\) 17.5219 1.83680
\(92\) −0.583159 −0.0607985
\(93\) 2.90828 0.301574
\(94\) −13.6162 −1.40440
\(95\) −2.14976 −0.220561
\(96\) −5.07502 −0.517968
\(97\) 4.16270 0.422658 0.211329 0.977415i \(-0.432221\pi\)
0.211329 + 0.977415i \(0.432221\pi\)
\(98\) −30.3978 −3.07064
\(99\) 0.340624 0.0342340
\(100\) 7.56684 0.756684
\(101\) −14.3403 −1.42691 −0.713457 0.700699i \(-0.752872\pi\)
−0.713457 + 0.700699i \(0.752872\pi\)
\(102\) −4.84607 −0.479833
\(103\) −6.59348 −0.649675 −0.324838 0.945770i \(-0.605310\pi\)
−0.324838 + 0.945770i \(0.605310\pi\)
\(104\) 8.05083 0.789448
\(105\) −39.9595 −3.89964
\(106\) 9.58024 0.930515
\(107\) −12.4197 −1.20066 −0.600328 0.799754i \(-0.704963\pi\)
−0.600328 + 0.799754i \(0.704963\pi\)
\(108\) 2.64335 0.254356
\(109\) 1.00000 0.0957826
\(110\) −19.5034 −1.85958
\(111\) 1.76709 0.167725
\(112\) −24.3894 −2.30458
\(113\) 6.88445 0.647634 0.323817 0.946120i \(-0.395034\pi\)
0.323817 + 0.946120i \(0.395034\pi\)
\(114\) −1.36366 −0.127718
\(115\) −4.96047 −0.462566
\(116\) −3.03243 −0.281554
\(117\) 0.420085 0.0388368
\(118\) −16.9612 −1.56141
\(119\) −8.83431 −0.809840
\(120\) −18.3602 −1.67605
\(121\) −3.28064 −0.298240
\(122\) 10.2519 0.928160
\(123\) −20.6914 −1.86568
\(124\) −0.855605 −0.0768356
\(125\) 42.2545 3.77935
\(126\) −0.995186 −0.0886582
\(127\) −1.11615 −0.0990420 −0.0495210 0.998773i \(-0.515769\pi\)
−0.0495210 + 0.998773i \(0.515769\pi\)
\(128\) −13.6492 −1.20643
\(129\) 19.3359 1.70243
\(130\) −24.0532 −2.10960
\(131\) 6.75498 0.590185 0.295093 0.955469i \(-0.404649\pi\)
0.295093 + 0.955469i \(0.404649\pi\)
\(132\) −2.55237 −0.222156
\(133\) −2.48593 −0.215557
\(134\) −14.6294 −1.26378
\(135\) 22.4849 1.93519
\(136\) −4.05912 −0.348066
\(137\) −1.65774 −0.141630 −0.0708151 0.997489i \(-0.522560\pi\)
−0.0708151 + 0.997489i \(0.522560\pi\)
\(138\) −3.14658 −0.267854
\(139\) 3.91965 0.332461 0.166230 0.986087i \(-0.446840\pi\)
0.166230 + 0.986087i \(0.446840\pi\)
\(140\) 11.7559 0.993558
\(141\) −15.1574 −1.27648
\(142\) 8.16237 0.684971
\(143\) 9.52012 0.796112
\(144\) −0.584730 −0.0487275
\(145\) −25.7945 −2.14212
\(146\) 10.3418 0.855896
\(147\) −33.8385 −2.79095
\(148\) −0.519871 −0.0427331
\(149\) −20.7255 −1.69790 −0.848949 0.528474i \(-0.822764\pi\)
−0.848949 + 0.528474i \(0.822764\pi\)
\(150\) 40.8288 3.33366
\(151\) −3.07484 −0.250227 −0.125114 0.992142i \(-0.539930\pi\)
−0.125114 + 0.992142i \(0.539930\pi\)
\(152\) −1.14221 −0.0926458
\(153\) −0.211801 −0.0171231
\(154\) −22.5533 −1.81740
\(155\) −7.27795 −0.584579
\(156\) −3.14779 −0.252025
\(157\) −0.520753 −0.0415606 −0.0207803 0.999784i \(-0.506615\pi\)
−0.0207803 + 0.999784i \(0.506615\pi\)
\(158\) −14.3155 −1.13888
\(159\) 10.6646 0.845759
\(160\) 12.7002 1.00404
\(161\) −5.73616 −0.452073
\(162\) 14.8467 1.16646
\(163\) 7.29872 0.571680 0.285840 0.958277i \(-0.407727\pi\)
0.285840 + 0.958277i \(0.407727\pi\)
\(164\) 6.08734 0.475342
\(165\) −21.7110 −1.69020
\(166\) 6.66375 0.517207
\(167\) −10.1775 −0.787561 −0.393781 0.919204i \(-0.628833\pi\)
−0.393781 + 0.919204i \(0.628833\pi\)
\(168\) −21.2313 −1.63803
\(169\) −1.25905 −0.0968497
\(170\) 12.1273 0.930120
\(171\) −0.0595997 −0.00455770
\(172\) −5.68857 −0.433749
\(173\) −19.8165 −1.50662 −0.753309 0.657667i \(-0.771544\pi\)
−0.753309 + 0.657667i \(0.771544\pi\)
\(174\) −16.3622 −1.24042
\(175\) 74.4302 5.62639
\(176\) −13.2514 −0.998861
\(177\) −18.8810 −1.41919
\(178\) −21.6254 −1.62090
\(179\) 10.1010 0.754981 0.377491 0.926013i \(-0.376787\pi\)
0.377491 + 0.926013i \(0.376787\pi\)
\(180\) 0.281846 0.0210076
\(181\) −11.3631 −0.844616 −0.422308 0.906452i \(-0.638780\pi\)
−0.422308 + 0.906452i \(0.638780\pi\)
\(182\) −27.8145 −2.06175
\(183\) 11.4123 0.843619
\(184\) −2.63560 −0.194299
\(185\) −4.42213 −0.325121
\(186\) −4.61663 −0.338508
\(187\) −4.79991 −0.351004
\(188\) 4.45924 0.325224
\(189\) 26.0009 1.89129
\(190\) 3.41255 0.247573
\(191\) 11.5261 0.833998 0.416999 0.908907i \(-0.363082\pi\)
0.416999 + 0.908907i \(0.363082\pi\)
\(192\) −8.80002 −0.635087
\(193\) 19.2702 1.38710 0.693549 0.720410i \(-0.256046\pi\)
0.693549 + 0.720410i \(0.256046\pi\)
\(194\) −6.60792 −0.474421
\(195\) −26.7757 −1.91745
\(196\) 9.95517 0.711083
\(197\) 12.7645 0.909432 0.454716 0.890637i \(-0.349741\pi\)
0.454716 + 0.890637i \(0.349741\pi\)
\(198\) −0.540711 −0.0384266
\(199\) −8.52369 −0.604229 −0.302114 0.953272i \(-0.597692\pi\)
−0.302114 + 0.953272i \(0.597692\pi\)
\(200\) 34.1986 2.41820
\(201\) −16.2852 −1.14867
\(202\) 22.7639 1.60167
\(203\) −29.8281 −2.09352
\(204\) 1.58707 0.111117
\(205\) 51.7802 3.61649
\(206\) 10.4666 0.729240
\(207\) −0.137523 −0.00955853
\(208\) −16.3426 −1.13316
\(209\) −1.35067 −0.0934278
\(210\) 63.4321 4.37723
\(211\) 25.2348 1.73724 0.868618 0.495483i \(-0.165009\pi\)
0.868618 + 0.495483i \(0.165009\pi\)
\(212\) −3.13749 −0.215484
\(213\) 9.08626 0.622581
\(214\) 19.7151 1.34770
\(215\) −48.3881 −3.30004
\(216\) 11.9467 0.812869
\(217\) −8.41604 −0.571318
\(218\) −1.58741 −0.107513
\(219\) 11.5124 0.777937
\(220\) 6.38731 0.430632
\(221\) −5.91963 −0.398197
\(222\) −2.80509 −0.188265
\(223\) 21.7036 1.45338 0.726692 0.686964i \(-0.241057\pi\)
0.726692 + 0.686964i \(0.241057\pi\)
\(224\) 14.6862 0.981265
\(225\) 1.78445 0.118963
\(226\) −10.9284 −0.726949
\(227\) −27.4608 −1.82264 −0.911318 0.411704i \(-0.864934\pi\)
−0.911318 + 0.411704i \(0.864934\pi\)
\(228\) 0.446593 0.0295764
\(229\) 13.8667 0.916337 0.458169 0.888865i \(-0.348506\pi\)
0.458169 + 0.888865i \(0.348506\pi\)
\(230\) 7.87430 0.519216
\(231\) −25.1061 −1.65186
\(232\) −13.7052 −0.899788
\(233\) 11.6555 0.763574 0.381787 0.924250i \(-0.375309\pi\)
0.381787 + 0.924250i \(0.375309\pi\)
\(234\) −0.666847 −0.0435931
\(235\) 37.9312 2.47436
\(236\) 5.55473 0.361582
\(237\) −15.9359 −1.03515
\(238\) 14.0237 0.909020
\(239\) −13.3886 −0.866039 −0.433020 0.901385i \(-0.642552\pi\)
−0.433020 + 0.901385i \(0.642552\pi\)
\(240\) 37.2701 2.40577
\(241\) −18.1093 −1.16652 −0.583261 0.812285i \(-0.698223\pi\)
−0.583261 + 0.812285i \(0.698223\pi\)
\(242\) 5.20772 0.334765
\(243\) 1.27329 0.0816818
\(244\) −3.35745 −0.214939
\(245\) 84.6807 5.41005
\(246\) 32.8458 2.09417
\(247\) −1.66575 −0.105989
\(248\) −3.86693 −0.245550
\(249\) 7.41802 0.470098
\(250\) −67.0752 −4.24221
\(251\) 1.12054 0.0707276 0.0353638 0.999375i \(-0.488741\pi\)
0.0353638 + 0.999375i \(0.488741\pi\)
\(252\) 0.325920 0.0205310
\(253\) −3.11661 −0.195939
\(254\) 1.77178 0.111172
\(255\) 13.5000 0.845400
\(256\) 11.7069 0.731683
\(257\) 19.0728 1.18973 0.594864 0.803826i \(-0.297206\pi\)
0.594864 + 0.803826i \(0.297206\pi\)
\(258\) −30.6941 −1.91093
\(259\) −5.11364 −0.317746
\(260\) 7.87732 0.488531
\(261\) −0.715123 −0.0442650
\(262\) −10.7229 −0.662465
\(263\) 5.92816 0.365546 0.182773 0.983155i \(-0.441493\pi\)
0.182773 + 0.983155i \(0.441493\pi\)
\(264\) −11.5355 −0.709963
\(265\) −26.6882 −1.63944
\(266\) 3.94619 0.241956
\(267\) −24.0732 −1.47326
\(268\) 4.79106 0.292661
\(269\) 4.87237 0.297073 0.148537 0.988907i \(-0.452544\pi\)
0.148537 + 0.988907i \(0.452544\pi\)
\(270\) −35.6927 −2.17219
\(271\) −28.0688 −1.70506 −0.852529 0.522679i \(-0.824932\pi\)
−0.852529 + 0.522679i \(0.824932\pi\)
\(272\) 8.23974 0.499608
\(273\) −30.9628 −1.87395
\(274\) 2.63151 0.158975
\(275\) 40.4399 2.43862
\(276\) 1.03049 0.0620284
\(277\) −12.2931 −0.738624 −0.369312 0.929306i \(-0.620407\pi\)
−0.369312 + 0.929306i \(0.620407\pi\)
\(278\) −6.22210 −0.373177
\(279\) −0.201773 −0.0120798
\(280\) 53.1313 3.17520
\(281\) −10.3174 −0.615486 −0.307743 0.951470i \(-0.599574\pi\)
−0.307743 + 0.951470i \(0.599574\pi\)
\(282\) 24.0609 1.43281
\(283\) −13.3640 −0.794407 −0.397203 0.917731i \(-0.630019\pi\)
−0.397203 + 0.917731i \(0.630019\pi\)
\(284\) −2.67315 −0.158622
\(285\) 3.79882 0.225022
\(286\) −15.1123 −0.893611
\(287\) 59.8773 3.53445
\(288\) 0.352099 0.0207476
\(289\) −14.0154 −0.824436
\(290\) 40.9464 2.40446
\(291\) −7.35586 −0.431208
\(292\) −3.38691 −0.198204
\(293\) −9.31413 −0.544138 −0.272069 0.962278i \(-0.587708\pi\)
−0.272069 + 0.962278i \(0.587708\pi\)
\(294\) 53.7156 3.13276
\(295\) 47.2497 2.75098
\(296\) −2.34957 −0.136566
\(297\) 14.1270 0.819730
\(298\) 32.8999 1.90584
\(299\) −3.84364 −0.222284
\(300\) −13.3713 −0.771991
\(301\) −55.9548 −3.22518
\(302\) 4.88103 0.280872
\(303\) 25.3406 1.45578
\(304\) 2.31862 0.132982
\(305\) −28.5591 −1.63529
\(306\) 0.336215 0.0192201
\(307\) −20.7612 −1.18490 −0.592451 0.805606i \(-0.701840\pi\)
−0.592451 + 0.805606i \(0.701840\pi\)
\(308\) 7.38612 0.420863
\(309\) 11.6513 0.662817
\(310\) 11.5531 0.656172
\(311\) 19.7030 1.11726 0.558628 0.829418i \(-0.311328\pi\)
0.558628 + 0.829418i \(0.311328\pi\)
\(312\) −14.2265 −0.805418
\(313\) −19.9593 −1.12816 −0.564082 0.825719i \(-0.690770\pi\)
−0.564082 + 0.825719i \(0.690770\pi\)
\(314\) 0.826648 0.0466504
\(315\) 2.77234 0.156204
\(316\) 4.68829 0.263737
\(317\) −13.5256 −0.759675 −0.379838 0.925053i \(-0.624020\pi\)
−0.379838 + 0.925053i \(0.624020\pi\)
\(318\) −16.9291 −0.949338
\(319\) −16.2064 −0.907384
\(320\) 22.0220 1.23107
\(321\) 21.9467 1.22494
\(322\) 9.10564 0.507437
\(323\) 0.839849 0.0467305
\(324\) −4.86223 −0.270124
\(325\) 49.8736 2.76649
\(326\) −11.5861 −0.641692
\(327\) −1.76709 −0.0977202
\(328\) 27.5119 1.51909
\(329\) 43.8627 2.41823
\(330\) 34.4643 1.89720
\(331\) 17.7616 0.976268 0.488134 0.872769i \(-0.337678\pi\)
0.488134 + 0.872769i \(0.337678\pi\)
\(332\) −2.18235 −0.119772
\(333\) −0.122598 −0.00671835
\(334\) 16.1559 0.884013
\(335\) 40.7538 2.22662
\(336\) 43.0982 2.35120
\(337\) 21.8009 1.18757 0.593786 0.804623i \(-0.297633\pi\)
0.593786 + 0.804623i \(0.297633\pi\)
\(338\) 1.99862 0.108711
\(339\) −12.1654 −0.660735
\(340\) −3.97164 −0.215392
\(341\) −4.57266 −0.247623
\(342\) 0.0946091 0.00511587
\(343\) 62.1272 3.35455
\(344\) −25.7096 −1.38617
\(345\) 8.76558 0.471923
\(346\) 31.4569 1.69113
\(347\) 3.17023 0.170187 0.0850933 0.996373i \(-0.472881\pi\)
0.0850933 + 0.996373i \(0.472881\pi\)
\(348\) 5.35857 0.287250
\(349\) −5.31212 −0.284351 −0.142176 0.989841i \(-0.545410\pi\)
−0.142176 + 0.989841i \(0.545410\pi\)
\(350\) −118.151 −6.31545
\(351\) 17.4225 0.929944
\(352\) 7.97941 0.425304
\(353\) 11.1143 0.591556 0.295778 0.955257i \(-0.404421\pi\)
0.295778 + 0.955257i \(0.404421\pi\)
\(354\) 29.9719 1.59299
\(355\) −22.7383 −1.20683
\(356\) 7.08225 0.375359
\(357\) 15.6110 0.826222
\(358\) −16.0344 −0.847443
\(359\) 6.58045 0.347303 0.173651 0.984807i \(-0.444443\pi\)
0.173651 + 0.984807i \(0.444443\pi\)
\(360\) 1.27381 0.0671358
\(361\) −18.7637 −0.987562
\(362\) 18.0380 0.948055
\(363\) 5.79718 0.304273
\(364\) 9.10914 0.477449
\(365\) −28.8098 −1.50797
\(366\) −18.1159 −0.946936
\(367\) −1.92109 −0.100280 −0.0501401 0.998742i \(-0.515967\pi\)
−0.0501401 + 0.998742i \(0.515967\pi\)
\(368\) 5.35010 0.278893
\(369\) 1.43555 0.0747316
\(370\) 7.01973 0.364939
\(371\) −30.8615 −1.60225
\(372\) 1.51193 0.0783899
\(373\) 9.79966 0.507407 0.253703 0.967282i \(-0.418351\pi\)
0.253703 + 0.967282i \(0.418351\pi\)
\(374\) 7.61943 0.393991
\(375\) −74.6674 −3.85581
\(376\) 20.1537 1.03935
\(377\) −19.9870 −1.02938
\(378\) −41.2741 −2.12291
\(379\) 11.4383 0.587545 0.293772 0.955875i \(-0.405089\pi\)
0.293772 + 0.955875i \(0.405089\pi\)
\(380\) −1.11760 −0.0573316
\(381\) 1.97233 0.101045
\(382\) −18.2966 −0.936136
\(383\) 24.8518 1.26987 0.634933 0.772567i \(-0.281027\pi\)
0.634933 + 0.772567i \(0.281027\pi\)
\(384\) 24.1193 1.23083
\(385\) 62.8279 3.20200
\(386\) −30.5897 −1.55697
\(387\) −1.34150 −0.0681925
\(388\) 2.16407 0.109864
\(389\) 14.9924 0.760145 0.380072 0.924957i \(-0.375899\pi\)
0.380072 + 0.924957i \(0.375899\pi\)
\(390\) 42.5041 2.15228
\(391\) 1.93791 0.0980044
\(392\) 44.9927 2.27247
\(393\) −11.9366 −0.602124
\(394\) −20.2625 −1.02081
\(395\) 39.8796 2.00656
\(396\) 0.177081 0.00889864
\(397\) −20.8047 −1.04416 −0.522080 0.852897i \(-0.674844\pi\)
−0.522080 + 0.852897i \(0.674844\pi\)
\(398\) 13.5306 0.678228
\(399\) 4.39285 0.219918
\(400\) −69.4208 −3.47104
\(401\) −23.0011 −1.14862 −0.574310 0.818638i \(-0.694730\pi\)
−0.574310 + 0.818638i \(0.694730\pi\)
\(402\) 25.8514 1.28935
\(403\) −5.63936 −0.280916
\(404\) −7.45511 −0.370906
\(405\) −41.3591 −2.05515
\(406\) 47.3494 2.34991
\(407\) −2.77837 −0.137719
\(408\) 7.17281 0.355107
\(409\) −28.7199 −1.42011 −0.710053 0.704148i \(-0.751329\pi\)
−0.710053 + 0.704148i \(0.751329\pi\)
\(410\) −82.1964 −4.05939
\(411\) 2.92937 0.144495
\(412\) −3.42776 −0.168874
\(413\) 54.6384 2.68858
\(414\) 0.218306 0.0107291
\(415\) −18.5636 −0.911249
\(416\) 9.84083 0.482486
\(417\) −6.92637 −0.339186
\(418\) 2.14407 0.104870
\(419\) 7.51258 0.367013 0.183507 0.983018i \(-0.441255\pi\)
0.183507 + 0.983018i \(0.441255\pi\)
\(420\) −20.7738 −1.01366
\(421\) −0.630207 −0.0307144 −0.0153572 0.999882i \(-0.504889\pi\)
−0.0153572 + 0.999882i \(0.504889\pi\)
\(422\) −40.0580 −1.94999
\(423\) 1.05160 0.0511305
\(424\) −14.1800 −0.688641
\(425\) −25.1456 −1.21974
\(426\) −14.4236 −0.698827
\(427\) −33.0251 −1.59820
\(428\) −6.45663 −0.312093
\(429\) −16.8229 −0.812216
\(430\) 76.8118 3.70419
\(431\) 5.39531 0.259883 0.129941 0.991522i \(-0.458521\pi\)
0.129941 + 0.991522i \(0.458521\pi\)
\(432\) −24.2510 −1.16678
\(433\) −17.1859 −0.825902 −0.412951 0.910753i \(-0.635502\pi\)
−0.412951 + 0.910753i \(0.635502\pi\)
\(434\) 13.3597 0.641287
\(435\) 45.5811 2.18545
\(436\) 0.519871 0.0248973
\(437\) 0.545318 0.0260861
\(438\) −18.2749 −0.873210
\(439\) 23.4994 1.12157 0.560784 0.827962i \(-0.310500\pi\)
0.560784 + 0.827962i \(0.310500\pi\)
\(440\) 28.8676 1.37621
\(441\) 2.34768 0.111794
\(442\) 9.39688 0.446964
\(443\) −9.77816 −0.464574 −0.232287 0.972647i \(-0.574621\pi\)
−0.232287 + 0.972647i \(0.574621\pi\)
\(444\) 0.918658 0.0435976
\(445\) 60.2431 2.85580
\(446\) −34.4526 −1.63138
\(447\) 36.6238 1.73224
\(448\) 25.4657 1.20314
\(449\) 19.2866 0.910190 0.455095 0.890443i \(-0.349605\pi\)
0.455095 + 0.890443i \(0.349605\pi\)
\(450\) −2.83265 −0.133533
\(451\) 32.5329 1.53191
\(452\) 3.57902 0.168343
\(453\) 5.43351 0.255289
\(454\) 43.5915 2.04585
\(455\) 77.4842 3.63252
\(456\) 2.01839 0.0945199
\(457\) −23.4362 −1.09630 −0.548149 0.836381i \(-0.684667\pi\)
−0.548149 + 0.836381i \(0.684667\pi\)
\(458\) −22.0121 −1.02856
\(459\) −8.78418 −0.410010
\(460\) −2.57880 −0.120237
\(461\) −31.1498 −1.45079 −0.725396 0.688332i \(-0.758343\pi\)
−0.725396 + 0.688332i \(0.758343\pi\)
\(462\) 39.8536 1.85416
\(463\) −6.53567 −0.303739 −0.151869 0.988401i \(-0.548529\pi\)
−0.151869 + 0.988401i \(0.548529\pi\)
\(464\) 27.8206 1.29154
\(465\) 12.8608 0.596404
\(466\) −18.5020 −0.857088
\(467\) 41.4275 1.91703 0.958517 0.285035i \(-0.0920051\pi\)
0.958517 + 0.285035i \(0.0920051\pi\)
\(468\) 0.218390 0.0100951
\(469\) 47.1266 2.17611
\(470\) −60.2124 −2.77739
\(471\) 0.920215 0.0424013
\(472\) 25.1048 1.15554
\(473\) −30.4017 −1.39787
\(474\) 25.2968 1.16192
\(475\) −7.07584 −0.324662
\(476\) −4.59270 −0.210506
\(477\) −0.739899 −0.0338776
\(478\) 21.2533 0.972102
\(479\) 8.54881 0.390605 0.195303 0.980743i \(-0.437431\pi\)
0.195303 + 0.980743i \(0.437431\pi\)
\(480\) −22.4424 −1.02435
\(481\) −3.42651 −0.156235
\(482\) 28.7469 1.30938
\(483\) 10.1363 0.461218
\(484\) −1.70551 −0.0775231
\(485\) 18.4080 0.835865
\(486\) −2.02124 −0.0916853
\(487\) −4.08692 −0.185196 −0.0925981 0.995704i \(-0.529517\pi\)
−0.0925981 + 0.995704i \(0.529517\pi\)
\(488\) −15.1741 −0.686898
\(489\) −12.8975 −0.583244
\(490\) −134.423 −6.07261
\(491\) 3.91957 0.176888 0.0884438 0.996081i \(-0.471811\pi\)
0.0884438 + 0.996081i \(0.471811\pi\)
\(492\) −10.7569 −0.484957
\(493\) 10.0772 0.453853
\(494\) 2.64423 0.118970
\(495\) 1.50629 0.0677025
\(496\) 7.84962 0.352458
\(497\) −26.2940 −1.17945
\(498\) −11.7754 −0.527670
\(499\) −18.9502 −0.848329 −0.424164 0.905585i \(-0.639432\pi\)
−0.424164 + 0.905585i \(0.639432\pi\)
\(500\) 21.9669 0.982389
\(501\) 17.9846 0.803492
\(502\) −1.77875 −0.0793895
\(503\) 14.0224 0.625227 0.312614 0.949880i \(-0.398795\pi\)
0.312614 + 0.949880i \(0.398795\pi\)
\(504\) 1.47300 0.0656128
\(505\) −63.4147 −2.82192
\(506\) 4.94733 0.219936
\(507\) 2.22485 0.0988089
\(508\) −0.580252 −0.0257445
\(509\) −20.1107 −0.891389 −0.445695 0.895185i \(-0.647043\pi\)
−0.445695 + 0.895185i \(0.647043\pi\)
\(510\) −21.4300 −0.948935
\(511\) −33.3149 −1.47376
\(512\) 8.71466 0.385137
\(513\) −2.47182 −0.109134
\(514\) −30.2764 −1.33543
\(515\) −29.1572 −1.28482
\(516\) 10.0522 0.442523
\(517\) 23.8318 1.04812
\(518\) 8.11744 0.356660
\(519\) 35.0174 1.53709
\(520\) 35.6018 1.56124
\(521\) 20.1187 0.881417 0.440709 0.897650i \(-0.354727\pi\)
0.440709 + 0.897650i \(0.354727\pi\)
\(522\) 1.13519 0.0496861
\(523\) −15.9364 −0.696852 −0.348426 0.937336i \(-0.613284\pi\)
−0.348426 + 0.937336i \(0.613284\pi\)
\(524\) 3.51172 0.153410
\(525\) −131.525 −5.74021
\(526\) −9.41042 −0.410314
\(527\) 2.84329 0.123855
\(528\) 23.4164 1.01907
\(529\) −21.7417 −0.945292
\(530\) 42.3651 1.84022
\(531\) 1.30994 0.0568467
\(532\) −1.29236 −0.0560310
\(533\) 40.1221 1.73788
\(534\) 38.2141 1.65368
\(535\) −54.9214 −2.37446
\(536\) 21.6533 0.935282
\(537\) −17.8493 −0.770254
\(538\) −7.73444 −0.333456
\(539\) 53.2039 2.29166
\(540\) 11.6892 0.503024
\(541\) −2.14379 −0.0921686 −0.0460843 0.998938i \(-0.514674\pi\)
−0.0460843 + 0.998938i \(0.514674\pi\)
\(542\) 44.5567 1.91387
\(543\) 20.0797 0.861701
\(544\) −4.96161 −0.212727
\(545\) 4.42213 0.189423
\(546\) 49.1506 2.10345
\(547\) −19.8007 −0.846618 −0.423309 0.905985i \(-0.639132\pi\)
−0.423309 + 0.905985i \(0.639132\pi\)
\(548\) −0.861810 −0.0368147
\(549\) −0.791770 −0.0337919
\(550\) −64.1947 −2.73727
\(551\) 2.83566 0.120803
\(552\) 4.65734 0.198230
\(553\) 46.1157 1.96104
\(554\) 19.5143 0.829082
\(555\) 7.81429 0.331698
\(556\) 2.03771 0.0864184
\(557\) −3.59104 −0.152157 −0.0760786 0.997102i \(-0.524240\pi\)
−0.0760786 + 0.997102i \(0.524240\pi\)
\(558\) 0.320296 0.0135592
\(559\) −37.4938 −1.58582
\(560\) −107.853 −4.55762
\(561\) 8.48187 0.358105
\(562\) 16.3780 0.690863
\(563\) 21.2772 0.896728 0.448364 0.893851i \(-0.352007\pi\)
0.448364 + 0.893851i \(0.352007\pi\)
\(564\) −7.87987 −0.331802
\(565\) 30.4439 1.28079
\(566\) 21.2141 0.891696
\(567\) −47.8267 −2.00853
\(568\) −12.0814 −0.506923
\(569\) −11.7051 −0.490702 −0.245351 0.969434i \(-0.578903\pi\)
−0.245351 + 0.969434i \(0.578903\pi\)
\(570\) −6.03028 −0.252581
\(571\) −42.3921 −1.77406 −0.887028 0.461716i \(-0.847234\pi\)
−0.887028 + 0.461716i \(0.847234\pi\)
\(572\) 4.94923 0.206938
\(573\) −20.3676 −0.850868
\(574\) −95.0498 −3.96730
\(575\) −16.3271 −0.680889
\(576\) 0.610535 0.0254390
\(577\) −2.68638 −0.111835 −0.0559177 0.998435i \(-0.517808\pi\)
−0.0559177 + 0.998435i \(0.517808\pi\)
\(578\) 22.2482 0.925403
\(579\) −34.0521 −1.41516
\(580\) −13.4098 −0.556812
\(581\) −21.4664 −0.890577
\(582\) 11.6768 0.484018
\(583\) −16.7679 −0.694454
\(584\) −15.3073 −0.633419
\(585\) 1.85767 0.0768051
\(586\) 14.7854 0.610777
\(587\) −12.3327 −0.509023 −0.254512 0.967070i \(-0.581915\pi\)
−0.254512 + 0.967070i \(0.581915\pi\)
\(588\) −17.5917 −0.725468
\(589\) 0.800086 0.0329670
\(590\) −75.0047 −3.08789
\(591\) −22.5560 −0.927828
\(592\) 4.76948 0.196024
\(593\) −46.8281 −1.92300 −0.961500 0.274803i \(-0.911387\pi\)
−0.961500 + 0.274803i \(0.911387\pi\)
\(594\) −22.4253 −0.920121
\(595\) −39.0665 −1.60157
\(596\) −10.7746 −0.441344
\(597\) 15.0621 0.616451
\(598\) 6.10144 0.249506
\(599\) 26.1827 1.06980 0.534898 0.844916i \(-0.320350\pi\)
0.534898 + 0.844916i \(0.320350\pi\)
\(600\) −60.4319 −2.46712
\(601\) −34.8891 −1.42316 −0.711579 0.702606i \(-0.752020\pi\)
−0.711579 + 0.702606i \(0.752020\pi\)
\(602\) 88.8232 3.62016
\(603\) 1.12985 0.0460111
\(604\) −1.59852 −0.0650429
\(605\) −14.5074 −0.589810
\(606\) −40.2259 −1.63407
\(607\) −4.39048 −0.178204 −0.0891020 0.996023i \(-0.528400\pi\)
−0.0891020 + 0.996023i \(0.528400\pi\)
\(608\) −1.39617 −0.0566222
\(609\) 52.7089 2.13587
\(610\) 45.3351 1.83556
\(611\) 29.3912 1.18904
\(612\) −0.110109 −0.00445090
\(613\) 16.6726 0.673402 0.336701 0.941612i \(-0.390689\pi\)
0.336701 + 0.941612i \(0.390689\pi\)
\(614\) 32.9565 1.33002
\(615\) −91.5001 −3.68964
\(616\) 33.3818 1.34499
\(617\) −7.24082 −0.291505 −0.145752 0.989321i \(-0.546560\pi\)
−0.145752 + 0.989321i \(0.546560\pi\)
\(618\) −18.4953 −0.743991
\(619\) −37.5708 −1.51010 −0.755049 0.655669i \(-0.772387\pi\)
−0.755049 + 0.655669i \(0.772387\pi\)
\(620\) −3.78360 −0.151953
\(621\) −5.70361 −0.228878
\(622\) −31.2768 −1.25408
\(623\) 69.6636 2.79101
\(624\) 28.8789 1.15608
\(625\) 114.079 4.56314
\(626\) 31.6835 1.26633
\(627\) 2.38675 0.0953177
\(628\) −0.270724 −0.0108031
\(629\) 1.72760 0.0688839
\(630\) −4.40084 −0.175334
\(631\) 27.7660 1.10535 0.552674 0.833398i \(-0.313607\pi\)
0.552674 + 0.833398i \(0.313607\pi\)
\(632\) 21.1889 0.842848
\(633\) −44.5921 −1.77238
\(634\) 21.4707 0.852711
\(635\) −4.93574 −0.195869
\(636\) 5.54422 0.219843
\(637\) 65.6152 2.59977
\(638\) 25.7262 1.01851
\(639\) −0.630394 −0.0249380
\(640\) −60.3584 −2.38588
\(641\) −28.1153 −1.11049 −0.555243 0.831688i \(-0.687375\pi\)
−0.555243 + 0.831688i \(0.687375\pi\)
\(642\) −34.8384 −1.37496
\(643\) 5.94671 0.234515 0.117258 0.993102i \(-0.462590\pi\)
0.117258 + 0.993102i \(0.462590\pi\)
\(644\) −2.98206 −0.117510
\(645\) 85.5060 3.36680
\(646\) −1.33319 −0.0524535
\(647\) −7.30140 −0.287048 −0.143524 0.989647i \(-0.545843\pi\)
−0.143524 + 0.989647i \(0.545843\pi\)
\(648\) −21.9750 −0.863259
\(649\) 29.6865 1.16530
\(650\) −79.1699 −3.10530
\(651\) 14.8719 0.582875
\(652\) 3.79439 0.148600
\(653\) 6.35953 0.248868 0.124434 0.992228i \(-0.460289\pi\)
0.124434 + 0.992228i \(0.460289\pi\)
\(654\) 2.80509 0.109688
\(655\) 29.8714 1.16717
\(656\) −55.8474 −2.18047
\(657\) −0.798718 −0.0311610
\(658\) −69.6281 −2.71439
\(659\) 20.5644 0.801074 0.400537 0.916281i \(-0.368824\pi\)
0.400537 + 0.916281i \(0.368824\pi\)
\(660\) −11.2869 −0.439343
\(661\) −32.1941 −1.25221 −0.626103 0.779741i \(-0.715351\pi\)
−0.626103 + 0.779741i \(0.715351\pi\)
\(662\) −28.1950 −1.09583
\(663\) 10.4605 0.406252
\(664\) −9.86321 −0.382767
\(665\) −10.9931 −0.426294
\(666\) 0.194614 0.00754114
\(667\) 6.54315 0.253352
\(668\) −5.29100 −0.204715
\(669\) −38.3522 −1.48278
\(670\) −64.6929 −2.49931
\(671\) −17.9434 −0.692697
\(672\) −25.9518 −1.00111
\(673\) 25.4698 0.981789 0.490894 0.871219i \(-0.336670\pi\)
0.490894 + 0.871219i \(0.336670\pi\)
\(674\) −34.6070 −1.33301
\(675\) 74.0078 2.84856
\(676\) −0.654542 −0.0251747
\(677\) 33.6943 1.29498 0.647488 0.762076i \(-0.275820\pi\)
0.647488 + 0.762076i \(0.275820\pi\)
\(678\) 19.3115 0.741654
\(679\) 21.2866 0.816903
\(680\) −17.9499 −0.688349
\(681\) 48.5256 1.85950
\(682\) 7.25868 0.277949
\(683\) 47.1946 1.80585 0.902926 0.429796i \(-0.141415\pi\)
0.902926 + 0.429796i \(0.141415\pi\)
\(684\) −0.0309841 −0.00118471
\(685\) −7.33073 −0.280093
\(686\) −98.6213 −3.76538
\(687\) −24.5037 −0.934873
\(688\) 52.1889 1.98968
\(689\) −20.6794 −0.787824
\(690\) −13.9146 −0.529719
\(691\) −29.5757 −1.12511 −0.562556 0.826759i \(-0.690182\pi\)
−0.562556 + 0.826759i \(0.690182\pi\)
\(692\) −10.3020 −0.391624
\(693\) 1.74183 0.0661667
\(694\) −5.03245 −0.191029
\(695\) 17.3332 0.657487
\(696\) 24.2182 0.917990
\(697\) −20.2290 −0.766229
\(698\) 8.43251 0.319175
\(699\) −20.5962 −0.779020
\(700\) 38.6941 1.46250
\(701\) −8.11350 −0.306443 −0.153221 0.988192i \(-0.548965\pi\)
−0.153221 + 0.988192i \(0.548965\pi\)
\(702\) −27.6566 −1.04383
\(703\) 0.486137 0.0183350
\(704\) 13.8362 0.521471
\(705\) −67.0278 −2.52441
\(706\) −17.6430 −0.664003
\(707\) −73.3311 −2.75790
\(708\) −9.81570 −0.368897
\(709\) −39.4395 −1.48118 −0.740590 0.671957i \(-0.765454\pi\)
−0.740590 + 0.671957i \(0.765454\pi\)
\(710\) 36.0951 1.35462
\(711\) 1.10561 0.0414638
\(712\) 32.0084 1.19957
\(713\) 1.84616 0.0691392
\(714\) −24.7811 −0.927408
\(715\) 42.0992 1.57442
\(716\) 5.25120 0.196246
\(717\) 23.6589 0.883558
\(718\) −10.4459 −0.389837
\(719\) −8.24918 −0.307642 −0.153821 0.988099i \(-0.549158\pi\)
−0.153821 + 0.988099i \(0.549158\pi\)
\(720\) −2.58575 −0.0963654
\(721\) −33.7167 −1.25567
\(722\) 29.7856 1.10851
\(723\) 32.0007 1.19012
\(724\) −5.90737 −0.219546
\(725\) −84.9014 −3.15316
\(726\) −9.20250 −0.341537
\(727\) −28.4855 −1.05647 −0.528235 0.849098i \(-0.677146\pi\)
−0.528235 + 0.849098i \(0.677146\pi\)
\(728\) 41.1690 1.52583
\(729\) 25.8083 0.955862
\(730\) 45.7329 1.69265
\(731\) 18.9038 0.699184
\(732\) 5.93291 0.219286
\(733\) 28.5200 1.05341 0.526706 0.850048i \(-0.323427\pi\)
0.526706 + 0.850048i \(0.323427\pi\)
\(734\) 3.04956 0.112561
\(735\) −149.638 −5.51949
\(736\) −3.22160 −0.118750
\(737\) 25.6051 0.943177
\(738\) −2.27880 −0.0838838
\(739\) 2.71011 0.0996931 0.0498466 0.998757i \(-0.484127\pi\)
0.0498466 + 0.998757i \(0.484127\pi\)
\(740\) −2.29894 −0.0845106
\(741\) 2.94353 0.108133
\(742\) 48.9899 1.79848
\(743\) −18.3544 −0.673358 −0.336679 0.941619i \(-0.609304\pi\)
−0.336679 + 0.941619i \(0.609304\pi\)
\(744\) 6.83321 0.250518
\(745\) −91.6508 −3.35783
\(746\) −15.5561 −0.569548
\(747\) −0.514653 −0.0188302
\(748\) −2.49534 −0.0912385
\(749\) −63.5098 −2.32060
\(750\) 118.528 4.32802
\(751\) 24.5853 0.897131 0.448565 0.893750i \(-0.351935\pi\)
0.448565 + 0.893750i \(0.351935\pi\)
\(752\) −40.9106 −1.49186
\(753\) −1.98008 −0.0721583
\(754\) 31.7275 1.15545
\(755\) −13.5973 −0.494858
\(756\) 13.5171 0.491613
\(757\) −2.34333 −0.0851697 −0.0425849 0.999093i \(-0.513559\pi\)
−0.0425849 + 0.999093i \(0.513559\pi\)
\(758\) −18.1572 −0.659501
\(759\) 5.50732 0.199903
\(760\) −5.05102 −0.183220
\(761\) 42.7488 1.54964 0.774821 0.632181i \(-0.217840\pi\)
0.774821 + 0.632181i \(0.217840\pi\)
\(762\) −3.13089 −0.113420
\(763\) 5.11364 0.185126
\(764\) 5.99207 0.216786
\(765\) −0.936611 −0.0338632
\(766\) −39.4500 −1.42539
\(767\) 36.6117 1.32197
\(768\) −20.6872 −0.746484
\(769\) 29.4532 1.06211 0.531054 0.847338i \(-0.321796\pi\)
0.531054 + 0.847338i \(0.321796\pi\)
\(770\) −99.7336 −3.59415
\(771\) −33.7033 −1.21379
\(772\) 10.0180 0.360556
\(773\) −20.9131 −0.752193 −0.376096 0.926581i \(-0.622734\pi\)
−0.376096 + 0.926581i \(0.622734\pi\)
\(774\) 2.12952 0.0765440
\(775\) −23.9550 −0.860490
\(776\) 9.78057 0.351102
\(777\) 9.03625 0.324174
\(778\) −23.7991 −0.853238
\(779\) −5.69234 −0.203949
\(780\) −13.9199 −0.498413
\(781\) −14.2862 −0.511202
\(782\) −3.07626 −0.110007
\(783\) −29.6588 −1.05992
\(784\) −91.3322 −3.26186
\(785\) −2.30284 −0.0821917
\(786\) 18.9483 0.675865
\(787\) −42.4487 −1.51313 −0.756566 0.653917i \(-0.773124\pi\)
−0.756566 + 0.653917i \(0.773124\pi\)
\(788\) 6.63589 0.236394
\(789\) −10.4756 −0.372940
\(790\) −63.3052 −2.25230
\(791\) 35.2046 1.25173
\(792\) 0.800321 0.0284382
\(793\) −22.1292 −0.785830
\(794\) 33.0256 1.17204
\(795\) 47.1603 1.67260
\(796\) −4.43122 −0.157060
\(797\) 35.7010 1.26460 0.632298 0.774726i \(-0.282112\pi\)
0.632298 + 0.774726i \(0.282112\pi\)
\(798\) −6.97326 −0.246851
\(799\) −14.8186 −0.524246
\(800\) 41.8022 1.47793
\(801\) 1.67017 0.0590126
\(802\) 36.5122 1.28929
\(803\) −18.1009 −0.638765
\(804\) −8.46623 −0.298581
\(805\) −25.3660 −0.894036
\(806\) 8.95197 0.315320
\(807\) −8.60990 −0.303083
\(808\) −33.6936 −1.18534
\(809\) −31.9045 −1.12170 −0.560852 0.827916i \(-0.689526\pi\)
−0.560852 + 0.827916i \(0.689526\pi\)
\(810\) 65.6539 2.30684
\(811\) 38.8036 1.36258 0.681289 0.732014i \(-0.261420\pi\)
0.681289 + 0.732014i \(0.261420\pi\)
\(812\) −15.5068 −0.544181
\(813\) 49.6000 1.73955
\(814\) 4.41042 0.154585
\(815\) 32.2759 1.13057
\(816\) −14.5603 −0.509714
\(817\) 5.31944 0.186104
\(818\) 45.5902 1.59402
\(819\) 2.14816 0.0750628
\(820\) 26.9190 0.940053
\(821\) −42.7537 −1.49211 −0.746057 0.665883i \(-0.768055\pi\)
−0.746057 + 0.665883i \(0.768055\pi\)
\(822\) −4.65011 −0.162191
\(823\) 3.35599 0.116983 0.0584913 0.998288i \(-0.481371\pi\)
0.0584913 + 0.998288i \(0.481371\pi\)
\(824\) −15.4919 −0.539684
\(825\) −71.4608 −2.48795
\(826\) −86.7335 −3.01784
\(827\) 34.0233 1.18311 0.591553 0.806266i \(-0.298515\pi\)
0.591553 + 0.806266i \(0.298515\pi\)
\(828\) −0.0714944 −0.00248460
\(829\) 40.8090 1.41736 0.708678 0.705532i \(-0.249292\pi\)
0.708678 + 0.705532i \(0.249292\pi\)
\(830\) 29.4680 1.02285
\(831\) 21.7231 0.753565
\(832\) 17.0639 0.591583
\(833\) −33.0823 −1.14623
\(834\) 10.9950 0.380726
\(835\) −45.0064 −1.55751
\(836\) −0.702174 −0.0242852
\(837\) −8.36828 −0.289250
\(838\) −11.9255 −0.411961
\(839\) 30.7121 1.06030 0.530149 0.847904i \(-0.322136\pi\)
0.530149 + 0.847904i \(0.322136\pi\)
\(840\) −93.8876 −3.23943
\(841\) 5.02446 0.173257
\(842\) 1.00040 0.0344760
\(843\) 18.2318 0.627936
\(844\) 13.1188 0.451569
\(845\) −5.56767 −0.191534
\(846\) −1.66932 −0.0573924
\(847\) −16.7760 −0.576430
\(848\) 28.7844 0.988462
\(849\) 23.6153 0.810476
\(850\) 39.9164 1.36912
\(851\) 1.12174 0.0384527
\(852\) 4.72369 0.161831
\(853\) 18.6869 0.639827 0.319914 0.947447i \(-0.396346\pi\)
0.319914 + 0.947447i \(0.396346\pi\)
\(854\) 52.4243 1.79392
\(855\) −0.263557 −0.00901347
\(856\) −29.1809 −0.997384
\(857\) −10.9252 −0.373199 −0.186599 0.982436i \(-0.559747\pi\)
−0.186599 + 0.982436i \(0.559747\pi\)
\(858\) 26.7048 0.911687
\(859\) 22.4774 0.766919 0.383460 0.923558i \(-0.374733\pi\)
0.383460 + 0.923558i \(0.374733\pi\)
\(860\) −25.1556 −0.857798
\(861\) −105.808 −3.60594
\(862\) −8.56457 −0.291710
\(863\) 34.2217 1.16492 0.582460 0.812859i \(-0.302090\pi\)
0.582460 + 0.812859i \(0.302090\pi\)
\(864\) 14.6029 0.496800
\(865\) −87.6310 −2.97954
\(866\) 27.2811 0.927048
\(867\) 24.7664 0.841113
\(868\) −4.37526 −0.148506
\(869\) 25.0559 0.849962
\(870\) −72.3560 −2.45310
\(871\) 31.5782 1.06999
\(872\) 2.34957 0.0795665
\(873\) 0.510341 0.0172724
\(874\) −0.865644 −0.0292808
\(875\) 216.074 7.30464
\(876\) 5.98497 0.202213
\(877\) −14.8590 −0.501752 −0.250876 0.968019i \(-0.580719\pi\)
−0.250876 + 0.968019i \(0.580719\pi\)
\(878\) −37.3033 −1.25892
\(879\) 16.4589 0.555145
\(880\) −58.5994 −1.97538
\(881\) 6.96375 0.234615 0.117307 0.993096i \(-0.462574\pi\)
0.117307 + 0.993096i \(0.462574\pi\)
\(882\) −3.72672 −0.125485
\(883\) 27.8071 0.935782 0.467891 0.883786i \(-0.345014\pi\)
0.467891 + 0.883786i \(0.345014\pi\)
\(884\) −3.07744 −0.103506
\(885\) −83.4944 −2.80663
\(886\) 15.5219 0.521470
\(887\) 34.7010 1.16514 0.582572 0.812779i \(-0.302046\pi\)
0.582572 + 0.812779i \(0.302046\pi\)
\(888\) 4.15190 0.139329
\(889\) −5.70757 −0.191426
\(890\) −95.6305 −3.20554
\(891\) −25.9855 −0.870546
\(892\) 11.2831 0.377786
\(893\) −4.16988 −0.139540
\(894\) −58.1369 −1.94439
\(895\) 44.6678 1.49308
\(896\) −69.7970 −2.33175
\(897\) 6.79205 0.226780
\(898\) −30.6157 −1.02166
\(899\) 9.60005 0.320180
\(900\) 0.927683 0.0309228
\(901\) 10.4263 0.347350
\(902\) −51.6431 −1.71953
\(903\) 98.8770 3.29042
\(904\) 16.1755 0.537989
\(905\) −50.2493 −1.67034
\(906\) −8.62522 −0.286554
\(907\) 12.1165 0.402322 0.201161 0.979558i \(-0.435528\pi\)
0.201161 + 0.979558i \(0.435528\pi\)
\(908\) −14.2761 −0.473768
\(909\) −1.75810 −0.0583125
\(910\) −122.999 −4.07738
\(911\) 7.69811 0.255050 0.127525 0.991835i \(-0.459297\pi\)
0.127525 + 0.991835i \(0.459297\pi\)
\(912\) −4.09720 −0.135672
\(913\) −11.6633 −0.385998
\(914\) 37.2028 1.23056
\(915\) 50.4665 1.66837
\(916\) 7.20889 0.238189
\(917\) 34.5425 1.14070
\(918\) 13.9441 0.460224
\(919\) −28.3823 −0.936247 −0.468123 0.883663i \(-0.655070\pi\)
−0.468123 + 0.883663i \(0.655070\pi\)
\(920\) −11.6550 −0.384253
\(921\) 36.6868 1.20887
\(922\) 49.4475 1.62847
\(923\) −17.6189 −0.579933
\(924\) −13.0519 −0.429377
\(925\) −14.5552 −0.478573
\(926\) 10.3748 0.340937
\(927\) −0.808351 −0.0265497
\(928\) −16.7523 −0.549923
\(929\) 15.3153 0.502479 0.251240 0.967925i \(-0.419162\pi\)
0.251240 + 0.967925i \(0.419162\pi\)
\(930\) −20.4153 −0.669445
\(931\) −9.30919 −0.305096
\(932\) 6.05933 0.198480
\(933\) −34.8170 −1.13986
\(934\) −65.7624 −2.15181
\(935\) −21.2258 −0.694159
\(936\) 0.987019 0.0322617
\(937\) 28.4763 0.930279 0.465139 0.885237i \(-0.346004\pi\)
0.465139 + 0.885237i \(0.346004\pi\)
\(938\) −74.8093 −2.44261
\(939\) 35.2698 1.15098
\(940\) 19.7193 0.643174
\(941\) 37.0245 1.20696 0.603481 0.797377i \(-0.293780\pi\)
0.603481 + 0.797377i \(0.293780\pi\)
\(942\) −1.46076 −0.0475941
\(943\) −13.1348 −0.427728
\(944\) −50.9610 −1.65864
\(945\) 114.979 3.74028
\(946\) 48.2600 1.56907
\(947\) 58.6024 1.90432 0.952161 0.305597i \(-0.0988559\pi\)
0.952161 + 0.305597i \(0.0988559\pi\)
\(948\) −8.28462 −0.269072
\(949\) −22.3234 −0.724648
\(950\) 11.2323 0.364422
\(951\) 23.9010 0.775042
\(952\) −20.7569 −0.672734
\(953\) 56.8330 1.84100 0.920501 0.390741i \(-0.127781\pi\)
0.920501 + 0.390741i \(0.127781\pi\)
\(954\) 1.17452 0.0380266
\(955\) 50.9698 1.64934
\(956\) −6.96037 −0.225114
\(957\) 28.6381 0.925739
\(958\) −13.5705 −0.438442
\(959\) −8.47707 −0.273739
\(960\) −38.9148 −1.25597
\(961\) −28.2913 −0.912624
\(962\) 5.43927 0.175369
\(963\) −1.52263 −0.0490662
\(964\) −9.41449 −0.303220
\(965\) 85.2152 2.74317
\(966\) −16.0905 −0.517702
\(967\) 46.5744 1.49773 0.748866 0.662722i \(-0.230599\pi\)
0.748866 + 0.662722i \(0.230599\pi\)
\(968\) −7.70810 −0.247748
\(969\) −1.48409 −0.0476758
\(970\) −29.2211 −0.938232
\(971\) −45.9141 −1.47345 −0.736727 0.676191i \(-0.763630\pi\)
−0.736727 + 0.676191i \(0.763630\pi\)
\(972\) 0.661948 0.0212320
\(973\) 20.0437 0.642571
\(974\) 6.48762 0.207877
\(975\) −88.1310 −2.82245
\(976\) 30.8024 0.985960
\(977\) 22.8651 0.731519 0.365760 0.930709i \(-0.380809\pi\)
0.365760 + 0.930709i \(0.380809\pi\)
\(978\) 20.4736 0.654673
\(979\) 37.8501 1.20969
\(980\) 44.0230 1.40626
\(981\) 0.122598 0.00391427
\(982\) −6.22196 −0.198551
\(983\) −55.7627 −1.77855 −0.889276 0.457370i \(-0.848791\pi\)
−0.889276 + 0.457370i \(0.848791\pi\)
\(984\) −48.6160 −1.54982
\(985\) 56.4462 1.79853
\(986\) −15.9966 −0.509435
\(987\) −77.5092 −2.46715
\(988\) −0.865976 −0.0275504
\(989\) 12.2743 0.390302
\(990\) −2.39109 −0.0759939
\(991\) −16.9098 −0.537156 −0.268578 0.963258i \(-0.586554\pi\)
−0.268578 + 0.963258i \(0.586554\pi\)
\(992\) −4.72670 −0.150073
\(993\) −31.3864 −0.996017
\(994\) 41.7394 1.32389
\(995\) −37.6929 −1.19494
\(996\) 3.85641 0.122195
\(997\) 9.24358 0.292747 0.146374 0.989229i \(-0.453240\pi\)
0.146374 + 0.989229i \(0.453240\pi\)
\(998\) 30.0818 0.952222
\(999\) −5.08462 −0.160870
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.e.1.18 82
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
4033.2.a.e.1.18 82 1.1 even 1 trivial